IMPLICATVRA -- in 18 volumes, vol. IX

mediatum: Grice is all about the mediatum. This he call a ‘soul-to-soul’ transfer. Imagine you pick up a rose, the thorn hurts you. You are in pain. You say “Ouch.” You transmit this to the fellow gardener. The mediacy means, “Beware of the thorn. It may hurt you.” “I am amazed that in The New World, it’s all about immediacy (Chisholm) when there’s so much which is mediately of immediate philosophical importance!”

immediatum: Grice: “Here the ‘in-’ is negative!” – the presence to the mind without intermediaries. The term ‘immediatum’ and its cognates have been used extensively throughout the history of philosophy, generally without much explanation. Descartes, e.g., explains his notion of thought thus: “I use this term to include everything that is within us in a way that we are IMMEDIATELY aware of it” (Second Replies). Descartes offers no explanation of immediate awareness, but the implicaturum is “contextually cancellable.” “Only an idiot would not realise that he is opposing it to mediated experience.” – Grice. Grice is well aware of this. “Check with Lewis and Short.” “mĕdĭo , 1, v. a. medius, I.to halve, divide in the middle (post-class.), Apic. 3, 9. — B. Neutr., to be in the middle: “melius Juno mediante,” Pall. Mart. 10, 32.” “So you see, ‘mediare’ can be transitive, but surely Descartes means it in the intransitive way – something mediates or something doesn’t – Clear as water!” However, when used as a primitive in this way, ‘immediatum’ may simply mean that thoughts are the immediate objects of perception because thoughts are the only things perceived in the strict and proper sense that no perception of an intermediary is required for the person’s awareness of them. Sometimes ‘immediate’ means ‘not mediated’. (1) An inference from a premise to a conclusion can exhibit logical immediacy because it does not depend on other premises. This is a technical usage of proof theory to describe the form of a certain class of inference rules. (2) A concept can exhibit conceptual immediacy because it is definitionally primitive, as in the Berkeleian doctrine that perception of qualities is immediate, and perception of objects is defined by the perception of their qualities, which is directly understood. (3) Our perception of something can exhibit causal immediacy because it is not caused by intervening acts of perception or cognition, as with seeing someone immediately in the flesh rather than through images on a movie screen. (4) A belief-formation process can possess psychological immediacy because it contains no subprocess of reasoning and in that sense has no psychological mediator. (5) Our knowledge of something can exhibit epistemic immediacy because it is justified without inference from another proposition, as in intuitive knowledge of the existence of the self, which has no epistemic mediator. A noteworthy special application of immediacy is to be found in Russell’s notion of knowledge by acquaintance. This notion is a development of the venerable doctrine originating with Plato, and also found in Augustine, that understanding the nature of some object requires that we can gain immediate cognitive access to that object. Thus, for Plato, to understand the nature of beauty requires acquaintance with beauty itself. This view contrasts with one in which understanding the nature of beauty requires linguistic competence in the use of the word ‘beauty’ or, alternatively, with one that requires having a mental representation of beauty. Russell offers sense-data and universals as examples of things known by acquaintance. To these senses of immediacy we may add another category whose members have acquired special meanings within certain philosophical traditions. For example, in Hegel’s philosophy if (per impossibile) an object were encountered “as existing in simple immediacy” it would be encountered as it is in itself, unchanged by conceptualization. In phenomenology “immediate” experience is, roughly, bracketed experience.

partiale.

impartialis – impartiality: Grice found this amusing. “Surely conversational maxims, constituting the conversational immanuel, are impartial – i.e. they are not part of any other part!” – “However, it’s only because they can be partial that’s the only way they can have a bite on us!” -- a state or disposition achieved to the degree that one’s actions or attitudes are not influenced in a relevant respect by which members of a relevant group are benefited or harmed by one’s actions or by the object of one’s attitudes. For example, a basketball referee and that referee’s calls are impartial when the referee’s applications of the rules are not affected by whether the calls help one team or the other. A fan’s approval of a call lacks impartiality if that attitude results from the fan’s preference for one team over the other. Impartiality in this general sense does not exclude arbitrariness or guarantee fairness; nor does it require neutrality among values, for a judge can be impartial between parties while favoring liberty and equality for all. Different situations might call for impartiality in different respects toward different groups, so disagreements arise, for example, about when morality requires or allows partiality toward friends or family or country. Moral philosophers have proposed various tests of the kind of impartiality required by morality, including role reversibility (Kurt Baier), universalizability (Hare), a veil of ignorance (Rawls), and a restriction to beliefs shared by all rational people (Bernard Gert).

imperatum – While of course there is a verb in the infinitive for this, Grice prefers the past participle – “It’s so diaphanous!” -- This starts with the Greeks, who had the klesis porstktike, modus imperativus. But then, under the modus subjunctives, the Romans added the modus prohibitivus. So this is interesting, because it seems that most of Grice’s maxims are ‘prohibitions’: “Do not say what you believe to be false.” “Do not that for which you lack adequate evidence.” And some while formally in the ‘affirmative,’ look prohibitive with ‘negative-loaded’ verbs like ‘avoid ambiguity,’ etc. hile an imperatus, m. is a command, ‘imperatum’ refers, diaphanously, to what is commanded. “Impero” is actually a derivation from the intensive “in-“ and the “paro,” as in “prepare,” “Paratum” would thus reflect the ssame cognateness with ‘imperatum.”  Modus imperativus -- imperative mode: At one point, Grice loved the “psi,” Actions are alright, but we need to stop at the psi level. The emissor communicates that the addressee thinks that the emissor has propositional attitude psi. No need to get into the logical form of action. One can just do with the logical form of a ‘that’-clause in the ascription of a state of the soul. This should usually INVOLVE an action, as in Hare, “The door is shut, please.” like Hare, Grice loves an imperative. In this essay, Grice attempts an exploration of the logical form of Kant’s concoction. Grice is especially irritated by the ‘the.’ ‘They speak of Kant’s categorical imperative, when he cared to formulate a few versions of it!” Grice lists them all in Abbott’s version. There are nine of them!  Grice is interested in the conceptual connection of the categorical imperative with the hypothetical or suppositional imperative, in terms of the type of connection between the protasis and the apodosis. Grice spends the full second Carus lecture on the conception of value on this. Grice is aware that the topic is central to Oxonian philosophers such as Hare, a member of Austin’s Play Group, too, who regard the universability of an imperative as a mark of its categoricity, and indeed, moral status. Grice chose some of the Kantian terminology on purpose.Grice would refer to this or that ‘conversational maxim.’A ‘conversational maxim’ contributes to what Grice jocularly refers to as the ‘conversational immanuel.’But there is an admission test.The ‘conversational maxim’ has to be shown that, qua items under an overarching principle of conversational helpfulness, the maxim displays a quality associated with conceptual, formal, and applicational generality. Grice never understood what Kant meant by the categoric imperative. But for Grice, from the acceptability of the the immanuel you can deduce the acceptability of this or that maxim, and from the acceptability of the conversational immanuel, be conversationally helpful, you can deduce the acceptability of this or that convesational maxim. Grice hardly considered Kants approach to the categoric imperative other than via the universability of this or that maxim. This or that conversational maxim, provided by Grice, may be said to be universalisable if and only if it displays what Grice sees as these three types of generality: conceptual, formal, and applicational. He does the same for general maxims of conduct. The results are compiled in a manual of universalisable maxims, the conversational immanuel, an appendix to the general immanuel. The other justification by Kant of the categoric imperative involve an approach other than the genitorial justification, and an invocation of autonomy and freedom. It is the use by Plato of imperative as per categoric imperative that has Grice expanding on modes other than the doxastic, to bring in the buletic, where the categoric imperative resides. Note that in the end Kant DOES formulate the categoric imperative, as Grice notes, as a real imperative, rather than a command, etc. Grice loved Kant, but he loved Kantotle best. In the last Kant lecture, he proposes to define the categorical imperative as a counsel of prudence, with a protasis Let Grice be happy. The derivation involves eight stages! Grice found out that out of his play-group activities with this or that linguistic nuance he had arrived at the principle, or imperative of conversational helpfulness, indeed formulated as an imperative: Make your contribution such as is required, at the stage at which it occurs, by the accepted purpose of the conversation in which you are engaged. He notes that the rationality behind the idea of conversation as rational co-operation does not preclude seeing rationality in conversation as other than cooperation. The fact that he chooses maxim, and explicitly echoes Kant, indicates where Grice is leading! An exploration on Paton on the categorical imperative. Grice had previously explored the logical form of hypothetical or suppositional imperatives in the Kant (and later Locke) lectures, notably in Lecture IV, Further remarks on practical and alethic reasons. Here he considers topics related to Hares tropic-clistic neustic-phrastic quartet. What does it mean to say that a command is conditional? The two successors of Grices post as Tutorial Fellow at St. Johns, Baker Hacker, will tackle the same issue with humour, in Sense and nonsense, published by Blackwell (too irreverent to be published by the Clarendon). Is the logical form of a maxim, .p⊃!q, or !(.p ⊃.q), etc. Kant thought that there is a special sub-class of hypothetical or suppositional  imperative (which he called a counsels of prudence) which is like his class of technical imperative, except in that the end specified in a full specfication of the imperative is the special end of eudæmonia (the agents eudæmonia). For Grice, understanding Kant’s first version of the categorical imperative involves understanding what a maxim is supposed to be. Grice explores at some length four alternative interpretations of an iffy buletic (as opposed to a non-iffy buletic): three formal, one material. The first interpretation is the horseshoe interpretation. A blind logical nose might lead us or be led to the assumption of a link between a buletically iffy utterance and a doxastically iffy utterance. Such a link no doubt exists, but the most obvious version of it is plainly inadequate. At least one other philosopher besides Grice has noticed that If he torments the cat, have him arrested! is unlikely to express an buletically iffy utterance, and that even if one restricts oneself to this or that case in which the protasis specifies a will, we find pairs of examples like If you will to go to Oxford, travel by AA via Richmond! or If you will to go to Cambridge, see a psychiatrist! where it is plain that one is, and the other is not, the expression of a buletically iffy utterance. For fun, Grice does not tell which! A less easily eliminable suggestion, yet one which would still interprets the notion of a buletically iffy utterance in terms of that particular logical form to which if, hypothetical or suppositional  and conditional attach, would be the following. Let us assume that it is established, or conceded, as legitimate to formulate an if utterance in which not only the apodosis is couched in some mode other than the doxastic, as in this or that conditional command. If you see the whites of their eyes, shoot fire! but also the protasis or some part (clause) of them. In which case all of the following might be admissible conditionals. Thus, we might have a doxastic protasis (If the cat is sick, take it to the vet), or a mixed (buletic-cum-doxastic protasis (If you are to take the cat to the vet and theres no cage available, put it on Marthas lap!), and buletic protasis (If you are to take the cat to the vet, put it in a cage!). If this suggestion seems rebarbative, think of this or that quaint if utterance (when it is quaint) as conditionalised versions of this or that therefore-sequence, such as: buletic-cum-doxastic premises (Take the cat to the vet! There isnt a cage. Therefore; Put the cat on Marthas lap!), buletic premise (Take the cat to the vet! Put it in a cage!). And then, maybe, the discomfort is reduced. Grice next considers a second formal interpretation or approach to the buletically iffy/non-iffy utterance. Among if utterances with a buletic apodosis some will have, then, a mixed doxastic-cum buletic protasis (partly doxastic, partly buletic), and some will have a purely doxastic protasis (If the cat is sick, take him to the vet!). Grice proposes a definition of the iffy/non-iffy distinction. A buletically iffy utterance is an iffy utterance the apodosis of which is buletic and the protasis of which is buletic or mixed (buletic-cum-dxastic) or it is an elliptical version of such an iffy utterance. A buletically non-iffy utterance is a buletic utterance which is not iffy or else, if it is iffy, has a purely doxastic protasis. Grice makes three quick comments on this second interpretation. First, re: a real imperative. The structures which are being offered as a way of interpreting an iffy and a non-iffy  imperative do not, as they stand, offer any room for the appearance this or that buletic modality like ought and should which are so prominently visible in the standard examples of those kinds of imperatives. The imperatives suggested by Grice are explicit imperatives. An explicit buletic utterance is Do such-and-such! and not You ought to do such and such or, worse, One ought to do such and such. Grice thinks, however, that one can modify this suggestion to meet the demand for the appearance or occurrence of ought (etc) if such occurrence is needed. Second, it would remain to be decided how close the preferred reading of Grices deviant conditional imperatives would be to the accepted interpretation of standard hypothetical or suppositional imperatives. But even if there were some divergence that might be acceptable if the new interpretation turns out to embody a more precise notion than the standard conception. Then theres the neustical versus tropical protases. There are, Grice thinks, serious doubts of the admissibility of conditionals with a NON-doxastic protasis, which are for Grice connected with the very difficult question whether the doxastic and the buletic modes are co-ordinate or whether the doxastic mode is in some crucial fashion (but not in other) prior (to use Suppess qualification) to the buletic. Grice confesses he does not know the answer to that question. A third formal interpretation links the iffy/non-iffy distinction to the absolute-relative value distinction. An iffy imperatives would be end-relative and might be analogous to an evidence-relative probability. A non-iffy imperatives would not be end-relative. Finally, a fourth Interpretation is not formal, but material. This is close to part of what Kant says on the topic. It is a distinction between an imperative being escapable (iffy), through the absence of a particular will and its not being escapable (non-iffy). If we understand the idea of escabability sufficiently widely, the following imperatives are all escapable, even though their logical form is not in every case the same: Give up popcorn!, To get slim, give up popcorn!, If you will to get slim, give up popcorn! Suppose Grice has no will to get slim. One might say that the first imperative (Give up popcorn!) is escaped, provided giving up popcorn has nothing else to recommend it, by falsifying You should give up popcorn. The second and the third imperatives (To get slim, give up pocorn! and If you will to get slim, give up popcorn!) would not, perhaps, involve falsification but they would, in the circumstances, be inapplicable to Grice – and inapplicability, too, counts, as escape. A non-iffy imperative however, is in no way escapable. Re: the Dynamics of Imperatives in Discourse, Grice then gives three examples which he had discussed in “Aspects,” which concern arguments (or therefore-chains). This we may see as an elucidation to grasp the logical form of buletically iffy utterance (elided by the therefore, which is an if in the metalanguage) in its dynamics in argumentation. We should, Grice suggests, consider not merely imperatives of each sort, together with the range of possible characterisations, but also the possible forms of argument into which_particular_ hypothetical or suppositional imperatives might enter. Consider: Defend the Philosophy Department! If you are to defend the philosophy department, learn to use bows and arrows! Therefore, learn to use bows and arrows! Grice says he is using the dichotomy of original-derived value. In this example, in the first premise, it is not specified whether the will is original or derived, the second premise specifies conducive to (means), and the conclusion would involve a derived will, provided the second premise is doxastically satisfactory. Another example would be: Fight for your country! If you are to fight for your country, join up one of the services! Therefore, join up! Here, the first premise and the conclusion do not specify the protasis. If the conclusion did, it would repeat the second premise. Then theres Increase your holdings in oil shares! If you visit your father, hell give you some oil shares. Therefore, visit your father! This argument (purportedly) transmits value. Let us explore these characterisations by Grice with the aid of Hares distinctions. For Hare in a hypothetical or suppositional imperative, the protasis contains a neustic-cum-tropic. A distinction may be made between this or that hypothetical or suppositional imperative and a term used by Grice in his first interpretation of the hypothetical or suppositional imperative, that of conditional command (If you see the whites of their eyes, shoot fire!). A hypothetical or suppositional imperative can be distinguished from a conditional imperative (If you want to make bread, use yeast! If you see anything suspicious, telephone the police!) by the fact that modus ponens is not valid for it. One may use hypothetical, suppositional or conditional imperative for a buletic utterance which features if, and reserve conditional command for a command which is expressed by an imperative, and which is conditional on the satisfaction of the protasis. Thus, on this view, treating the major premise of an argument as a hypothetical or suppositional imperative turns the therefore-chain invalid. Consider the sequence with the major premise as a hypothetical or suppositional imperative. If you will to make someone mad, give him drug D! You will to make Peter mad; therefore, give Peter drug D! By uttering this hypothetical or suppositional imperative, the utterer tells his addressee A only what means to adopt to achieve a given end in  a way which does not necessarily endorse the adoption of that end, and hence of the means to it. Someone might similarly say, if you will to make someone mad, give him drug D! But, of course, even if you will to do that, you must not try to do so. On the other hand, the following is arguably valid because the major premise is a conditional imperative and not a mere hypothetical or suppositional one. We have a case of major premise as a conditional imperative: You will to make someone mad, give him drug D! Make Peter mad! Therefore, give Peter drug D!. We can explain this in terms of the presence of the neustic in the antecedent of the imperative working as the major premise. The supposition that the protasis of a hypothetical or suppositional imperative contains a clause in the buletic mode neatly explains why the argument with the major premise as a hypothetical or suppositional imperative is not valid. But the argument with the major premise as a conditional imperative is, as well as helping to differentiate a suppositional or hypothetical or suppositional iffy imperative from a conditional iffy imperative. For, if the protasis of the major premise in the hypothetical or suppositional imperative is volitival, the mere fact that you will to make Peter mad does not license the inference of the imperative to give him the drug; but this _can_ be inferred from the major premise of the hypothetical or suppositional imperative together with an imperative, the minor premise in the conditional imperative, to make Peter mad. Whether the subordinate clause contains a neustic thus does have have a consequence as to the validity of inferences into which the complex sentence enters. Then theres an alleged principle of mode constancy in buletic and and doxastic inference. One may tries to elucidate Grices ideas on the logical form of the hypothetical or suppositional imperative proper. His suggestion is, admittedly, rather tentative. But it might be argued, in the spirit of it, that an iffy imperative is of the form ((!p⊃!q) Λ .p)) ∴ !q But this violates a principle of mode constancy. A phrastic must remain in the same mode (within the scope of the same tropic) throughout an argument. A conditional imperative does not violate the principle of Modal Constancy, since it is of the form ((p⊃!q) Λ !p)) ∴ !q The question of the logical form of the hypothetical or suppositional  imperative is too obscure to base much on arguments concerning it. There is an alternative to Grices account of the validity of an argument featuring a conditional imperative.  This is to treat the major premise of a conditional imperative, as some have urged it should be as a doxastic utterance tantamount to In order to make someone mad, you have to give him drug D.  Then an utterer who explicitly conveys or asserts the major premise of a conditional imperative and commands the second premise is in consistency committed to commanding the conclusion. If does not always connect phrastic with phrastic but sometimes connects two expressions consisting of a phrastic and a tropic. Consider: If you walk past the post office, post the letter! The antecedent of this imperative states, it seems, the condition under which the imperative expressed becomes operative, and so can not be construed buletically, since by uttering a buletic utterance, an utterer cannot explicitly convey or assert that a condition obtains. Hence, the protasis ought not be within the scope of the buletic !, and whatever we take to represent the form of the utterance above we must not take !(if p, q) to do so. One way out. On certain interpretation of the isomorphism or æqui-vocality Thesis between Indicative and Imperative Inference the utterance has to be construed as an imperative (in the generic reading)  to make the doxasatic conditional If you will walk past the post office,  you will post the letter satisfactory. Leaving aside issues of the implicaturum of if, that the utterance can not be so construed  seems to be shown by the fact that the imperative to make the associated doxastically iffy utterance satisfactory is conformed with by one who does not walk past the post office. But it seems strange at best to say that the utterance is conformed with in the same circumstances. This strangeness or bafflingliness, as Grice prefers, is aptly explained away in terms of the implicaturum. At Oxford, Dummett is endorsing this idea that a conditional imperative be construed as an imperative to make an indicative if utterance true. Dummett urges to divide conditional imperatives into those whose antecedent is within the power of the addressee, like the utterance in question, and those in which it is not. Consider: If you go out, wear your coat! One may be not so much concerned with how to escape this, as Grice is, but how to conform it. A child may choose not to go out in order to comply with the imperative. For an imperative whose protasis is_not_ within the power of the addressee (If anyone tries to escape, shoot him!) it is indifferent whether we treat it as a conditional imperative or not, so why bother. A small caveat here. If no one tries to escape, the imperative is *not violated*. One might ask, might there not be an important practical difference bewteen saying that an imperative has not been violated and that it has been complied with? Dummett ignores this distinction. One may feel think there is much of a practical difference there. Is Grice an intuitionist? Suppose that you are a frontier guard and the antecedent has remained unfulfilled. Then, whether we say that you complied with it, or simply did not *violate* it will make a great deal of difference if you appear before a war crimes tribunal.  For Dummett, the fact that in the case of an imperative expressed by a conditional imperative in which the antecedent is not within the agents power, we should *not* say that the agent had obeyed just on the ground that the protassi is false, is no ground for construing an imperative as expressing a conditional command: for there is no question of fixing what shall constitute obedience independently of the determination of what shall constitute disobedience. This complicates the issues. One may with Grice (and Hare, and Edgley) defend imperative inference against other Oxonian philosophers, such as Kenny or Williams. What is questioned by the sceptics about imperative inference is whether if each one of a set of imperatives is used with the force of a command, one can infer a _further_ imperative with that force from them. Cf. Wiggins on Aristotle on the practical syllogism. One may be more conservative than Hare, if not Grice. Consider If you stand by Jane, dont look at her! You stand by Jane; therefore, dont look at her! This is valid. However, the following, obtained by anti-logism, is not: If you stand by Jane, dont look at her! Look at her! Therefore, you dont stand by Jane. It may seem more reasonable to some to deny Kants thesis, and maintain that anti-logism is valid in imperative inference than it is to hold onto Kants thesis and deny that antilogism is valid in the case in question. Then theres the question of the implicatura involved in the ordering of modes. Consider: Varnish every piece of furniture you make! You are going to make a table; therefore, varnish it! This is prima facie valid. The following, however, switching the order of the modes in the premises is not. You are going to varnish every piece of furniture that you make. Make a table! Therefore; varnish it! The connection between the if and the therefore is metalinguistic, obviously – the validity of the therefore chain is proved by the associated if that takes the premise as, literally, the protasis and the consequence as the apodosis.  Conversational Implicaturum at the Rescue. Problems with or: Consider Rosss infamous example: Post the letter! Therefore, post the letter or burn it! as invalid, Ross – and endorsed at Oxford by Williams. To permit to do p or q is to permit to do p and to permit to do q. Similarly, to give permission to do something is to lift a prohibition against doing it. Admittedly, Williams does not need this so we are stating his claim more strongly than he does. One may review Grices way out (defense of the validity of the utterance above in terms of the implicaturum. Grice claims that in Rosss infamous example (valid, for Grice), whilst (to state it roughly) the premises permissive presupposition (to use the rather clumsy term introduced by Williams) is entailed by it, the conclusions is only conversationally implicated. Typically for an isomorphist, Grice says this is something shared by indicative inferences. If, being absent-minded, Grice asks his wife, What have I done with the letter? And she replies, You have posted it or burnt it, she conversationally implicates that she is not in a position to say which Grice has done. She also conversationally implicates that Grice may not have post it, so long as he has burnt it. Similarly, the future tense indicative, You are going to post the letter has the conversational implicaturum You may be not going to post the letter so long as you are going to burn it.  But this surely does not validate the introduction rule for OR, to wit:  p; therefore, p or q. One can similarly, say: Eclipse will win. He may not, of course, if it rains. And I *know* it will *not* rain. Problems with and. Consider: Put on your parachute AND jump out! Therefore, jump out! Someone who _only_ jumps out of an æroplane does not fulfil Put on your parachute and jump out!  He has done only what is necessary, but not sufficient to fulfil it.  Imperatives do not differ from indicatives in this respect, except that fulfilment takes the place of belief or doxa, which is the form of acceptance apprpriate to a doxasatic utterance, as the Names implies.  Someone who is told Smith put on his parachute AND jumped out is entitled to believe that Smith jumped out. But if he believes that this is _all_ Smith did he is in error (Cf. Edgley). One may discuss Grices test of cancellability in the case of the transport officer who says: Go via Coldstream or Berwick! It seems the transport officers way of expressing himself is extremely eccentric, or conversationally baffling, as Grice prefers – yet validly. If the transport officer is not sure if a storm may block one of the routes, what he should say is _Prepare_ to go via Coldstream or Berwick! As for the application of Grices test of explicit cancellation here, it yield, in the circumstances, the transport officer uttering Go either via Coldstream or Berwick!  But you may not go via Coldstream if you do not go via Berwick, and you may not go via Berwick if you do not go via Coldstream. Such qualifications  ‒ what Grice calls explicit cancellation of the implicaturum  ‒ seem to the addressee to empty the buletic mode of utterance of all content and is thus reminiscent of Henry Fords utterance to the effect that people can choose what colour car they like provided it is black. But then Grice doesnt think Ford is being illogical, only Griceian and implicatural! Grice was fascinated by “if” clauses in mode other than the indicative: “if the cat is on the mat, she is purring.” “If the cat had been, make her purr!” etc. He spent years at Clifton mastering this – only to have Ayer telling him at Oxford he didn’t need it! “I won’t take that!” -- Refs.: There is at least one essay just about the categorical imperative, but there are scattered references wherever Grice considers the mood markers, The H. P. Grice Papers, BANC.

implicaturum: or, Grice’s implication. Grice makes an important distinction which he thinks Austin doesn’t make because what a philosopher EXPLICITLY conveys and what he IMPLICITLY conveys. It was only a few years Grice was interacting philosophically with Austin and was reading some material by Witters, when Grice comes with this criticism and complaint. Austin ignores “all too frequently” a distinction that Witters apparently dnies. This is a distinction between what an emissor communicates (e. g. that p), which can be either explicitly (that p1) or implicitly (that p2) and what, metabolically, and derivatively, the emissum ‘communictates’ (explicitly or implicitly). At the Oxford Philosophical Society, he is considering Moore’s ‘entailment.’ This is not a vernacular expression, but a borrowing from a Romance language. But basically, Moore’s idea is that ‘p’ may be said to ‘entail’ q iff at least two conditions follow. Surely ‘entail’ has only one sense. In this metabolically usage where it is a ‘p’ that ‘entails’ the conditions are that there is a property and that there is a limitation. Now suppose Grice is discussing with Austin or reading Witters. Grice wants to distinguish various things: what the emissor communicates (explicitly or implicitly) and the attending diaphanous but metabolical, what WHAT THE EMSSOR COMMUNICATES (explicitly or implicitly) ENTAILS, AND the purely metabolical what the emissum ‘entails’ (explicitly or implicitly). This is Grice’s wording:“If we can elucidate the meaning of "A meantNN by x that p (on a particular occasion)," this might reasonably be expected to help us with the explication of "entails.”The second important occasion is in the interlude or excursus of his Aristotelian Society talk. How does he introduce the topic of ‘implication’? At that time there was a lot being written about ‘contextual’ or ‘pragmatic’ implication – even within Grice’s circle – as in D. K. Grant’s essay on pragmatic implication for Philosophy, and even earlier Nowell-Smith’s on ‘contextual implication’ in “Ethics,” and even earlier, and this is perhaps Grice’s main trigger, P. F. Strawson’s criticism of Whitehead and Russell, with Strawson having that, by uttering ‘The king of France is not bald,’ the emissor IMPLIES that there is a king of France (Strawson later changes the idiom from ‘imply,’ and the attending ‘implication, to ‘presuppose,’ but he keeps ‘imply’ in all the reprints of his earlier essays).  In “Causal Theory,” Grice surely cannot just ‘break’ the narrative and start with ‘implication’ in an excursus. So the first stage is to explore the use of ‘implication’ or related concepts in the first part of “Causal Theory” LEADING to the excursus for which need he felt. The first use appears in section 2.  The use is the noun, ‘implication.’ And Grice is reporting the view of an objector, so does not care to be to careful himself.“the OBJECTION MIGHT run as follows.” “… When someone makes a remark such as “The pillar box seems red” A CERTAIN IMPLICATION IS CARRIED.” He goes on “This implication is “DISJUNCTIVE IN FORM,” which should not concerns us here. Since we are considering the status of the implication, as seen by the objector as reported by Grice. He does not give a source, so we may assume G. A. Paul reading Witters, and trying to indoctrinate a few Oxonians into Wittgensteinianism (Grice notes that besides the playgroup there was Ryle’s group at Oxford and a THIRD, “perhaps more disciplined” group, that tended towards Witters.Grice goes on:“It IS implied that…” p. Again, he expands it, and obviously shows that he doesn’t care to be careful. And he is being ironic, because the implication is pretty lengthy! Yet he says, typically:“This may not be an absolutely EXACT or complete characterisation of the implication, but it is, perhaps, good ENOUGH to be going with!” Grice goes on to have his objector a Strawsonian, i. e. as REFUSING TO ASSIGN A TRUTH-VALUE to the utterance, while Grice would have that it is ‘uninterestingly true. In view of this it may to explore the affirmative and negative versions. Because the truth-values may change:In Grice’s view: “The pillar box seems red to me” IS “UNINTERESTINGLY TRUE,” in spite of the implication.As for “It is not the case that the pillar box seems red,” this is more of a trick. In “Negation,” Grice has a similar example. “That pillar box is red; therefore, it is not blue.”He is concerned with “The pillar box is not blue,” or “It is not the case that the pillar box is blue.”What about the truth-value now of the utterance in connection with the implication attached to it?Surely, Grice would like, unless accepting ‘illogical’ conversationalists (who want to make that something is UNASSERTIBLE or MISLEADING by adding ‘not’), the utterance ‘It is not the case that the pillar box seems red to me’ is FALSE in the scenario where the emissor would be truthful in uttering ‘The pillar box seems red to me.” Since Grice allows that the affirmative is ‘uninterestingly true,’ he is committed to having ‘It is not the case that the pillar box seems red’ as FALSE.For the Strawsonian Wittgensteinian, or truth-value gap theorist, the situation is easier to characterise. Both ‘The pillar box seems red to me” and its negation, “The pillar box does not seem red to me” lack a truth value, or in Grice’s word, as applied to the affirmative, “far from being uninterestingly true, is neither true nor false,” i. e. ‘neuter.’ It wold not be true but it would not be false either – breakdown of bivalence. Grice’s case is a complicated one because he distinguishes between the sub-perceptual “The pillar box seems red” from the perceptual ‘vision’ statement, “Grice sees that the pillar box is red.” So the truth of “The pillar box seems red” is a necessary condition for the statement about ‘seeing.’ This is itself controversial. Some philosophers have claimed that “Grice knows that p” does NOT entail “Grice believes that p,” for example. But for the causal theory Grice is thinking of an analysis of “Grice sees that the pillar box is red” in terms of three conditions: First, the pillar box seems red to Grice. Second, the pillar box is red. And third, it is the pillar box being red that causes it seeming red to Grice. Grice goes to reformulate the idea that “The pillar box seems red” being true. But now not “uninterestingly true,” but “true (under certain conditions),” or as he puts it “(subject to certain qualifications) true.” He may be having in mind a clown in a circus confronted with the blue pillar box and making a joke about it. Those ‘certain qualifications’ would not apply to the circus case. Grice goes on to change the adverb, it’s ‘boringly true,’ or ‘highly boringly true.’ He adds ‘suggestio falsi,’ which seems alright but which would not please the Wittgensteinian who would also reject the ‘false.’ We need a ‘suggestio neutri.’ In this second section, he gives the theoretical explanation. The “implication” arises “in virtue of a GENERAL FEATURE OR PRINCIPLE” of conversation, or pertaining to a system put in ‘communication,’ or a general feature or principle governing an emissor communicating that p. Note that ‘feature’ and ‘principle’ are appropriately ‘vague.’ “Feature” can be descriptive. “Principle” is Aristotelian. Boethius’s translation for Aristotle’s ‘arche.’ It can be descriptive. The first use of ‘principle’ in a ‘moral’ or ‘practical’ context seems to post-date its use in, say, geometry – Euclid’s axioms as ‘principia mathematica,’ or Newton’s “Principia.” Grice may be having in mind Moore’s ‘paradox’ (true, surely) when Grice adds ‘it is raining.’Grice’s careful wording is worth exploring. “The mistake [incorrectness, falsehood] of supposing the implication to constitute a "part of the meaning [sense]” of "The Alpha seems Beta" is somewhat similar to, though MORE INSIDUOUS …”[moral implication here: 1540s, from Middle French insidieux "insidious" (15c.) or directly from Latin insidiosus "deceitful, cunning, artful, treacherous," from insidiae (plural) "plot, snare, ambush," from insidere "sit on, occupy," from in- "in" (from PIE root *en "in") + sedere "to sit," from PIE root *sed- (1) "to sit." Figurative, usually with a suggestion of lying in wait and the intent to entrap. Related: Insidiously; insidiousness]“than, the mistake which one IF one supposes that the SO-CALLED [‘pragmatic’ or ‘contextual – implicaturum, “as I would not,” and indeed he does not – he prefers “expresses” here, not the weak ‘imply’] “implication” that one believes it to be raining is "a part of the meaning [or sense]" of the expression [or emissum] "It is raining.”Grice allows that no philosopher may have made this mistake. He will later reject the view that one conversationally implicates that one believes that it is raining by uttering ‘It is raining.’ But again he does not give sources. In these case, while without the paraphernalia about the ‘a part of the ‘sense’” bit, can be ascribed at Oxford to Nowell-Smith and Grant (but not, we hope to Strawson). Nowell-Smith is clear that it is a contextual implication, but one would not think he would make the mistake of bringing in ‘sense’ into the bargain. Grice goes on:“The short and literally inaccurate reply to such a supposition [mistake] might be that the so-called “implication” attaches because the expression (or emissum) is a PROPOSITIONAL one [expressable by a ‘that so-and-so’ clause] not because it is the particular propositional expression which it happens to be.”By ‘long,’ Grice implicates: “And it is part of the function of the informative mode that you utter an utterance in the informative mode if you express your belief in the content of the propositonal expression.”Grice goes on to analyse ‘implication’ in terms of ‘petitio principii.’ This is very interesting and requires exploration. Grice claims that his success the implicaturum in the field of the philosophy of perception led his efforts against Strawson on the syncategoremata.But here we see Grice dealing what will be his success.One might, for example, suggest that it is open to the champion of sense_data to lay down that the sense-datum sentence " I have a pink sense-datum " should express truth if and only if the facts are as they would have to be for it to be true, if it were in order, to say .. Something looks pink to me ", even though it may not actually be in ordei to say this (because the D-or-D condition is unfulfilled). But this attempt to by-pass the objector's position would be met by the reply that it begs the question; for it assumes that there is some way of specifying the facts in isolation from the implication standardly carried by such a specification; and this is precisely what the objector is denying.Rephrasing that:“One might, for example, suggest that it is open to the champion of sense_data to lay down that the sense-datum sentence "The pillar box seems red” is TRUE if and only if the facts are as the facts WOULD HAVE to be for “The pillar box seems red” to be true, IF (or provided that) it were IN ORDER [i. e. conversationally appropriate], to utter or ‘state’ or explicitly convey that the pillar box seems red, even though it may NOT actually be in order [conversationally appropriate] to explicitly convey that the pillar box seems red (because the condition specified in the implication is unfulfilled).”“But this attempt to by-pass the objector's position would be met by a charge of ‘petitio principia,’ i. e. the reply that it begs the question.”“Such a  manoeuvre is invalid in that it assumes that there IS some way of providing a SPECIFICATION of the facts of the matter in isolation from, or without recourse to, the implication that is standardly carried by such a specification.”“This is precisely what the objector is denying, i. e. the objector believes it is NOT the case that there is a way of giving a specification of the scenario without bringing in the implication.”Grice refers to the above as one of the “frustrations,” implicating that the above, the ‘petitio principia,’ is just one of the trials Grice underwent before coming with the explanation in terms of the general feature of communication, or as he will late express, in terms of ‘what the hell’ the ‘communication-function’ of “The pillar seems red to me” might be when the implicaturum is not meant – and you have to go on and cancel it (“That pillar box seems red; mind, I’m not suggesting that it’s not – I’m practicing my sub-perceptual proficiency.”).Grice goes on to note the generality he saw in the idea of the ‘implication.’ Even if “The pillar box seems red” was his FIRST attack, the reason he was willing to do the attacking was that the neo-Wittgensteinian was saying things that went against THE TENOR OF THE THINGS GRICE would say with regard to other ‘linguistic philosophical’ cases OTHER than in the philosophy of perception, notably his explorations were against Malcolm reading of Moore, about Moore ‘misusing’ “know.”Grice:“I was inclined to rule against my objector, partly because his opponent's position was more in line with the kind of thing I was inclined to say about other linguistic phenomena which are in some degree comparable.”Rephrase:“My natural inclination was to oppose the objector.”“And that was because his opponent's position is more “in line” with the kind of thing Grice is inclined to say – or thesis he is willing to put forward-- about OTHER phenomena involving this or that ‘communication-function’ of this or that philosophical adage, which are in some degree comparable to “The pillar box seems red.””So just before the ‘excursus,’ or ‘discursus,’ as he has it – which is then not numbered – but subtitlted (‘Implication’), he embark on a discursus about “certain ASPECTS of the concept OR CONCEPTS of implication.”He interestingly adds: “using some more or less well-worn examples.” This is not just a reference to Strawson, Grant, Moore, Hungerland and Nowell-Smith, but to the scholastics and the idea of the ‘suppositio’ as an ‘implicatio,’: “Tu non cessas edere ferrum.” Grice says he will consider only four aspects or FOUR IDEAS (used each as a ‘catalyst’) in particular illustrations.“Smith has not ceased beating his wife.”“Smith’s girlfriend is poor, but honest.”“Smith’s handwriting is beautiful”“Smith’s wife is in the kitchen or in the bathroom.”Each is a case, as Grice puts it, “in which in ordinary parlance, or at least in Oxonian philosophical parlance, something might be said to be ‘implied’ (hopefully by the emissor) -- as distinct from being ‘stated,’ or ‘explicitly put.’One first illustrationEXPLICITLY CONVEYED: “Smith has not ceased beating his wife.” IMPLICITLY CONVEYED, but cancellable: “Smith has been beating his wife.”CANCELLATION: “Smith has not ceased beating his wife; he never started.”APPLY THREE OTHER IDEAS.A second illustrationEXPLICITLY CONVEYED:“Smith’s girlfriend is poor, but honest.”IMPLICITLY CONVEYED: “There is some contrast between Smith’s girlfriend’s honesty and her poverty; and possibly between Smith and the utterer.”CANCELLATION: “I’m sorry, I cannot cancel that.”TRY OTHER THREE IDEAS.A third illustrationEXPLICITLY CONVEYED “Smith’s handwriting is beautiful” – “Or “If only his outbursts were more angelic.”IMPLICITLY CONVEYED: “He possibly cannot read Hegel in German.”CANCELLATION: “Smith’s handwriting is beautiful; on top, he reads Hegel in German.”TRY THREEOTHER IDEASA fourth illustration:EXPLICITLY CONVEYED: “Smith’s wife is in the kitchen or in the bathroom.”IMPLICITLY CONVEYED: “It is not the case that I have truth-functional grounds to express disjunct D1, and it is not the case that I have truth-functional grounds to express disjunct D2; therefore, I am introducting the disjunction EITHER than by the way favoured by Gentzen.” (Grice actually focuses on the specific ‘doxastic’ condition: emissor believes …CANCELLATION: “I know perfectly well where she is, but I want you to find out for yourself.”TRY THREE OTHER IDEAS.Within the discursus he gives SIX (a sextet) other examples, of the philosophical type, because he is implicating the above are NOT of the really of philosophical type, hence his reference to ‘ordinary parlance.’ He points out that he has no doubt there are other candidates besides his sextet.FIRST IN THE SEXTETEXPLICITLY CONVEYED: “You cannot see a knife as a knife, though you may see what is not a knife as a knife.”IMPLICITLY CONVEYED: “”AS” REQUIRES A GESTALT.”CANCELLATION: “I see the horse as a horse, because my gestalt is mine.”TRY THREE OTHER IDEASSECOND IN THE SEXTET:EXPLICITLY CONVEYED:“When Moore said he knew that the objects before him were human hands, he was guilty of misusing the word "know".”IMPLICITLY CONVEYED: “You can only use ‘know’ for ‘difficult cases.’CANCELLATION: “If I know that p iff I believe that p, p, and p causes my belief in p, I know that the objects before me are human hands.”TRY THREE OTHER IDEAS.THIRD IN THE SEXTETEXPLICITLY CONVEYED: “For an occurrence to be properly said to have a ‘cause,’ the occurrence must be something abnormal or unusual.”IMPLICILTY CONVEYED: “Refrain from using ‘cause’ when the thing is normal and usual.”CANCELLATION: “If I see that the pillar box is red iff the pillar box seems red, the pillar box is red, and the pillar box being red causes the pillar box seeming red, the cause of the pillar box seeming red is that the pillar box is red.”TRY OTHER THREE IDEAS.FOURTH IN THE SEXTET:  EXPLICITLY CONVEYED: “For an action to be properly described as one for which the agent is responsible, it must be the sort of action for which people are condemned.”IMPLICITLY CONVEYED: “Refrain ascribing ‘responsibility’ to Timmy having cleaned up his bedroom.”CANCELLATION: “Timmy is very responsible. He engages in an action for which people are not condemned.”TRY THREE OTHER IDEAS.FIFTH IN THE SEXTET:EXPLICITLY CONVEYED: “What is actual is not also possible.”IMPLICITLY CONVEYED: “There is a realm of possibilities which does not overlap with the realm of actualities.”CANCELLATION: “If p is actual iff p obtains in world w1, and p is possible iff p obtains in any world wn which includes w1, p is possible.”TRY THREE OTHER IDEAS.SIXTH IN THE SEXTETEXPLICITLY CONVEYED: “What is known by me to be the case is not also believed by me to be the case.”IMPLICITLY CONVEYED: “To know is magical!”CANCELLATION: “If I know that p iff I believe that p, p, and p causes my believing that p, then what is known by me to be the case is also believed by me to be the case.”TRY THREE OTHER IDEAS.CASE IN QUESTION:EXPLICITLY CONVEYED: “The pillar box seems red.”IMPLICITLY CONVEYED: “One will doubt it is.”CANCELLATION: “The pillar box seems red and I hope no one doubt it is.”TRY THREE OTHER IDEAS. THAT LISTING became commonplace for Grice. In ProlegomenaGROUP A: EXAMPLE I: RYLE on ‘voluntarily’ and “involuntarily” in “The Concept of Mind.” RYLE WAS LISTENING! BUT GRICE WAS without reach! Grice would nothavecriticised Ryle at a shorter distance.EXAMPLE II: MALCOLM IN “Defending common sense” in the Philosophical Review, on Moore’s misuse of ‘know’ – also in Causal, above, as second in the sextet.EXPLICITLY CONVEYED:“When Moore said he knew that the objects before him were human hands, he was guilty of misusing the word "know".REPHRASE IN “PROLEGOMENA.”IMPLICITLY CONVEYED: “You can only use ‘know’ for ‘difficult cases.’CANCELLATION: “If I know that p iff I believe that p, p, and p causes my belief in p, I know that the objects before me are human hands.”EXAMPLE III: BENJAMIN ON BROAD ON THE “SENSE” OF “REMEMBERING”EXPLICITLY CONVEYED;IMPLICITLY CONVEYEDCANCELLATIONEXAMPLES, GROUP A, CLASS IV: philosophy of perception FIRST EXAMPLE: Witters on ‘seeing as’ in Philosophical InvestigationsEXPLICITLY CONVEYEDIMPLICITLY CONVEYEDCANCELLATION.Previously used in Causal as first in the sextet: FIRST IN THE SEXTETEXPLICITLY CONVEYED: “You cannot see a knife as a knife, though you may see what is not a knife as a knife.”Rephrased in Prolegomena. IMPLICITLY CONVEYED: “”AS” REQUIRES A GESTALT.”CANCELLATION: “I see the horse as a horse, because my gestalt is mine.”GROUP A – CLASS IV – PHILOSOPHY OF PERCEPTIONEXAMPLE II – “The pillar box seems red to me.”Used in“Causal”EXPLICITLY CONVEYED: “The pillar box seems red.”IMPLICITLY CONVEYED: “One will doubt it is.”CANCELLATION: “The pillar box seems red and I hope no one doubt it is.”GROUP A – CLASS V – PHILOSOPHY OF ACTION – Here unlike Class IV, he uses (a), etc.EXAMPLE A: WITTERS AND OTHERS on ‘trying’ EXPLICITLY CONVEYEDIMPLICITLY CONVEYED:CANCELLATIONGROUP A – CLASS V – “ACTION,” not ‘philosophy of action’ – cf. ‘ordinary parlance.’EXAMPLE B: Hart on ‘carefully.’EXPLICITLY CONVEYEDIMPLICITLY CONVEYEDCANCELLATION GROUP A – CLASS V – ACTIONEXAMPLE C: Austin in “A plea for excuses” on ‘voluntarily’ and ‘involuntarily’ – a refinement on Ryle above – using variable “Mly” – Grice would not have criticised Austin in the play group. He rather took it against his tutee, Strawson.EXPLICITLY CONVEYED IMPLICITLY CONVEYEDCANCELLATIONGROUP B: syncategorema – not lettered butFIRST EXAMPLE: “AND” (not ‘not’)SECOND EXAMPLE: “OR”THIRD EXAMPLE: “IF” – particularly relevant under ‘implication.’ STRAWSON, Introduction to logical theory.GRICE’S PHRASING: “if p, q” ENTAILS ‘p horseshoe q.’ The reverse does not hold: it is not the case that ‘p horseshoe q’ ENTAILS ‘if p, q’. Odd way of putting it, but it was all from Strawson. It may be argued that ‘entail’ belongs in a system, and ‘p horseshoe q’ and ‘if p, q’ are DISPARATE. Grice quotes verbatim from Strawson:a ‘primary or standard’ use of “if … then …,” or “if,” of which the main characteristics were: that for each hypothetical statement made by this use of “if,” there could be made just one statement which would be the antecedent of the hypothetical and just onestatement which would be its consequent; that the hypothetical statement is acceptable (true, reasonable) if the antecedent statement, if made or accepted, would, in the circumstances, be a good ground or reason for accepting the consequent statement; and that the making of the hypothetical statement carries the implicationeither of uncertainty about, or of disbelief in, the fulfilment of both antecedent and consequent.Grice rephrases that by stating that for Grice “a primary or standard use of ‘if, then’” is characterised as follows:“for each hypothetical statement made by this use of “if,” there could be made just one statement which would be the antecedent of the hypothetical and just one statement which would be its consequent; that the hypothetical statement is acceptable (true, reasonable) if the antecedent statement, if made or accepted, would, in the circumstances, be a good ground or reason for accepting the consequent statement; and that the making of the hypothetical statement carries the implication either of uncertainty about, or of disbelief in, the fulfilment of both antecedent and consequent.”Grice rephrases the characterisation as from “each” and eliding a middle part, but Grice does not care to add the fastidious “[…],” or quote, unquote.“each hypothetical ‘statement’ made by this use of “if” is acceptable (TRUE, reasonable) if the antecedent ‘statement,’ IF made or accepted, would, in the circumstances, be a good ground or reason for accepting the consequent ‘statement;’ and that the making of thehypothetical statement carries the implication either of uncertainty about, or of disbelief in, the fulfilment of both antecedent and consequent.  “A hypothetical, or conditional ‘statement’ or composite proposition such as “If it is day, I talk”is acceptable (or TRUE, or ‘reasonable’) if (but not only if), first, the antecedent ‘statement,’ ‘It is day,’ IF made on its own, or accepted on its own, i. e. simpliciter, would, in the circumstances, be a good ground or ‘reason’ for accepting the consequent ‘statement,’ to wit: “I talk;” and, second, that the making of the conditional proposition or hypothetical ‘statement’ carries the implication, or rather the emissor of the emissum IMPLIES, either it is not the case that the emissor is CERTAIN about or that it is day and CERTAIN about or that he talks, or BELIEVES that it is day and BELIEVES that he talks.”More or less Grice’s denial or doubt. Or rather ‘doubt’ (Strawson’s ‘uncertainty about’) or denial (‘disbelief in’). But it will do at this point to explore the argument by Strawson to which Grice is responding. First two comments. Strawson has occasion to respond to Grice’s response in more than one opportunity. But Grice never took up the issue again in a detailed fashion – after dedicating a full lecture to it. One occasion was Strawson’s review of the reprint of Grice in 1989. Another is in the BA memorial. The crucial one is repr. by Strawson (in a rather otiose way) in his compilation, straight from PGRICE. This is an essay which Strawson composed soon after the delivery by Grice of the lecture without consulting. Once Stawson is aware of Grice’s terminology, he is ready to frame his view in Grice’s terms: for Strawson, there IS an implicaturum, but it is a conventional one. His analogy is with the ‘asserted’ “therefore” or “so.” Since this for Grice was at least the second exemplar of his manoeuvre, it will do to revise the argument from which Grice extracts the passage in “Prolegomena.” In the body of the full lecture IV, Grice does not care to mention Strawson at all; in fact, he makes rather hasty commentaries generalising on both parties of the debate: the formalists, who are now ‘blue-collared practitioners of the sciences,” i. e. not philosophers like Grice and Strawson; and the informalists or ‘traditionalists’ like Strawson who feel offended by the interlopers to the tranquil Elysium of philosophy. Grice confesses a sympathy for the latter, of course. So here is straight from the tranquil Elysium of philosophy. For Strawson, the relations between “if” and “⊃” have already, but only in part, been discussed (Ch. 2, S. 7).” So one may need to review those passages. But now he has a special section that finishes up the discussion which has been so far only partial. So Strawson resumes the points of the previous partial discussion and comes up with the ‘traditionalist’ tenet.  The sign “⊃” is called the material implication sign. Only by Whitehead and Russell, that is, ‘blue-collared practitioners of the sciences,’ in Grice’s wording. Whitehead and Russell think that ‘material’ is a nice opposite to ‘formal,’ and ‘formal implication’ is something pretty complex that only they know to which it refers! Strawson goes on to explain, and this is a reminder of his “Introduction” to his “Philosophical Logic” where he reprints Grice’s Meaning (for some reason). There Strawson has a footnote quoting from Quine’s “Methods of Logic,” where the phrasing is indeed about the rough phrase, ‘the meaning of ‘if’’ – cf. Grice’s laughter at philosophers talking of ‘the sense of ‘or’’ – “Why, one must should as well talk of the ‘sense’ of ‘to,’ or ‘of’!’ – Grice’s implicaturum is to O. P. Wood, whose claim to fame is for having turned Oxford into the place where ‘the sense of ‘or’’ was the key issue with which philosophers were engaged.  Strawson goes on to say that its meaning is given by the ‘rule’ that any statement of the form ‘p⊃q’ is FALSE in the case in which the first of its constituent statements is true and the second false, and is true in every other case considered in the system; i. e., the falsity of the first constituent statement or the truth of the second are, equally, sufficient conditions of the truth of a statement of material implication. The combination of truth in the first with falsity in the second is the single, NECESSARY AND SUFFICIENT, condition of its falsity. The standard or primary -- the importance of this qualifying phrase, ‘primary,’ can scarcely be overemphasized – Grice omits this bracket when he expolates the quote. The bracket continues. The place where Strawson opens the bracket is a curious one: it is obvious he is talking about the primary use of ‘if’. So here he continues the bracket with the observation that there are uses of “if”  which do not answer to the description given here, or to any other descriptions given in this [essay] -- use of “if” sentence, on the other hand [these are Strawson’s two hands], are seen to be in circumstances where, not knowing whether some statement which could be made by the use of a sentence corresponding in a certain way to the sub-ordinated clause of the utterance is true or not, or believing it to be false, the emissor nevertheless considers that a step in reasoning from THAT statement to a statement related in a similar way to the main clause would be a sound or reasonable step [a reasonable reasoning, that is]; this statement related to the main clause also being one of whose truth the emissor is in doubt, or which the emissor believes to be false. Even in such circumstances as these a philosopher may sometimes hesitate to apply ‘true’ to a conditional or hypothetical statement, i.e., a statement which could be made by the use of “if ”(Philo’s ‘ei,’ Cicero’s ‘si’)  in its standard significance, preferring to call a conditional statement reasonable or well-founded. But if the philosopher does apply ‘true’ to an ‘if’ utterance at all, it will be in such circumstances as these. Now one of the sufficient conditions of the truth of a ‘statement’ or formula of material implication may very well be fulfilled without the conditions for the truth, or reasonableness, of the corresponding hypothetical or conditional statement being fulfilled. A statement of the form ‘p ⊃ q’ (where the horseshoe is meant to represent an inverted ‘c’ for ‘contentum’ or ‘consequutum’ -- does not entail the corresponding statement of the ‘form’ “if p, q.” But if the emissor is prepared to accept the hypothetical statement, he must in consistency be prepared to deny the conjunction of the statement corresponding to the sub-ordinated clause of the sentence used to make the hypothetical statement with the negation of the statement corresponding to its main or super-ordinated clause. A statement of the ‘form’ “if p, q” does entail the corresponding statement of the form ‘p ⊃ q.’ The force of “corresponding” may need some elucidation. Consider the following very ‘ordinary’ or ‘natural’ specimens of a hypothetical sentence. Strawson starts with a totally unordinary subjective counterfactual ‘if,’ an abyss with Philo, “If it’s day, I talk.” Strawson surely involves The Hun. ‘If the Germans had invaded England in 1940, they, viz. the Germans, would have won the war.’ Because for the Germans, invading England MEANT winning the war. They never cared much for Wales or Scotland, never mind Northern Ireland. Possibly ‘invaded London’ would suffice. Strawson’s second instantiation again is the odd subjective counter-factual ‘if,’ an abyss or chasm from Philo, ‘If it’s day, I talk.’ “If Smith were in charge, half the staff would have been dismissed.’ Strawson is thinking Noel Coward, who used to make fun of the music-hall artist Wade. “If you WERE the only girl in the world, and I WAS the only boy…’. The use of ‘were’ is Oxonian. A Cockney is forbidden to use it, using ‘was’ instead. The rationale is Philonian. ‘was’ is indicative.  “If Smith were in charge, half the staff would have been dismissed.’ Strawson’s third instantiation is, at last, more or less Philonian, a plain indicative ‘weather’ protasis, etc. “If it rains, the match will be cancelled.” The only reservation Philo would have is ‘will’. Matches do not have ‘will,’ and the sea battle may never take place – the world may be destroyed by then. “If it rains, the match will be cancelled.” Or “If it rains, the match is cancelled – but there is a ‘rain date.’” The sentence which could be used to make a statement corresponding in the required ‘sense’ to the sub-ordinate clause can be ascertained by considering what it is that the emissor of each hypothetical sentence must (in general) be assumed either to be in doubt about or to believe to be not the case. Thus, the corresponding sentences. ‘The Germans invaded England in 1940.’ Or ‘The Germans invade England’ – historical present -- ‘The Germans won the war.’ Or ‘The Germans win the war’ – historical present. ‘Smith is in charge.’ ‘Half the staff has been dismissed.’ Or ‘Half the staff is dismissed.’ ‘It will rain.’ Or ‘It rains.’‘The match will be cancelled.’ Or ‘The match is cancelled.’ A sentence could be used to make a statement of material implication corresponding to the hypothetical statement made by the  sentence is framed, in each case, from these pairs of sentences as follows. ‘The Germans invaded England in 1940 ⊃ they won the war.’ Or in the historical present,’The Germans invade London ⊃ The Germans win the war. ‘ ‘Smith is in charge ⊃ half the staff has been, dismissed.’ Or in the present tense, ‘Smith is in charge ⊃ half the staff is dismissed.’ ‘ It will rain ⊃ the match will be cancelled.’ Or in the present ‘It rains ⊃ the match is cancelled.’  The very fact that a few verbal modifications are necessary to please the Oxonian ear, in order to obtain from the clauses of the hypothetical sentence the clauses of the corresponding material implication sentence is itself a symptom of the radical difference between a hypothetical statement and a truth-functional statement. Some detailed differences are also evident from these instantiations. The falsity of a statement made by the use of ‘The Germans invade London in 1940’ or ‘Smith is in charge’ is a sufficient condition of the truth of the corresponding statements made by the use of the ⊃-utterances. But not, of course, of the corresponding statement made by the use of the ‘if’ utterance. Otherwise, there would normally be no point in using an ‘if’ sentence at all.An ‘if’ sentence would normally carry – but not necessarily: one may use the pluperfect or the imperfect subjunctive when one is simply working out the consequences of an hypothesis which one may be prepared eventually to accept -- in the tense or mode of the verb, an implication (or implicaturum) of the emissor’s belief in the FALSITY of the statements corresponding to the clauses of the hypothetical.That it is not the case that it rains is sufficient to verify (or truth-functionally confirm) a statement made by the use of “⊃,” but not a statement made by the use of ‘if.’ That it is not the case that it rains is also sufficient to verify (or truth-functionally confirm) a statement made by the use of ‘It will rain ⊃ the match will not be cancelled.’ Or ‘It rains ⊃ the match is cancelled.’ The formulae ‘p ⊃ q’ and ‘p ⊃ ~ q' are consistent with one another.The joint assertion of corresponding statements of these forms is equivalent to the assertion of the corresponding statement of the form ‘~ p.’ But, and here is one of Philo’s ‘paradoxes’: “If it rains, the match will be cancelled” (or ‘If it rains, the match is cancelled’) seems (or sounds) inconsistent with “If it rains, the match will not be cancelled,’ or ‘If it rains, it is not the case that the match is cancelled.’But here we add ‘not,’ so Philo explains the paradox away by noting that his account is meant for ‘pure’ uses of “ei,” or “si.”Their joint assertion in the same context sounds self-contradictory. But cf. Philo, who wisely said of ‘If it is day, it is night’ “is true only at night.” (Diog. Laert. Repr. in Long, The Hellenistic Philosophers). Suppose we call the statement corresponding to the sub-ordinated clause of a sentence used to make a hypothetical statement the antecedent of the hypothetical statement; and the statement corresponding to the super-ordinated clause, its consequent. It is sometimes fancied that, whereas the futility of identifying a conditional ‘if’ statement with material implication is obvious in those cases where the implication of the falsity of the antecedent is normally carried by the mode or tense of the verb – as in “If the Germans invade London in 1940, they, viz. the Germans, win the war’ and ‘If Smith is in charge, half the staff is dismissed’ -- there is something to be said for at least a PARTIAL identification in cases where no such implication is involved, i.e., where the possibility of the truth of both antecedent and consequent is left open – as in ‘If it rains, the match is cancelled.’ In cases of the first kind (an ‘unfulfilled,’ counterfactual, or ‘subjunctive’ conditional) the intended addressee’s attention is directed, as Grice taught J. L. Mackie, in terms of the principle of conversational helpfulness, ONLY TO THE LAST TWO ROWS of the truth-tables for ‘ p ⊃ q,’ where the antecedent has the truth-value, falsity. Th suggestion that ‘~p’ ‘entails’ ‘if p, q’ is felt or to be or ‘sounds’ – if not to Philo’s or Grice’s ears -- obviously wrong.  But in cases of the second kind one inspects also the first two ROWS. The possibility of the antecedent's being fulfilled is left open. It is claimed that it is NOT the case that the suggestion that ‘p ⊃ q’ ‘entails’ ‘if p, q’ is felt to be or sound obviously wrong, to ANYBODY, not just the bodies of Grice and Philo. This Strawson calls, to infuriate Grice, ‘an illusion,’ ‘engendered by a reality.’The fulfilment of both antecedent and consequent of a hypothetical statement does not show that the man who made the hypothetical statement is right. It is not the case that the man would be right, Strawson claims, if the consequent is made true as a result of this or that factor unconnected with, or in spite of, rather than ‘because’ of, the fulfilment of the antecedent.  E. g. if Grice’s unmissable match is missed because the Germans invade – and not because of the ‘weather.’ – but cf. “The weather in the streets.” Strawson is prepared to say that the man (e. g., Grice, or Philo) who makes the hypothetical statement is right only if Strawson is also prepared to say that the antecedent being true is, at least in part, the ‘explanation’ of the consequent being true. The reality behind the illusion Strawson naturally finds ‘complex,’ for surely there ain’t one! Strawson thinks that this is due to two phenomena. First, Strawson claims, in many cases, the fulfilment of both antecedent and consequent provides confirmation for the view that the existence of states of affairs like those described by the antecedent IS a good ‘reason’ for expecting (alla Hume, assuming the uniformity of nature, etc.) a states of affair like that described by the consequent. Second, Starwson claims, a man (e. g. Philo, or Grice) who (with a straight Grecian or Griceian face) says, e. g. ‘If it rains, the match is cancelled’ makes a bit of a prediction, assuming the ‘consequent’ to be referring to t2>t1 – but cf. if he is reporting an event taking place at THE OTHER PLACE. The prediction Strawson takes it to be ‘The match is cancelled.’And the man is making the prediction ONLY under what Strawson aptly calls a “proviso,” or “caveat,” – first used by Boethius to translate Aristotle -- “It rains.” Boethius’s terminology later taken up by the lawyers in Genoa. mid-15c., from Medieval Latin proviso (quod) "provided (that)," phrase at the beginning of clauses in legal documents (mid-14c.), from Latin proviso "it being provided," ablative neuter of provisus, past participle of providere (see provide). Related: Provisory. And that the cancellation of the match because of the rain therefore leads us to say, not only that the reasonableness of the prediction was confirmed, but also that the prediction itself was confirmed.  Because it is not the case that a statement of the form ‘ p ⊃ q’ entails the corresponding statement of the form ' if p, q ' (in its standard employment), Strawson thinks he can find a divergence between this or that ‘rule’ for '⊃' and this or that ‘rule’ for '’if ,’ in its standard employment. Because ‘if p, q’ does entail ‘p ⊃ q,’ we shall also expect to find some degree of parallelism between the rules. For whatever is entailed by ‘p ⊃ q’ is entailed by ‘if p, q,’ though not everything which entails ‘p ⊃ q’ does Strawson claims, entail ‘if p, q.’  Indeed, we find further parallels than those which follow simply from the facts that ‘if p, q’ entails ‘p ⊃ q’ and that entailment is transitive.  To some laws for ‘⊃,’ Strawson finds no parallels for ‘if.’ Strawson notes that for at least four laws for ‘⊃,’ we find that parallel laws ‘hold’ good for ‘if. The first law is mentioned by Grice, modus ponendo ponens, as elimination of ‘⊃.’ Strawson does not consider the introduction of the horseshoe, where p an q forms a collection of all active assumptions previously introduced which could have been used in the deduction of  ‘if p, q.’ When inferring ‘if p, q’ one is allowed to discharge assumptions of the form p. The fact that after deduction of ‘if p, q’  this assumption is discharged (not active is pointed out by using [ ] in vertical notation, and by deletion from the set of assumptions in horizontal notation. The latter notation shows better the character of the rule; one deduction is transformed into the other. It shows also that the rule for the introduction of ‘if’ corresponds to an important metatheorem, the Deduction Theorem, which has to be proved in axiomatic formalizations of logic. But back to the elimination of ‘if’. Modus ponendo ponens. ‘‘((p ⊃ q).p) ⊃ q.’ For some reason, Strawson here mixes horseshoes and ifs as if Boethius is alive! Grice calls these “half-natural, half-artificial.’ Chomsky prefers ‘semi-native.’ ‘(If p, q, and p) ⊃q.’ Surely what Strawson wants is a purely ‘if’ one, such as ‘If, if p, q, and p, q.’ Some conversational implicaturum!  As Grice notes: “Strawson thinks that one can converse using his converses, but we hardly.’ The second law. Modus tollendo tollens. ‘((p⊃q). ~ q)) ⊃ (~ p).’ Again, Strawson uses a ‘mixed’ formula: (if p, q, and it is not the case that q) ⊃ it is not the case that p. Purely unartificial: If, if p, q, and it is not the case that q, it is not the case that p. The third law, which Strawson finds problematic, and involves an operator that Grice does not even consider. ‘(p ⊃ q) ≡ (~ q  ⊃ ~ p). Mixed version, Strawson simplifies ‘iff’ to ‘if’ (in any case, as Pears notes, ‘if’ IMPLICATES ‘iff.’). (If p, q) ⊃ if it is not the case that q, it is not the case that p. Unartificial: If, if p, q, it is not the case that if q, it is not the case that p. The fourth law. ((p ⊃ q).(q ⊃ r)) ⊃ (p ⊃ r). Mixed: (if p, q, and if q, r) ⊃ (if p, r). Unartificial: ‘If, if p, q, and if q, r, if p, r.’ Try to say that to Mrs. Grice! (Grice: “It’s VERY SURPRISING that Strawson think we can converse in his lingo!”). Now Strawson displays this or that ‘reservation.’ Mainly it is an appeal to J. Austen and J. Austin. Strawson’s implicaturum is that Philo, in Megara, has hardly a right to unquiet the tranquil Elysium. This or that ‘reservation’ by Strawson takes TWO pages of his essay. Strawson claims that the reservations are important. It is, e. g., often impossible to apply entailment-rule (iii) directly without obtaining incorrect or absurd results. Some modification of the structure of the clauses of the hypothetical is commonly necessary. Alas, Whitehead and Russell give us little guide as to which modifications are required.  If we apply rule (iii) to our specimen hypothetical sentences, without modifying at all the tenses or moods of the individual clauses, we obtain expressions which Austin would not call ‘ordinary language,’ or Austen, for that matter, if not Macaulay.  If we preserve as nearly as possible the tense-mode structure, in the simplest way consistent with grammatical requirements, we obtain this or that sentence. TOLLENDO TOLLENS. ‘If it is not the case that the Germans win the war, it is not the case that they, viz. the Germans, invade England in 1940.’ ‘If it is not the case that half the staff is dismissed, it is not the case that Smith is in charge.’ ‘If it is not the case that the match is cancelled, it is not the case that it rains.’ But, Strawson claims, these sentences, so far from SOUNDING or seeming logically equivalent to the originals, have in each case a quite different ‘sense.’ It is possible, at least in some cases, to frame, via tollendo tollens a target setence of more or less the appropriate pattern for which one can imagine a use and which DOES stand in the required relationship to the source sentence. ‘If it is not the case that the Germans win the war, (trust) it is not the case that they, viz. the Germans, invade England in 1940,’ with the attending imlicatum: “only because they did not invade England in 1940.’ or even, should historical evidence be scanty). ‘If it is not the case that the Germans win the war, it SURELY is not the case that they, viz. the Germans, invade London in 1940.’ ‘If it is not the case that half the staff is dismissed, it surely is not the case that Smith is in charge.’ These changes reflect differences in the circumstances in which one might use these, as opposed to the original, sentences.  The sentence beginning ‘If Smith is in charge …’ is normally, though not necessarily, used by a man who antecedently knows that it is not the case that Smith is in charge. The sentence beginning ‘If it is not the case that half the staff is dismissed …’  is normally, though not necessarily, used by by a man who is, as Cook Wilson would put it, ‘working’ towards the ‘consequent’ conclusion that Smith is not in charge.  To say that the sentences are nevertheless truth-functionally equivalent seems to point to the fact that, given the introduction rule for ‘if,’ the grounds for accepting the original ‘if’-utterance AND the ‘tollendo tollens’ correlatum, would, in two different scenarios, have been grounds for accepting the soundness or validity of the passage or move from a premise ‘Smith is in charge’ to its ‘consequentia’ ‘consequutum,’ or ‘conclusion,’ ‘Half the staff is dismissed.’ One must remember that calling each formula (i)-(iv) a LAW or a THEOREM is the same as saying that, e.g., in the case of (iii), ‘If p, q’ ‘ENTAILS’ ‘If it is not the case that q, it is not the case that p.’ Similarly, Strawson thinks, for some steps which would be invalid for ‘if,’ there are corresponding steps that would be invalid for ‘⊃.’ He gives two example using a symbol Grice does not consider, for ‘therefore,’ or ‘ergo,’ and lists a fallacy. First example. ‘(p ⊃ q).q ∴ p.’ Second example of a fallacy:‘(p ⊃ q). ~p ∴ ~q.’ These are invalid inference-patterns, and so are the correlative patterns with ‘if’: ‘If p, q; and q  ∴ p’ ‘If p, q; and it is not the case that p ∴ it is not the case that q. The formal analogy here may be described by saying that neither ‘p ⊃  q’ nor ‘if p, q’ is a simply convertible (“nor hardly conversable” – Grice) formula. Strawson thinks, and we are getting closer to Philo’s paradoxes, revisied, that there may be this or that laws which holds for ‘p ⊃ q’ and not for ‘If p, q.’  As an example of a law which holds for ‘if’ but not for ‘⊃,’ one may give an analytic formula. ~[(if p, q) . (if p, it is not the case that q)]’. The corresponding formula with the horseshoe is not analytic. ‘~[(p ⊃ q) . (p ⊃ ~q)]’ is not analytic, and is equivalent to the contingent formula ‘~ ~p.’ The rules to the effect that this or that formula is analytic is referred to by Johnson, in the other place, as the ‘paradox of implication.’ This Strawson finds a Cantabrigian misnomer. If Whitehead’s and Russell’s ‘⊃’ is taken as identical either with Moore’s ‘entails’ or, more widely, with  Aelfric’s‘if’ – as in his “Poem to the If,” MSS Northumberland – “If” meant trouble in Anglo-Saxon -- in its standard use, the rules that yield this or that so-called ‘paradox’ -- are not, for Strawson, “just paradoxical.” With an attitude, he adds. “They are simply incorrect.”This is slightly illogical.“That’s not paradoxical; that’s incorrect.”Cf. Grice, “What is paradoxical is not also incorrect.” And cf. Grice: “Philo defines a ‘paradox’ as something that surprises _his father_.’ He is ‘using’ “father,” metaphorically, to refer to his tutor. His father was unknown (to him). On the other hand (vide Strawson’s Two Hands), with signs you can introduce alla Peirce and Johnson by way of ostensive definition any way you wish! If ‘⊃’ is given the meaning it is given by what Grice calls the ‘truth-table definition,’ or ‘stipulation’ in the system of truth functions, the rules and the statements they represent, may be informally dubbed ‘paradoxical,’ in that they don’t agree with the ‘man in the street,’ or ‘the man on High.’ The so-called ‘paradox’ would be a simple and platitudinous consequence of the meaning given to the symbol. Strawson had expanded on the paradoxes in an essay he compiled while away from Oxford. On his return to Oxford, he submitted it to “Mind,” under the editorship by G. Ryle, where it was published. The essay concerns the ‘paradoxes’ of ‘entailment’ in detail, and mentions Moore and C. I. Lewis. He makes use of modal operators, nec. and poss. to render the ‘necessity’ behind ‘entail.’ He thinks the paradoxes of ‘entailment’ arise from inattention to this modality. At the time, Grice and Strawson were pretty sure that nobody then accepted, if indeed anyone ever did and did make, the identification of the relation symbolised by the horseshoe, ⊃, with the relation which Moore calls ‘entailment,’ p⊃q, i. e. The mere truth-functional ‘if,’ as in ‘p ⊃ q,’ ‘~(pΛ~q)’ is rejected as an analysis of the meta-linguistic ‘p entails q.’ Strawson thinks that the identification is rejected because ‘p ⊃ q’ involves this or that allegedly paradoxical implicaturum.Starwson explicitly mentions ‘ex falso quodlibeet.’ Any FALSE proposition entails any proposition, true or false. And any TRUE proposition is entailed by any proposition, true or falso (consequentia mirabilis). It is a commonplace  that  Lewis, whom Grice calls a ‘blue-collared practioner of the sciences,’ Strawson thinks, hardly solved the thing. The amendment by Lewis, for Strawson, has consequences scarcely less paradoxical in terms of the implicatura. For if p is impossible, i.e. self-contradictory, it is impossible that p and ~q. And if q is necessary, ~q is impossible and it is impossible that p and ~q; i. e., if p entails q means it is impossible that p and ~q any necessary proposition is entailed by any proposition and any self-contradictory proposition entails any proposition. On the other hand, the definition by Lewis of ‘strict’ implication or entailment (i.e. of the relation which holds from p to q whenever q is deducible from p), Strawson thinks, obviously commends itself in some respects. Now, it is clear that the emphasis laid on the expression-mentioning character of the intensional contingent statement by writing ‘ ‘pΛ~q’ is impossible instead’ of ‘It is impossible that p and ~q’ does not avoid the alleged paradoxes of entailment. But, Starwson optimistically thinks, it is equally clear that the addition of some provision does avoid them. Strawson proposes that one should use “p entails q” such that no necessary statement and no negation of a necessary statement can significantly be said to “entail” or be entailed by any statement; i. e. the function “p entails q” cannot take necessary or self-contradictory statements as arguments. The expression “p entails q” is to be used to mean “ ‘p ⊃ q’ is necessary, and neither ‘p’ nor ‘q’ is either necessary or self-contradictory.” Alternatively, “p entails q” should be used only to mean “ ‘pΛ~q’ is impossible and neither ‘p’ nor ‘q,’ nor either of their contradictories, is necessary. In this way, Strawson thinks the paradoxes are avoided. Strawson’s proof. Let us assume that p1 expresses a contingent, and q1 a necessary, proposition. p1 and ~q1 is now impossible because ~q1 is impossible. But q1 is necessary. So, by that provision, p1 does not entail q1. We may avoid the paradoxical assertion “p1 entails q2” as merely falling into the equally paradoxical assertion “ “p1 entails q1” is necessary.” For: If ‘q’ is necessary, ‘q is necessary’ is, though true, not necessary, but a CONTINGENT INTENSIONAL (Latinate)  statement. This becomes part of the philosophers lexicon: intensĭo, f. intendo, which L and S render as a stretching out, straining, effort. E. g. oculorum, Scrib. Comp. 255. Also an intensifying, increase. Calorem suum (sol) intensionibus ac remissionibus temperando fovet,” Sen. Q. N. 7, 1, 3. The tune: “gravis, media, acuta,” Censor. 12.  Hence: ‘~ (‘q’ is necessary)’ is, though false, possible. Hence “p1 Λ ~ (q1 is necessary)” is, though false, possible.  Hence ‘p1’ does NOT entail ‘q1 is necessary.’ Thus, by adopting the view that an entailment statement, and other intensional statements, are contingent, viz. non-necessary, and that no necessary statement or its contradictory can entail or be entailed by any statement, Strawson thinks he can avoid the paradox that a necessary proposition is entailed by any proposition, and indeed all the other associated paradoxes of entailment.  Grice objects that the alleged cure by Strawson is worse than disease of Moore!  The denial that a necessary proposition can entail or be entailed by any proposition, and, therefore, that necessary propositions can be related to each other by the entailment relation, is too high a price to pay for the solution of the paradoxes, which are perfectly true utterances with only this or that attending cancellable implicaturum. Strawson’s introduction of ‘acc.’ makes sense. Which makes sense in that Philo first supplied his truth-functional account of ‘if’ to criticise his tutor Diodorus on modality. Philo reported to Diodorus something he had heard from Neptune. In dreams, Neptune appeared to Philo and told him: “I saw down deep in the waters a wooden trunk of a plant that only grows under weather – algae -- The trunk can burn!” Neptune said.Awakening, Philo ran to Diodorus: “A wooden trunk deep down in the ocean can burn.”   Throughout this section, Strawson refers to a ‘primary or standard’ use of ‘if,’ of which the main characteristics are various. First, that for each hypothetical statement made by this use of ‘if,’ there could be made just one statement which would be the antecedent of the hypothetical and just one statement which would be its consequent. Second, that the hypothetical statement is acceptable (true, reasonable) if the antecedent statement, if made or accepted, would, in the circumstances, be a good ground or reason for accepting the consequent statement. Third, the making of the hypothetical statement carries the implication either of uncertainty about, or of disbelief in, the fulfilment of both antecedent and consequent.’ This above is the passage extrapolated by Grice. Grice does not care to report the platitudionous ‘first’ ‘characteristic’ as Strawson rather verbosely puts it. The way Grice reports it, it is not clear Strawson is listing THREE characteristics. Notably, from the extrapolated quote, it would seem as if Grice wishes his addressee to believe that Strawson thinks that characteristic 2 and characteristic 3 mix. On top, Grice omits a caveat immediately after the passage he extrapolates. Strawso notes: “There is much more than this to be said about this way of using ‘if;’ in particular, about the meaning of the question whether the antecedent would be a GOOD ground or reason for accepting the consequent, and about the exact way in which THIS question is related to the question of whether the hypothetical is TRUE {acceptable, reasonable) or not.’ Grice does not care to include a caveat by Strawson: “Not all uses of ‘if ,’ however, exhibit all these three characteristics.” In particular, there is a use which has an equal claim to rank as standard ‘if’ and which is closely connected with the use described, but which does not exhibit the first characteristic and for which the description of the remainder must consequently be modified.  Strawson has in mind what is sometimes called a ‘formal’ (by Whitehead and Russell) or 'variable' or 'general’ or ‘generic’ hypothetical. Strawson gives three examples. The first example is ‘lf ice is left in the sun, it melts.’ This is Kantian. Cf. Grice on indicative conditionals in the last Immanuel Kant Lecture.  Grice: "It should be, given that it is the case that one smears one's skin with peanut butter before retiring and that it is the case that one has a relatively insensitive skin, that it is the case that one preserves a youthful complexion." More generally, there is some plausibility to the idea that an exemplar of the form 'Should (! E, ⊢F; ! G)' is true just in case a corresponding examplar of the form 'Should (⊢ F, ⊢G; ⊢E)' is true. Before proceeding further, I will attempt to deal briefly with a possible objection which might be raised at this point. I can end imagine an ardent descriptivist, who first complains, in the face of someone who wishes to allow a legitimate autonomous status to practical acceptability generalizations, that truth-conditions for such generalizations are not available, and perhaps are in principle not available; so such generalizations are not to be taken seriously. We then point out to him that, at least for a class of such cases, truth-conditions are available, and that they are to be found in related alethic generalizations, a kind of generalization he accepts. He then complains that, if finding truth-conditions involves representing the practical acceptability generalizations as being true just in case related alethic generalizations are true, then practical acceptability generalizations are simply reducible to alethic generalizations, and so are not to be taken seriously for another reason, namely, that they are simply transformations of alethic generalizations, and we could perfectly well get on without them. Maybe some of you have heard some ardent descriptivists arguing in a style not so very different from this. Now a deep reply to such an objection would involve (I think) a display of the need for a system of reasoning in which the value to be transmitted by acceptable inference is not truth but practical value, together with a demonstration of the role of practical acceptability generalizations in such a system. I suspect that such a reply could be constructed, but I do not have it at my fingertips (or tongue-tip), so I shall not try to produce it. An interim reply, however, might take the following form: even though it may be true (which is by no means certain) that certain practical acceptability generalizations have the same truth-conditions as certain corresponding alethic generalizations, it is not to be supposed that the former generalizations are simply reducible to the latter (in some disrespectful sense of 'reducible'). For though both kinds of generalization are defeasible, they are not defeasible in the same way; more exactly, what is a defeating condition for a given practical generalization is not a defeating condition for its alethic counterpart. A generalization of the form 'should (! E, ⊢F; ! G)' may have, as a defeating condition, 'E*'; that is to say, consistently with the truth of this generalization, it may be true that 'should (! E & ! E*, ⊢F; ! G*)' where 'G*' is inconsistent with 'G'. But since, in the alethic counterpart generalization 'should (⊢ F, ⊢G; ⊢E)', 'E' does not occur in the antecedent, 'E*' cannot be a defeating end p.92 condition for this generalization. And, since liability to defeat by a certain range of defeating conditions is essential to the role which acceptability generalizations play in reasoning, this difference between a practical generalization and its alethic counterpart is sufficient to eliminate the reducibility of the former to the latter. To return to the main theme of this section. If, without further ado, we were to accept at this point the suggestion that 'should (! E, ⊢F; ! G)' is true just in case 'should (⊢ F, ⊢G; ⊢E)' is true, we should be accepting it simply on the basis of intuition (including, of course, linguistic or logical intuition under the head of 'intuition'). If the suggestion is correct then we should attain, at the same time, a stronger assurance that it is correct and a better theoretical understanding of the alethic and practical acceptability, if we could show why it is correct by deriving it from some general principle(s). Kant, in fact, for reasons not unlike these, sought to show the validity of a different but fairly closely related Technical Imperative by just such a method. The form which he selects is one which, in my terms, would be represented by "It is fully acceptable, given let it be that B, that let it be that A" or "It is necessary, given let it be that B, that let it be that A". Applying this to the one fully stated technical imperative given in Grundlegung, we get Kant’s hypothetical which is of the type Strawson calls ‘variable,’ formal, ‘generic,’ or ‘generic.’ Kant: “It is necessary, given let it be that one bisect a line on an unerring principle, that let it be that I draw from its extremities two intersecting arcs". Call this statement, (α). Though he does not express himself very clearly, I am certain that his claim is that this imperative is validated in virtue of the fact that it is, analytically, a consequence of an indicative statement which is true and, in the present context, unproblematic, namely, the statement vouched for by geometry, that if one bisects a line on an unerring principle, then one does so only as a result of having drawn from its extremities two intersecting arcs. Call this statement, (β). His argument seems to be expressible as follows. (1) It is analytic that he who wills the end (so far as reason decides his conduct), wills the indispensable means thereto. (2) So it is analytic that (so far as one is rational) if one wills that A, and judges that if A, then A as a result of B, then one wills that B. end p.93 (3) So it is analytic that (so far as one is rational) if one judges that if A, then A as a result of B, then if one wills that A then one wills that B. (4) So it is analytic that, if it is true that if A, then A as a result of B, then if let it be that A, then it must be that let it be that B. From which, by substitution, we derive (5): it is analytic that if β then α. Now it seems to me to be meritorious, on Kant's part, first that he saw a need to justify hypothetical imperatives of this sort, which it is only too easy to take for granted, and second that he invoked the principle that "he who wills the end, wills the means"; intuitively, this invocation seems right. Unfortunately, however, the step from (3) to (4) seems open to dispute on two different counts. (1) It looks as if an unwarranted 'must' has appeared in the consequent of the conditional which is claimed, in (4), as analytic; the most that, to all appearances, could be claimed as being true of the antecedent is that 'if let it be that A then let it be that B'. (2) (Perhaps more serious.) It is by no means clear by what right the psychological verbs 'judge' and 'will', which appear in (3), are omitted in (4); how does an (alleged) analytic connection between (i) judging that if A, A as a result of B and (ii) its being the case that if one wills that A then one wills that B yield an analytic connection between (i) it's being the case that if A, A as a result of B and (ii) the 'proposition' that if let it be that A then let it be that B? Can the presence in (3) of the phrase "in so far as one is rational" legitimize this step? I do not know what remedy to propose for the first of these two difficulties; but I will attempt a reconstruction of Kant's line of argument which might provide relief from the second. It might, indeed, even be an expansion of Kant's actual thinking; but whether or not this is so, I am a very long way from being confident in its adequacy. Back to Strawson. First example:  ‘lf ice is left in the sun, it melts.’Or “If apple goes up, apple goes down.” – Newton, “Principia Mathematica.” “If ice is left in the sun, it, viz. ice, melts.” Strawson’s second example of a formal, variable, generic, or general ‘if’ ‘If the side of a triangle is produced, the exterior angle is equal to the sum of the two interior and opposite angles.’ Cf. Kant: “If a line on an unerring principle is bisected, two intersecting arcs are drawn from its extremities.” Synthetical propositions must no doubt be employed in defining the means to a proposed end; but they do not concern the principle, the act of the will, but the object and its realization. E.g., that in order to bisect a line on an unerring principle I must draw from its extremities two intersecting arcs; this no doubt is taught by mathematics only in synthetical propositions; but if I know that it is only by this process that the intended operation can be performed, then to say that, if I fully will the operation, I also will the action required for it, is an analytical proposition; for it is one and the same thing to conceive something as an effect which I can produce in a certain way, and to conceive myself as acting in this way. Strawson’s third example: ‘If a child is very strictly disciplined in the nursery, it, viz. the child, that should be seen but not heard, will develop aggressive tendencies in adult life.’ To a statement made by the use of a sentence such as these there corresponds no single pair of statements which are, respectively, its antecedent and consequent.  On the other hand, for every such statement there is an indefinite number of NON-general, or not generic, hypothetical statements which might be called exemplifications, applications, of the variable hypothetical; e.g., a statement made by the use of the sentence ‘If THIS piece of ice is left in the sun, it, viz. this piece, melts.’Strawson, about to finish his section on “ ‘⊃’ and ‘if’,” – the expression, ‘’ ⊃’ and ‘if’” only occurs in the “Table of Contents,” on p. viii, not in the body of the essay, as found redundant – it is also the same title Strawson used for his essay which circulated (or ‘made the rounds’) soon after Grice delivered his attack on Strawson, and which Strawson had, first, the cheek to present it to PGRICE, and then, voiding the idea of a festschrift, reprint it in his own compilation of essays. -- from which Grice extracted the quote for “Prolegomena,” notes that there are two ‘relatively uncommon uses of ‘if.’‘If he felt embarrassed, he showed no signs of it.’It is this example that Grice is having in mind in the fourth lecture on ‘indicative conditionals.’ “he didn’t show it.”Grice is giving an instantiation of an IMPLICIT, or as he prefers, ‘contextual,’ cancellation of the implicaturum of ‘if.’  He does this to show that even if the implicaturum of ‘if’ is a ‘generalised,’ not ‘generic,’ or ‘general,’ one, it need not obtain or be present in every PARTICULAR case. “That is why I use the weakened form ‘generalISED, not general. It’s all ceteris paribus always with me).” The example Grice gives corresponds to the one Strawson listed as one of the two ‘relatively uncommon’ uses of ‘if.’ By sticking with the biscuit conditional, Grice is showing Strawson that this use is ‘relatively uncommon’ because it is absolutely otiose!  “If he was surprised, he didn’t show it.”Or cf. AustinIf you are hungry, there are. Variants by Grice on his own example:“If Strawson was surprised, he did not show it.”“If he was surprised, it is not the case that Strawson showed it, viz. that he was surprised.”Grice (on the phone with Strawson’s friend) in front of Strawson – present tense version:“If he IS surprised, it is not th case that he, Strawson, is showing it, viz. the clause that he is surprised. Are you implicating he SHOULD?”and a second group:‘If Rembrandt passes the exam at the Koninklijke Academie van Beeldende Kunsten, I am a Dutchman.’‘If the Mad Hatter is not mad, I'll eat my hat.’(as opposed to ‘If the Mad Hatter IS mad, I’ll eat HIS hat.’)Hats were made at Oxford in a previous generation, by mad ‘hatters.’ “To eat one’s hat,” at Oxford, became synonymous with ‘I’ll poison myself and die.’ The reason of the prevalence of Oxonian ‘lunatic’ hatters is chemical. Strawson is referring to what he calls an ‘old wives’ tale’As every grandmother at Oxford knows, the chemicals used in hat-making include mercurious nitrate, which is used in ‘curing’ felt. Now exposure to the mercury vapours cause mercury poisoning. Or, to use an ‘if’: “If Kant is exposed to mercury vapour, Kant gets poisoned. A poisoned victim  develops a severe and uncontrollable muscular tremors and twitching limbs, distorted vision and confused speech, hallucinations and psychosis, if not death. For a time, it was at Oxford believed that a wearer of a hat could similarly die, especially by eating the felt containing the mercurial nitrate. The sufficient and necessary condition of the truth of a statement made by “If he was surprised, it is not the case that Strawson showed it, viz. that he was surprised” is that it is not the case that Strawson showed that he was surprised. The antecedent is otiose. Cf. “If you are hungry, there are biscuits in the cupboard.’ Austin used to expand the otiose antecedent further, ‘If you are hungry – AND EVEN IF YOU ARE NOT – there are biscuits in the cupboard,” just in case someone was ignorant of Grice’s principle of conversational helpfulness. Consequently, Strawson claims that such a statement cannot be treated either as a standard hypothetical or as a material implication. This is funny because by the time Grice is criticizing Strawson he does take “If Strawson is surprised, it is not the case that he is showing it, viz. that he is surprised.” But when it comes to “Touch the beast and it will bite you” he is ready to say that here we do not have a case of ‘conjunction.’Why? Stanford.Stanford is the answer.Grice had prepared the text to deliver at Stanford, of all places. Surely, AT STANFORD, you don’t want to treat your addressee idiotically. What Grice means is:“Now let us consider ‘Touch the beast and it will bite you.’ Symbolise it: !p et !q. Turn it into the indicative: You tell your love and love bites you (variant on William Blake).” Grice: “One may object to the  use of ‘p.q’ on Whiteheadian grounds. Blue-collared practitioners of the sciences will usually proclaim that they do not care about the ‘realisability’ of this or that operator. In fact, the very noun, ‘realisability,’ irritated me so that I coined non-detachability as a balance. The blue-collared scientist will say that ‘and’ is really Polish, and should be PRE-FIXED as an “if,” or condition, or proviso. So that the conjunction becomes “Provided you tell your love, love bites you.”Strawson gives his reason about the ‘implicaturum’ of what P. L. Gardiner called the ‘dutchman’ ‘if,’ after G. F. Stout’s “ ‘hat-eating’ if.”  Examples of the second kind are sometimes erroneously treated as evidence that Philo was not crazy, and that ‘if’ does, after all, behave somewhat as ‘⊃’ behaves.  Boethius appropriately comments: “Philo had two drawbacks against his favour. He had no drawing board, and he couldn’t write. Therefore he never symbolized, other than ‘via verba,’  his ‘ei’ utterance, “If it is day, it is night,” which he held to be true “at night only.”” Strawson echoes Grice. The evidence for this conversational explanation of the oddity of the ‘dutcham’ if, as called by Gardiner, and the ‘hat-eating’ if, as called by Stout, is, presumably, the facts, first, that the relation between antecedent and consequent is non-Kantian. Recall that Kant has a ‘Funktion’ which, after Aristotle’s ‘pros ti,’ and Boethius’s ‘relatio,’ he called ‘Relation’ where he considers the HYPOTHETICAL. Kant expands in section 8.5. “In the hypothetical, ‘If God exists, I’ll eat my hat,’ existence is no predicate.”Strawson appeals to a second, “more convincing,” fact, viz. that the consequent is obviously not – in the Dutchman ‘if,’ or not to be, in the ‘hat-eating’ if, fulfilled, or true.Grice’s passing for a Dutchman and sitting for an exam at the Koninklijke Academie van Beeldende Kunsten, hardly makes him a Dutchman.Dickens was well aware of the idiocy of people blaming hatters for the increases of deaths at Oxford. He would often expand the consequent in a way that turned it “almost a Wittgensteinian ‘contradiction’” (“The Cricket in the House, vii). “If the Hatter is not mad, I will eat my hat, with my head in it.”Grice comments: “While it is analytic that you see with your eyes, it is not analytic that you eat with your mouth. And one can imagine Dickens’s mouth to be situated in his right hand. Therefore, on realizing that the mad hatter is not mad, Dickens is allowing for it to be the case that he shall eat his hat, with his head in it. Since not everybody may be aware of the position of Dickens’s mouth, I shall not allot this common-ground status.”Strawson gives a third Griciean fact.“The intention of the emissor, by uttering a ‘consequens falsum’ that renders the ‘conditionalis’ ‘verum’ only if the ‘antecedens’ is ‘falsum, is an emphatic, indeed, rude, gesture, with a gratuitious nod to Philo, to the conviction that the antecedens is not fulfilled either. The emissor is further abiding by what Grice calls the ‘principle of truth,’ for the emissor would rather see himself dead than uttering a falsehood, even if he has to fill the conversational space with idiocies like ‘dutchman-being’ and ‘hat-eating.’ The fourth Griceian fact is obviously Modus Tollendo Tollens, viz. that  “(p ⊃ q) . ~q” entails “~p,” or rather, to avoid the metalanguage (Grice’s Bootlace: Don’t use a metalanguage: you can only implicate that your object-language is not objectual.”), “[(p ⊃ q) . ~ q] ⊃ ~ p.”At this point, Strawson reminisces: “I was slightly surprised that on my first tutorial with Grice, he gave me “What the Tortoise Said To Achilles,” with the hint, which I later took as a defeasible implicaturum, “See if you can resolve this!” ACHILLEs had overtaken the Tortoise, and had seated himself comfortably on its back. "So you've got to the end of our race-course?" said the Tortoise. "Even though it does consist of an infinite series of distances ? I thought some wiseacre or other had proved that the thing couldnl't be doiie ? " " It can be done," said Achilles. " It has been done! Solvitur ambulando. You see the distances were constaiitly diminishing; and so-" "But if they had beenl constantly increasing?" the Tortoise interrupted. "How then?" "Then I shouldn't be here," Achilles modestly replied; "and you would have got several times round the world, by this time! " "You flatter me-flatten, I mean," said the Tortoise; "for you are a heavy weight, and no mistake! Well now, would you like to hear of a race-course, that most people fancy they can get to the end of in two or three steps, while it really consists of an infinite number of distances, each one longer than the previous one? " "Very much indeed !" said the Grecian warrior, as he drew from his helmet (few Grecian warriors possessed pockets in those days) an enormous note-book and a pencil. "Proceed! And speak slowly, please! Shorthand isn't invented yet !" "That beautiful First Proposition of Euclid! " the Tortoise miurmured dreamily. "You admire Euclid?" "Passionately! So far, at least, as one can admire a treatise that wo'n't be published for some centuries to come ! " "Well, now, let's take a little bit of the argument in that First Proposition-just two steps, and the conclusion drawn from them. Kindly enter them in your note-book. And in order to refer to them conveniently, let's call them A, B, and Z:- (A) Things that are equal to the same are equal to each other. (B) The two sides of this Triangle are things that are equal to the same. (Z) The two sides of this Triangle are equal to each other. Readers of Euclid will grant, I suppose, that Z follows logically from A and B, so that any one who accepts A and B as true, must accept Z as true?" " Undoubtedly! The youngest child in a High School-as. soon as High Schools are invented, which will not be till some two thousand years later-will grant that." " And if some reader had not yet accepted A and B as true, he might still accept the sequence as a valid one, I suppose?" NOTES. 279 "No doubt such a reader might exist. He might say 'I accept as true the Hypothetical Proposition that, if A and B be true, Z must be true; but, I don't accept A and B as true.' Such a reader would do wisely in abandoning Euclid, and taking to football." " And might there not also be some reader who would say ' I accept A anld B as true, but I don't accept the Hypothetical'?" "Certainly there might. He, also, had better take to football." "And neither of these readers," the Tortoise continued, "is as yet under any logical necessity to accept Z as true?" "Quite so," Achilles assented. "Well, now, I want you to consider me as a reader of the second kind, and to force me, logically, to accept Z as true." " A tortoise playing football would be--" Achilles was beginning " -an anomaly, of course," the Tortoise hastily interrupted. "Don't wander from the point. Let's have Z first, and football afterwards !" " I'm to force you to accept Z, am I?" Achilles said musingly. "And your present position is that you accept A and B, but you don't accept the Hypothetical-" " Let's call it C," said the Tortoise. "-but you don't accept (C) If A and B are true, Z must be true." "That is my present position," said the Tortoise. "Then I must ask you to accept C." - "I'll do so," said the Tortoise, "as soon as you've entered it in that note-book of yours. What else have you got in it?" " Only a few memoranda," said Achilles, nervously fluttering the leaves: "a few memoranda of-of the battles in which I have distinguished myself!" "Plenty of blank leaves, I see !" the Tortoise cheerily remarked. "We shall need them all !" (Achilles shuddered.) "Now write as I dictate: (A) Things that are equal to the same are equal to each other. (B) The two sides of this Triangle are things that are equal to the same. (C) If A and B are true, Z must be true. (Z) The two sides of this Triangle are equal to each other." " You should call it D, not Z," said Achilles. " It comes next to the other three. If you accept A and B and C, you must accept Z." "And why must I?" "Because it follows logically from them. If A and B and C are true, Z must be true. You don't dispute that, I imagine ?" "If A and B and C are true, Z must be true," the Tortoise thoughtfully repeated. " That's another Hypothetical, isn't it? And, if I failed to see its truth, I might accept A and B and C, and still not accept Z, mightn't I?" "You might," the candid hero admitted; "though such obtuseness would certainly be phenomenal. Still, the event is possible. So I must ask you to grant one more Hypothetical." " Very good. I'm quite willing to grant it, as soon as you've written it down. We will call it (D) If A and B and C are true, Z must be true. Have you entered that in your note-book ? " " I have! " Achilles joyfully exclaimed, as he ran the pencil into its sheath. "And at last we've got to the end of this ideal race-course! Now that you accept A and B and C and D, of course you accept Z." " Do I ? " said the Tortoise innocently. " Let's make that quite clear. I accept A and B and C and D. Suppose I still refused to accept Z? " 280 NOTES. " Then Logic would take you by the throat, and force you to do it !" Achilles triumphantly replied. "Logic would tell you 'You ca'n't help yourself. Now that you've accepted A and B and C and D, you mvust accept Z!' So you've no choice, you see." "Whatever Logic is good enough to tell me is worth writing down," said the Tortoise. " So enter it in your book, please. We will call it (E) If A and B and C and Dare true, Zmust be true. Until I've granted that, of course I needn't grant Z. So it's quite a necessary step, you see?" "I see," said Achilles; and there was a touch of sadness in his tone. Here the narrator, having pressing business at the Bank, was obliged to leave the happy pair, and did not again pass the spot until some months afterwards. When he did so, Achilles was still seated on the back of the much-enduring Tortoise, and was writing in his note-book, which appeared to be nearly full. The Tortoise was saying " Have you got that last step written down ? Unless I've lost count, that makes a thousand and one. There are several millions more to come. And would you mind, as a personal favour, considering what a lot of instruction this colloquy of ours will provide for the Logicians of the Nineteenth Century-would you mnind adopting a pun that my cousin the Mock-Turtle will then make, and allowing yourself to be re-named Taught- Us ?" "As you please !" replied the weary warrior, in the hollow tones of despair, as he buried his face in his hands. " Provided that you, for your part, will adopt a pun the Mock-Turtle never made, and allow yourself to be re-named A Kill-Ease !"Strawon protests:“But this is a strange piece of logic.”Grice corrects: “Piece – you mean ‘piece’ simpliciter.”“But what do you protest that much!?”“Well, it seems that, on any possible interpretation, “if p, q” has, in respect of modus tollendo tollens the same powers as ‘p ⊃ q.’“And it is just these  powers that you, and Cook Wilson before you, are jokingly (or fantastically) exploiting!”“Fantastically?” “You call Cook Wilson ‘fantastical’? You can call me exploitative.’Strawson: “It is the absence of Kantian ‘Relation,’ Boethius’s ‘relatio,’ Aristotle’s ‘pros ti,’ referred to in that makes both Stout’s hat-eating if and Gardiner’s dutchman if quirks (as per Sir Randolph Quirk, another Manx, like Quine), a verbal or conversational flourish, an otiosity, alla Albritton, an odd, call it Philonian, use of ‘if.’ If a hypothetical statement IS, as Grice, after Philo, claims, is what Whitehead and Russell have as a ‘material’ implication, the statements would be not a quirkish oddity, but a linguistic sobriety and a simple truth. Or rather they are each, the dutchman  if and the hat-eating if, each a ‘quirkish oddity’ BECAUSE each is a simple, sober, truth. “Recall my adage,” Grice reminded Strawson, “Obscurely baffling, but Hegelianly true!”Strawson notes, as a final commentary on the relevant section, that ‘if’  can be employed PERFORMATORILY, which will have Grice finding his topic for the Kant lectures at Stanford: “must” is univocal in “Apples must fall,” and “You must not lie.”An ‘if’ is used ‘performatorily’ when it is used not simply in making this or that statement, but in, e.g., making a provisional announcement of an intention. Strawson’s example:“If it rains, I shall stay at home.”Grice corrected:“*I* *will* stay at home. *YOU* *shall.*”“His quadruple implicatura never ceased to amaze me.”Grice will take this up later in ‘Ifs and cans.’“If I can, I intend to climb Mt Everest on hands and knees, if I may disimplicate that to Davidson.”This hich, like an unconditional announcement of intention, Strawson “would rather not” call ‘truly true’ or ‘falsely false.’ “I would rather describe it in some other way – Griceian perhaps.” “A quessertion, not to be iterated.”“If the man who utters the quoted sentence leaves home in spite of the rain, we do not say that what he said was false, though we might say that he lied (never really intended to stay in) ; or that he changed his mind – which, Strawson adds, “is a form of lying to your former self.” “I agreed with you!” Grice screamed from the other side of the Quadrangle!Strawson notes: “There are further uses of ‘if’ which I shall not discuss.”This is a pantomime for Austin (Strawson’s letter to Grice, “Austin wants me to go through the dictionary with ‘if.’ Can you believe it, Grice, that the OED has NINE big pages on it?! And the sad thing is that Austin has already did ‘if’ in “Ifs and cans.” Why is he always telling OTHERS what to do?”Strawson’s Q. E. D.: “The safest way to read the material implication sign is, perhaps, ‘not both … and not …,” and avoid the ‘doubt’ altogether. (NB: “Mr. H. P. Grice, from whom I never ceased to learn about logic since he was my tutor for my Logic paper in my PPE at St. John’s back in the day, illustrates me that ‘if’ in Frisian means ‘doubt.’ And he adds, “Bread, butter, green cheese; very good English, very good Friese!”. GROUP C – “Performatory” theories – descriptive, quasi-descriptive, prescriptive – examples not lettered.EXAMPLE I: Strawson on ‘true’ in Analysis.EXAMPLE II: Austin on ‘know’ EXAMPLE III: Hare on ‘good.’EXPLICITLY CONVEYED: if p, qIMPLICITLY CONVEYED: p is the consequensCANCELLATION: “I know perfectly well where your wife is, but all I’ll say is that if she is not in kitchen she is in the bedroom.”Next would be to consider uses of ‘implication’ in the essay on the ‘indicative conditional.’ We should remember that the titling came out in 1987. The lecture circulated without a title for twenty years. And in fact, it is about ‘indicative conditional’ AND MORE BESIDES, including Cook Wilson, if that’s a plus. Grice states the indirectness condition in two terms:One in the obviously false terms “q is INFERRABLE, that’s the word Grice uses, from p”The other one is in terms of truth-value assignment:The emissor has NON-TRUTH-FUNCTIONAL GROUNDS for the emissum, ‘if p, q’. In Grice’s parlance: “Grounds for ACCEPTING “p ⊃ q.”This way Grice chooses is controversial in that usually he holds ‘accept’ as followed by the ‘that’-clause. So ‘accepting ‘p ⊃ q’” is not clear in that respect. A rephrase would be, accepting that the emissor is in a position to emit, ‘if p, q’ provided that what he EXPLICITLY CONVEYS by that is what is explicitly conveyed by the Philonian ‘if,’ in other words, that the emissor is explicitly conveying that it is the case of p or it is not the case of q, or that it is not the case that a situation obtains such that it is the case that p and it is not the case that q.“p ⊃ q” is F only in the third row. It is no wonder that Grice says that the use-mention was only used correctly ONCE.For Grice freely uses ‘the proposition that p ⊃ q.’ But this may be licensed because it was meant as for ‘oral delivery.’ THE FIRST INSTANTIATION GRICE GIVES (WoW:58) is“If Smith is in London, he, viz. Smith, is attending the meeting.”Grice goes on (WoW:59) to give FIVE alternatives to the ‘if’ utterance, NOT using ‘if.’ For the first four, he notes that he fells the ‘implicaturum’ of ‘indirectness’ seems ‘persistent.’On WoW:59, Grice refers to Strawson as a ‘strong theorist,’ and himself as a ‘weak theorist,’ i. e. an Occamist. Grice gives a truth-table or the ‘appropriate truth table,’ and its formulation, and notes that he can still detect the indirectness condition implication. Grice challenges Strawson. How is one to learn that what one conveys by the scenario formulated in the truth-table for the pair “Smith is in London” and “Smith is attending the meeting” – without using ‘if’ because this is Grice’s exercise in detachment – is WEAKER than what one would convey by “If Smith is in London, he, viz. Smith, is attending the meeting”?This sort of rhetorical questions – “Of course he can’t” are a bit insidious. Grice failed to give Strawson a copy of the thing. And Strawson is then invited to collaborate with P. G. R. I. C. E., so he submits a rather vague “If and ⊃,” getting the rebuke by Grice’s friend Bennett – “Strawson could at least say that Grice’s views were published in three different loci.” BUT: Strawson compiled that essay in 1968. And Strawson was NOT relying on a specific essay by Grice, but on his memory of the general manoeuvre. Grice had been lecturing on ‘if’ before at Oxford, in seminars entitled “Logic and Convesation.” But surely at Oxford you are not supposed to ‘air’ your seminar views. Outside Oxford it might be different. It shoud not!And surely knowing Grice, why would *GRICE* provide the input to Strawson. For Grice, philosophy is very personal, and while Grice might have thought that Sir Peter was slightly interested in what his former tutor would say about ‘if,’ it would be inappropriate of the tutor to overwhelm the tutee, or keep informing the tutee how wrong he is. For a tutor, once a tutee, always a tutee. On WoW:59, Grice provides the FIRST CANCELLATION of an ‘if,’ and changes it slightly from the one on p. 58. The ‘if’ now becomesIf Smith is in the library, he, viz. Smith, is working.’In Wiltshire:“If Smith is in the swimming-pool library, he, viz. Smith, is swimming.”THE CANCELLATION GOES by ‘opting out’:“I know just where Smith is and what he, viz. Smith, is doing, but all I will tell you is that if he is in the library he is working.”Grice had to keep adding his ‘vizes’ – viz. Smith – because of the insidious contextualists – some of them philosophical!“What do you mean ‘he,’ – are you sure you are keeping the denotatum constant?”Grice is challenging Strawson’s ‘uncertainty and disbelief.’No one would be surprised if Grice’s basis for his saying “I know just where Smith is and what he, viz. Smith, is doing, but all I will tell you is that if he is in the library, he is working” is that Grice has just looked in the library and found Smith working. So, Grice IS uttering “If Smith is in the library, he is working” WHEN THE INDIRECT (strong) condition ceteris-paribus carried by what Grice ceteris paribus IMPLIES by uttering “If Smith is in the library, Smith is working.”The situation is a bit of the blue, because Grice presents it on purpose as UNVOLUNTEERED. The ‘communication-function’ does the trick. GRICE THEN GIVES (between pages WoW: 59 and 60) TWO IMPLICIT cancellations of an implicaturum, or, to avoid the alliteration, ‘contextual’ cancellation. Note incidentally that Grice is aware of the explicit/implicit when he calls the cancellation, first, EXPLICIT, and then contextual. By ‘explicit,’ he means, ‘conveying explicitly’ in a way that commits you. THE THIRD INSTANTIATION refers to this in what he calls a ‘logical’ puzzle, which may be a bit question-begging, cf. ‘appropriate truth-table.’ For Strawson would say that Grice is using ‘if’ as a conscript, when it’s a civil. “If Smith has black, Mrs. Smith has black.”Grice refers to ‘truth-table definition’ OR STIPULATION. Note that the horseshoe is an inverted “C” for ‘contentum.’F. Cajori, “A history of mathematical notations,” SYMBOLS IN MATHEMATICAL LOGIC, §667-on : [§674] “A theory of the ‘meccanisme du raisonnement’ is offered by J. D. Gergonne in his “Essai de dialectique rationnelle.”In Gergonne’s “Essai,” “H” stands for complete logical disjunction, X” for logical product, “I” for "identity," [cf. Grize on izzing] “C” for "contains," and "Ɔ (inverted C)" for "is contained in."  [§685] Gergonne is using the Latinate, contineoIn rhet., the neuter substantive “contĭnens” is rendered as  “that on which something rests or depends, the chief point, hinge: “causae,” Cic. Part. Or. 29, 103; id. Top. 25, 95: “intuendum videtur, quid sit quaestio, ratio, judicatio, continens, vel ut alii vocant, firmamentum,” Quint. 3, 11, 1; cf. id. ib. § 18 sqq.—Adv.: contĭnen-ter . So it is a natural evolution in matters of implication. while Giusberti (“Materiale per studio,” 31) always reads “pro constanti,” the MSS occasionally has the pretty Griciean “precontenti,” from “prae” and “contenti.” Cf. Quine, “If my father was a bachelor, he was male. And I can say that, because ‘male’ is CONTAINED in ‘bachelor.’”E. Schröder, in his “Vorlesungen über die Algebra der Logik,” [§690]  Leipzig, uses “⊂” for "untergeordnet”, roughly, “is included in,” and the inverted “⊃” for the passive voice, "übergeordnet,” or includes.  Some additional symbols are introduced by Peano into Number 2 of Volume II of his influential “Formulaire.” Thus "ɔ" becomes ⊃. By “p.⊃ x ... z. q” is expressed “from p one DEDUCES, whatever x ... z may be, and q."  In “Il calcolo geometrico,” – “according to the Ausdehnungslehre of H. Grassmann, preceded by the operations of deductive logic,” Peano stresses the duality of interpretations of “p.⊃ x ... z. q” in terms of classes and propositions. “We shall indicate [the universal affirmative proposition] by the expression  A < B, or B > A,  which can be read "every A is a B," or "the class B CONTAINS A." [...]  Hence, if a,b,... are CONDITIONAL propositions, we have:  a < b, or b > a, ‘says’ that "the class defined by the condition a is part of that defined by b," or [...] "b is a CONSEQUENCE of a," "if a is true, b is true."  In Peano’s “Arithmetices principia: nova methodo exposita,” we have:  “II. Propositions.” “The sign “C” means is a consequence of [“est consequentia.” Thus b C a is read b is a consequence of the proposition a.” “The sign “Ɔ” means one deduces [DEDUCITUR]; thus “a Ɔ b” ‘means’ the same as b C a. [...]  IV. Classes “The sign Ɔ ‘means’ is contained in. Thus a Ɔ b means class a is contained in class b.  a, b ∈ K Ɔ (a Ɔ b) :=: (x)(x ∈ a Ɔ x ∈ b).  In his “Formulaire,” Peano writes:  “Soient a et b des Cls. a ⊃ b signifie "tout a est b".  Soient p et q des propositions contenant une variable x; p ⊃x q, signifie "de p on déduit, quel que soit x, la q", c'est-à-dire: "les x qui satisfont à la condition p satisferont aussi à la q".  Russell criticizes Peano’s dualism in “The Principles of mathematics,” §13. “The subject of Symbolic Logic consists of three parts, the calculus of propositions, the calculus of classes and the calculus of relations. Between the first two, there is, within limits, a certain parallelism, which arises as follows: In any symbolic expression, the letters may be interpreted as classes or as propositions, and the relation of inclusion in the one case may be replaced by that of formal implication in the other.  A great deal has been made of this duality, and in the later editions of his “Formulaire,” Peano appears to have sacrificed logical precision to its preservation. But, as a matter of fact, there are many ways in which the calculus of propositions differs from that of classes.” Whiehead and Russell borrow the basic logical symbolism from Peano, but they freed it from the "dual" interpretation.  Thus, Whitehead and Russell adopt Schröder's ⊂ for class inclusion:  a ⊂ b :=: (x)(x ∈ a Ɔ x ∈ b) Df.  and restricted the use of the "horseshoe" ⊃ to the connective "if’: “p⊃q.’ Whitehead’s and Russell’s decision isobvious, if we consider the following example from Cesare Burali-Forti, “Logica Matematica,” a Ɔ b . b Ɔ c : Ɔ : a Ɔ c [...]  The first, second and fourth [occurrences] of the sign Ɔ mean is contained, the third one means one deduces.So the horseshoe is actually an inverted “C” meant to read “contentum” or “consequens” (“consequutum”). Active Nominal Forms Infinitive: implicā́re Present participle: implicāns; implicántis Future participle: implicītúrus; implicātúrus Gerund: implicándum Gerundive: implicándus  Passive Nominal Forms Infinitive: implicā́re Perfect participle: implicī́tum; implicā́tumGRICE’s second implicit or contextual cancellation does not involve a ‘logical puzzle’ but bridge – and it’s his fourth instantiation:“If I have a red king, I also have a black king.” – to announce to your competititve opponents upon inquiry a bid of five no trumps. Cf. Alice, “The red Queen” which is a chess queen, as opposed to the white queen. After a precis, he gives a FIFTH instantiation to prove that ‘if’ is always EXPLICITLY cancellable.WoW:60“If you put that bit of sugar in water, it will dissolve, though so far as I know there can be no way of knowing in advance that this will happen.”This is complex. The cancellation turns the ‘if p, q’ into a ‘guess,’ in which case it is odd that the emissor would be guessing and yet be being so fortunate as to make such a good guess. At the end of page 60, Grice gives THREE FURTHER instantations which are both of philosophical importance and a pose a problem to such a strong theorist as Strawson.The first of the trio is:“If the Australians win the first Test, they will win the series, you mark my words.”The second of the trio is:“Perhaps if he comes, he will be in a good mood.”The third in the trio is:“See that, if he comes, he gets his money.”Grice’s point is that in the three, the implicaturum is cancelled. So the strong theorist has to modify the thesis ‘a sub-primary case of a sub-primary use of ‘if’ is…” which seems like a heavy penalty for the strong theorist. For Grice, the strong theorist is attaching the implicaturum to the ‘meaning’ of ‘if,’ where, if attached at all, should attach to some mode-marker, such as ‘probably,’ which may be contextual. On p. 61 he is finding play and using ‘logically weaker’ for the first time, i. e. in terms of entailment. If it is logically weaker, it is less informative. “To deny that p, or to assert that q.”Grice notes it’s ceteris paribus.“Provided it would be worth contributing with the ‘more informative’ move (“why deny p? Why assert q?) While the presumption that one is interested in the truth-values of at least p or q, this is ceteris paribus. A philosopher may just be interested in “if p, q” for the sake of exploring the range of the relation between p and q, or the powers of p and q. On p. 62 he uses the phrase “non-truth functional” as applied not to grounds but to ‘evidence’: “non-truth-functional evidence.”Grice wants to say that emissor has implicated, in a cancellable way, that he has non-truth-functional evidence for “if p, q,” i. e. evidence that proceeds by his inability to utter “if p, q” on truth-functional grounds. The emissor is signaling that he is uttering “if p, q” because he cannot deny p, or that he cannot assert q(p ⊃ q) ≡ ((~p) v q)Back to the first instantiation“If Smith is in London, he, viz. Smith is attending the meeting there, viz. in London”I IMPLICATE, in a cancellable way, that I have no evidence for “Smith is not in London”I IMPLICATE, in a cancellable way, that I have no evidence for “Smith is attending the lecture.On p. 61 he gives an example of an contextual cancellation to show that even if the implicaturum is a generalised one, it need not be present in every PARTICULAR case (hence the weakned form ‘generalISED, not general). “If he was surprised, he didn’t show it.”Or cf. AustinIf you are hungry, there are biscuits in the cupboard. Traditionalist Grice on the tranquil Elysium of philosophyĒlysĭum , ii, n., = Ἠλύσιον, the abode of the blest, I.Elysium, Verg. A. 5, 735 Serv.; 6, 542; 744 al.; cf. Heyne Verg. A. 6, 675 sq.; and ejusd. libri Exc. VIII. p. 1019 Wagn.—Hence, II. Ēlysĭus , a, um, adj., Elysian: “campi,” Verg. G. 1, 38; Tib. 1, 3, 58; Ov. Ib. 175; cf. “ager,” Mart. 10, 101: “plagae,” id. 6, 58: “domus,” Ov. M. 14, 111; cf. “sedes,” Luc. 3, 12: “Chaos,” Stat. Th. 4, 520: “rosae,” Prop. 4 (5), 7, 60. “puella,” i. e. Proserpine, Mart. 10, 24.—On p. 63, Grice uses ‘sense’ for the first time to apply to a Philonian ‘if p, q.’He is exploring that what Strawson would have as a ‘natural’ if, not an artificial ‘if’ like Philo’s, may have a sense that descends from the sense of the Philonian ‘if,’ as in Darwin’s descent of man. Grice then explores the ‘then’ in some formulations, ‘if p, then q’, and notes that Philo never used it, “ei” simpliciter – or the Romans, “si.”Grice plays with the otiosity of “if p, in that case q.”And then there’s one that Grice dismisses as ultra-otiose:“if p, then, in that case, viz. p., q.”Grice then explores ‘truth-functional’ now applied not to ‘evidence’ but to ‘confirmation.’“p or q” is said to be truth-functionally confirmable.While “p horseshoe q’ is of course truth-functionally confirmable.Grice has doubts that ‘if p, q’ may be regarded by Strawson as NOT being ‘truth-functionally confirmable.’ If would involve what he previously called a ‘metaphysical excrescence.’Grice then reverts to his bridge example“If I have a red king, I have a black king.”And provides three scenarios for a post-mortem truth-functional confirmability.For each of the three rowsNo red, no blackRed, no blackRed, blackWhich goes ditto for  the ‘logical’ puzzleIf Jones has black, Mrs. Jones has black. The next crop of instantiations come from PM, and begins on p. 64.He kept revising these notes. And by the time he was submitting the essay to the publisher, he gives up and kept the last (but not least, never latter) version. Grice uses the second-floor ‘disagree,’ and not an explicit ‘not.’ So is partially agreeing a form of disagreeing? In 1970, Conservative Heath won to Labour Wilson.He uses ‘validate’ – for ‘confirm’. ‘p v q’ is validated iff proved factually satisfactory.On p. 66 he expands“if p, q”as a triple disjunction of the three rows when ‘if p, q’ is true:“(not-p and not-q) or (not-p and q) or (p and q)”The only left out is “(p and not-q).”Grice gives an instantiation for [p et]q“The innings closed at 3:15, Smith no batting.”as opposed to“The inning close at 3:15, and Smith did not bat.”as displayed byp.qAfter using ‘or’ for elections he gives the first instantation with ‘if’:“If Wilson will not be prime minister, it will be Heath.”“If Wilson loses, he loses to Heath.”‘if’ is noncommutative – the only noncommutative of the three dyadic truth-functors he considers (‘and,’ ‘or’ and ‘if’).This means that there is a ‘semantic’ emphasis here.There is a distinction between ‘p’ and ‘q’. In the case of ‘and’ and ‘or’ there is not, since ‘p and q’ iff ‘q and p’ and ‘p or q’ iff ‘q or p.’The distinction is expressed in terms of truth-sufficiency and false-sufficiency.The antecedent or protasis, ‘p’ is FALSE-SUFFICIENT for the TRUTH of ‘if p, q.’The apodosis is TRUE-sufficient for the truth of ‘if p, q.’On p. 67 he raises three questions.FIRST QUESTIONHe is trying to see ‘if’ as simpler:The three instantiations areIf Smith rings, the butler will let Smith inIt is not the case that Smith rings, or the butler will let Smith in.It is not the case both Smith rings and it is not the the butler will let Smith in. (Grice changes the tense, since the apodosis sometimes requires the future tense) (“Either Smith WILL RING…”)SECOND QUESTIONWhy did the Anglo-Saxons feel the need for ‘if’ – German ‘ob’? After all, if Whitehead and Russell are right, the Anglo-Saxons could have done with ‘not’ and ‘and,’ or indeed with ‘incompatible.’The reason is that ‘if’ is cognate with ‘doubt,’ but The Anglo-Saxons left the doubt across the North Sea. it originally from an oblique case of the substantive which may be rendered as "doubt,” and cognate with archaic German “iba,” which may be rendered as “condition, stipulation, doubt," Old Norse if "doubt, hesitation," modern Swedish jäf "exception, challenge")It’s all different with ‘ei’ and ‘si.’For sisī (orig. and ante-class. form seī ),I.conj. [from a pronominal stem = Gr. ἑ; Sanscr. sva-, self; cf. Corss. Ausspr. 1, 778; Georg Curtius Gr. Etym. 396], a conditional particle, if.As for “ei”εἰ , Att.-Ion. and Arc. (for εἰκ, v. infr. 11 ad init.), = Dor. and Aeol. αἰ, αἰκ (q. v.), Cypr.A.“ἤ” Inscr.Cypr.135.10 H., both εἰ and αἰ in Ep.:— Particle used interjectionally with imper. and to express a wish, but usu. either in conditions, if, or in indirect questions, whether. In the former use its regular negative is μή; in the latter, οὐ.THIRD QUESTION. Forgetting Grecian neutral apodosis and protasis, why did the Romans think that while ‘antecedens’ is a good Humeian rendition of ‘protasis,’ yet instead they chose for the Grecian Humeian ‘apodosis,’ the not necessarily Humeian ‘con-sequens,’ rather than mere ‘post-sequens’?The Latin terminology is antecedens and consequens, the ancestors and ... tothem the way the Greek grammatical termsή πρότασιs and ήαπόδοσιsBRADWARDINE: Note that a consequence is an argumentation made up of an antecedent and a consequent. He starts with the métiers.For ‘or’ he speaks of ‘semiotic economy’ (p. 69). Grice’s Unitarianism – unitary particle.If, like iff, is subordinating, but only if is non-commutative. Gazdar considers how many dyadic particles are possible and why such a small bunch is chosen. Grice did not even care, as Strawson did, to take care of ‘if and only if.’ Grice tells us the history behind the ‘nursery rhyme’ about Cock Robin. He learned it from his mother, Mabel Fenton, at Harborne. Clifton almost made it forget it! But he recovered in the New World, after reading from Colin Sharp that many of those nursery rhymes travelled “with the Mayflower.” "Who Killed Cock Robin" is an English nursery rhyme, which has been much used as a murder archetype[citation needed] in world culture. It has a Roud Folk Song Index number of 494.  Contents 1Lyrics 2Origin and meaning 3Notes 4 External links Lyrics[edit] The earliest record of the rhyme is in Tommy Thumb's Pretty Song Book, published c. 1744, which noted only the first four verses. The extended version given below was not printed until c. 1770.[1]  Who killed Cock Robin? I, said the Sparrow, with my bow and arrow, I killed Cock Robin. Who saw him die? I, said the Fly, with my little eye, I saw him die. Who caught his blood? I, said the Fish, with my little dish, I caught his blood. Who'll make the shroud? I, said the Beetle, with my thread and needle, I'll make the shroud. Who'll dig his grave? I, said the Owl, with my little trowel, I'll dig his grave. Who'll be the parson? I, said the Rook, with my little book, I'll be the parson. Who'll be the clerk? I, said the Lark, if it's not in the dark, I'll be the clerk. Who'll carry the link? I, said the Linnet, I'll fetch it in a minute, I'll carry the link. Who'll be chief mourner? I, said the Dove, I mourn for my love, I'll be chief mourner. Who'll carry the coffin? I, said the Kite, if it's not through the night, I'll carry the coffin. Who'll bear the pall? We, said the Wren, both the cock and the hen, We'll bear the pall. Who'll sing a psalm? I, said the Thrush, as she sat on a bush, I'll sing a psalm. Who'll toll the bell? I, said the Bull, because I can pull, I'll toll the bell. All the birds of the air fell a-sighing and a-sobbing, when they heard the bell toll for poor Cock Robin. The rhyme has often been reprinted with illustrations, as suitable reading material for small children.[citation needed] The rhyme also has an alternative ending, in which the sparrow who killed Cock Robin is hanged for his crime.[2] Several early versions picture a stocky, strong-billed bullfinch tolling the bell, which may have been the original intention of the rhyme.[3]  Origin and meaning[edit] Although the song was not recorded until the mid-eighteenth century,[4] there is some evidence that it is much older. The death of a robin by an arrow is depicted in a 15th-century stained glass window at Buckland Rectory, Gloucestershire,[5] and the rhyme is similar to a story, Phyllyp Sparowe, written by John Skelton about 1508.[1] The use of the rhyme 'owl' with 'shovel', could suggest that it was originally used in older middle English pronunciation.[1] Versions of the story appear to exist in other countries, including Germany.[1]  A number of the stories have been advanced to explain the meaning of the rhyme:  The rhyme records a mythological event, such as the death of the god Balder from Norse mythology,[1] or the ritual sacrifice of a king figure, as proposed by early folklorists as in the 'Cutty Wren' theory of a 'pagan survival'.[6][7] It is a parody of the death of King William II, who was killed by an arrow while hunting in the New Forest (Hampshire) in 1100, and who was known as William Rufus, meaning "red".[8] The rhyme is connected with the fall of Robert Walpole's government in 1742, since Robin is a diminutive form of Robert and the first printing is close to the time of the events mentioned.[1] All of these theories are based on perceived similarities in the text to legendary or historical events, or on the similarities of names. Peter Opie pointed out that an existing rhyme could have been adapted to fit the circumstances of political events in the eighteenth century.[1]  The theme of Cock Robin's death as well as the poem's distinctive cadence have become archetypes, much used in literary fiction and other works of art, from poems, to murder mysteries, to cartoons.[1]  Notes[edit] ^ Jump up to:a b c d e f g h I. Opie and P. Opie, The Oxford Dictionary of Nursery Rhymes (Oxford University Press, 1951, 2nd edn., 1997), pp. 130–3. ^ * Cock Robin at Project Gutenberg ^ M. C. Maloney, ed., English illustrated books for children: a descriptive companion to a selection from the Osborne Collection (Bodley Head, 1981), p. 31. ^ Lockwood, W. B. "The Marriage of the Robin and the Wren." Folklore 100.2 (1989): 237–239. ^ The gentry house that became the old rectory at Buckland has an impressive timbered hall that dates from the fifteenth century with two lights of contemporary stained glass in the west wall with the rebus of William Grafton and arms of Gloucester Abbey in one and the rising sun of Edward IV in the other light; birds in various attitudes hold scrolls "In Nomine Jesu"; none is reported transfixed by an arrow in Anthony Emery, Greater Medieval Houses of England and Wales, 1300–1500: Southern England, s.v. "Buckland Old Rectory, Gloucestershire", (Cambridge University Press, 2006), p. 80. ^ R. J. Stewart, Where is St. George? Pagan Imagery in English Folksong (1976). ^ B. Forbes, Make Merry in Step and Song: A Seasonal Treasury of Music, Mummer's Plays & Celebrations in the English Folk Tradition (Llewellyn Worldwide, 2009), p. 5. ^ J. Harrowven, The origins of rhymes, songs and sayings (Kaye & Ward, 1977), p. 92. External links[edit] Children's literature portal Death and Burial of Poor Cock Robin, by H. L. Stephens, from Project Gutenberg Death and Burial of Poor Cock Robin From the Collections at the Library of Congress Categories: Robert Walpole1744 songsFictional passerine birdsEnglish nursery rhymesSongwriter unknownEnglish folk songsEnglish children's songsTraditional children's songsSongs about birdsSongs about deathMurder balladsThe train from Oakland to Berkeley.Grice's aunt once visited him, and he picked her up at the Oakland Railway Station. On p. 74, Grice in terms of his aunt, mentions for the first time ‘premise’ and ‘conclusion.’On same p. for the record he uses ‘quality’ for affirmative, negative or infinite. On p. 74 he uses for the first time, with a point, the expression ‘conditional’ as attached to ‘if.’Oddly on the first line of p. 75, he uses ‘material conditional,’ which almost nobody does – except for a blue-collared practitioner of the sciences. ‘Material’ was first introduced by blue-collared Whitehead and Russell, practictioners of the sciences. They used ‘material’ as applied to ‘implication,’ to distinguish it, oddly, and unclassily, from ‘formal’ implication. It is only then he quotes Wilson verbatim in quotes“The question whether so and so is a case of a question whether such and such” This actually influenced Collingwood, and Grice is trying to tutor Strawson here once more!For the logic of question and answer has roots in the very philosophy that it was ... is John Cook Wilson, whose Statement and Inference can be regarded as the STATEMENT AND ITS RELATION TO THINKING AND APREHENSIOTHE DISTINCTION OF SUBJECT AND PREDICATE IN LOGIC AND GRAMMAR The influence of Strawson on Cook Wilson.“The building is the Bodleian.”As answer to“What is that building?”“Which building is the Bodleian”If the proposition is answer to first question, ‘that building’ is the subject, if the proposition is answer to second question, ‘the bodleian’ is the subject. Cf. “The exhibition was not visited by a bald king – of France, as it doesn’t happen.SUBJECT AS TOPICPREDICATE AS COMMENT.Cf. Grice, “The dog is a shaggy thig”What is shaggy?What is the dog?THIS DOG – Subject – TopicTHAT SHAGGY THING – Subject – occasionally, but usually Predicate, Comment.In fact, Wilson bases on StoutI am hungryWho is hungry?: subject IIs there anything amiss with you? ‘hungry’ is the subjectAre you really hungry? ‘am’ is the subject.Grice used to be a neo-Stoutian before he turned a neo-Prichardian so he knew. But perhaps Grice thought better of Cook Wilson. More of a philosopher. Stout seemed to have been seen as a blue-collared practioner of the SCIENCE of psychology, not philosophical psychology! Cf. Leicester-born B. Mayo, e: Magdalen, Lit. Hum. (Philosophy) under? on ‘if’ and Cook Wilson in Analysis.Other example by Wilson:“Glass is elastic.”Grice is motivated to defend Cook Wilson because Chomsky was criticizing him (via a student who had been at Oxford). [S]uppose instruction was being given in the properties of glass, and the instructor said ‘glass is elastic’, it would be natural to say that what was being talkedabout and thought about was ‘glass’, and that what was said of it was that it was elastic. Thus glass would be the subject and that it is elastic would be the predicate. (Cook Wilson 1926/1969, Vol. 1:117f.) What Cook Wilson discusses here is a categorical sentence. The next two quotes are concerned with an identificational sentence. [I]n the statement ‘glass is elastic’, if the matter of inquiry was elasticity and the question was what substances possessed the property of elasticity, glass, in accordance with the principle of the definition, would no longer be subject, and the kind of stress which fell upon ‘elastic’ when glass was the subject, would now be transferred to ‘glass’. [. . .] Thus the same form of words should be analyzed differently according as the words are the answer to one question or another. (Cook Wilson 1926/1969, Vol. 1:119f.) When the stress falls upon ‘glass’, in ‘glass is elastic’, there is no word in the sentence which denotes the actual subject elasticity; the word ‘elastic’ refers to what is already known of the subject, and glass, which has the stress, is the only word which refers to the supposed new fact in the nature of elasticity, that it is found in glass. Thus, according to the proposed formula, ‘glass’ would have to be the predicate. [. . .] Introduction and overview  But the ordinary analysis would never admit that ‘glass’ was the predicate in the given sentence and elasticity the subject. (Cook Wilson 1926/1969, Vol. 1:121)H. P. Grice knew that P. F. Strawson knew of J. C. Wilson  on “That building is the Bodleian” via Sellars’s criticism.There is  a  strong suggestion  in  Sellars' paper  that I would  have done better if I had stuck to Cook Wilson. This suggestion I want equally strongly to  repudiate.  Certainly  Cook  Wilson  draws  attention to  an interesting difference in ways  in which  items may appear in discourse. It may be roughly  expressed  as follows. When we  say Glass is elastic we may be talking  about glass or we may be talking about elasticity (and we may, in the relevant sense of  'about' be doing neither). We are talking about glass if  we are citing elasticity  as one of  the properties  of  glass, we  are talking  about  elasticity if  we  are  citing glass as one of  the substances which  are elastic.  Similarly when we  say Socrates is wise,  we  may be citing Socrates as an instance of  wisdom or wisdom as one of  the proper- ties  of  Socrates. And of  course  we  may be  doing neither  but, e.g., just imparting  miscellaneous  information.  Now  how,  if  at all,  could  this difference help me with my question? Would  it help at all, for example, if  it were plausible (which it is not) to say that we  were inevitably more interested in determining what properties  a given particular had,than in determining what particular had a given property? Wouldn't  this at least suggest that particulars were the natural subjects, in the sense of  subjects of  &erest?  Let me  answer this question  by the reminder  that what I have  to  do  is to establish  a connexion  between some formal  linguistic difference  and a  category  difference;  and  a  formal  linguistic  difference is one which logic can take cognizance of, in abstraction from pragmatic considerations,  like  the direction of  interest. Such  a  formal  ditference exists in the difference between appearing in discourse directly designated and  appearing  in  discourse under  the cloak of  quantification. ““But the difference in the use  of  unquantified  statements to which Cook Wilson draws attention is not a formal difference at all.”Both glass and elasticity, Socrates  and wisdom appear named  in  such  statements, whichever, in Cook  Wilson's  sense,  we  are talking about. An  appeal  to  pragmatic considerations  is,  certainly, an essential  part  of  my  own  account  at  a certain point: but this is the point  at which such considerations are in- voked to explain why  a certain formal difference should  be particularly closely linked, in common speech, with a certain category difference. The difference  of  which Cook  Wilson speaks is, then, though  interesting in itself, irrelevant to my question. Cook Wilson is, and I am not, concerned with  what  Sellars calls  dialectical  distinctions.” On p.76 Grice mentions for the first time the “ROLE” of if in an indefinite series of ‘interrogative subordination.”For Cook Wilson,as Price knew (he quotes him in Belief), the function of ‘if’ is to LINK TWO QUESTIONS. You’re the cream in my coffee as ‘absurd’ if literally (p. 83). STATEMENT In this entry we will explore how Grice sees the ‘implicaturum’ that he regards as ‘conversational’ as applied to the emissor and in reference to the Graeco-Roman classical tradition. Wht is implicated may not be the result of any maxim, and yet not conventional – depending on a feature of context. But nothing like a maxim – Strawson Wiggins p. 523. Only a CONVERSATIONAL IMPLICATURUM is the result of a CONVERSATIONAL MAXIM and the principle of conversational helpfulness. In a ‘one-off’ predicament, there may be an ‘implicaturum’ that springs from the interaction itself. If E draws a skull, he communicates that there is danger. If addressee runs away, this is not part of the implicaturum. This Grice considers in “Meaning.” “What is meant” should cover the immediate effect, and not any effect that transpires out of the addressee’s own will. Cf. Patton on Kripke. One thief to another: “The cops are coming!” The expressiom “IMPLICATION” is figures, qua entry, in a philosophical dictionary that Grice consulted at Oxford. In the vernacular, there are two prominent relata: entailment and implicaturum, the FRENCH have their “implication.” When it comes to the Germans, it’s more of a trick. There’s the “nachsichziehen,” the “zurfolgehaben,” the “Folge(-rung),” the “Schluß,” the “Konsequenz,” and of course the “Implikation” and the “Implikatur,” inter alia.  In Grecian, which Grice learned at Clifton, we have the “sumpeplegmenon,” or “συμπεπλεγμένον,” if you must, i. e. the “sum-peplegmenon,” but there’s also the “sumperasma,” or “συμπέϱασμα,” if you must, “sum-perasma;” and then there’s the “sunêmmenon,” or “συνημμένον,” “sun-emmenon,” not to mention (then why does Grice?) the “akolouthia,” or “ἀϰολουθία,” if you must, “akolouthia,” and the “antakolouthia,” ἀνταϰολουθία,” “ana-kolouthia.” Trust clever Cicero to regard anything ‘Grecian’ as not displaying enough gravitas, and thus rendering everything into Roman. There’s the “illatio,” from ‘in-fero.’ The Romans adopted two different roots for this, and saw them as having the same ‘sense’ – cf. referro, relatum, proferro, prolatum; and then there’s the “inferentia,”– in-fero; and then there’s the “consequentia,” -- con-sequentia. The seq- root is present in ‘sequitur,’ non sequitur. The ‘con-‘ is transliterating Greek ‘syn-’ in the three expressions with ‘syn’: sympleplegmenon, symperasma, and synemmenon. The Germans, avoiding the Latinate, have a ‘follow’ root: in “Folge,” “Folgerung,” and the verb “zur-folge-haben. And perhaps ‘implicatio,’  which is the root Grice is playing with. In Italian and French it underwent changes, making ‘to imply’ a doublet with Grice’s ‘to implicate’ (the form already present, “She was implicated in the crime.”). The strict opposite is ‘ex-plicatio,’ as in ‘explicate.’ ‘implico’ gives both ‘implicaturum’ and ‘implicitum.’ Consequently, ‘explico’ gives both ‘explicatum’ and ‘explicitum.’ In English Grice often uses ‘impicit,’ and ‘explicit,’ as they relate to communication, as his ‘implicaturum’ does. His ‘implicaturum’ has more to do with the contrast with what is ‘explicit’ than with ‘what follows’ from a premise. Although in his formulation, both readings are valid: “by uttering x, implicitly conveying that q, the emissor CONVERSATIONALY implicates that p’ if he has explicitly conveyed that p, and ‘q’ is what is required to ‘rationalise’ his conversational behavioiur. In terms of the emissor, the distinction is between what the emissor has explicitly conveyed and what he has conversationally implicated. This in turn contrasts what some philosophers refer metabolically as an ‘expression,’ the ‘x’ ‘implying’ that p – Grice does not bother with this because, as Strawson and Wiggins point out, while an emissor cannot be true, it’s only what he has either explicitly or implicitly conveyed that can be true. As Austin says, it’s always a FIELD where you do the linguistic botany. So, you’ll have to vide and explore: ANALOGY, PROPOSITION, SENSE, SUPPOSITION, and TRUTH. Implication denotes a relation between propositions and statements such that, from the truth-value of the protasis or antecedent (true or false), one can derive the truth of the apodosis or consequent. More broadly, we can say that one idea ‘implies’ another if the first idea cannot be thought without the second one -- RT: Lalande, Vocabulaire technique et critique de la philosophie. Common usage makes no strict differentiation between “to imply,” “to infer,” and “to lead to.” Against Dorothy Parker. She noted that those of her friends who used ‘imply’ for ‘infer’ were not invited at the Algonquin. The verb “to infer,” (from Latin, ‘infero,’ that gives both ‘inferentia,’ inference, and ‘illatio,’ ‘illatum’) meaning “to draw a consequence, to deduce” (a use dating to 1372), and the noun “inference,” meaning “consequence” (from 1606), do not on the face of it seem to be manifestly different from “to imply” and “implication.” But in Oxonian usage, Dodgson avoided a confusion. “There are two ways of confusing ‘imply’ with ‘infer’: to use ‘imply’ to mean ‘infer,’ and vice versa. Alice usually does the latter; the Dodo the former.” Indeed, nothing originally distinguishes “implication” as Lalande defines it — “a relation by which one thing ‘implies’ another”— from “inference” as it is defined in Diderot and d’Alembert’s Encyclopédie (1765): “An operation by which one ACCEPTS (to use a Griceism) a proposition because of its connection to other propositions held to be true.” The same phenomenon can be seen in the German language, in which the terms corresponding to “implication,” “Nach-sich-ziehen,” “Zur-folge-haben,” “inference,” “Schluß”-“Folgerung,” “Schluß,” “to infer,” “schließen,” “consequence,” “Folge” “-rung,” “Schluß,” “Konsequenz,” “reasoning,” “”Schluß-“ “Folgerung,” and “to reason,” “schließen,” “Schluß-folger-ung-en ziehen,” intersect or overlap to a large extent. In the French language, the expression “impliquer” reveals several characteristics that the expression does not seem to share with “to infer” or “to lead to.” First of all, “impliquer” is originally (1663) connected to the notion of contradiction, as shown in the use of impliquer in “impliquer contradiction,” in the sense of “to be contradictory.” The connection between ‘impliquer’ and ‘contradiction’ does not, however, explain how “impliquer” has passed into its most commonly accepted meaning — “implicitly entail” — viz. to lead to a consequence. Indeed, the two usages (“impliquer” connected with contradiction” and otherwise) constantly interfere with one another, which certainly poses a number of difficult problems. An analogous phenomenon can be found in the case of “import,” commonly given used as “MEAN” or “imply,” but often wavering instead, in certain cases, between “ENTAIL” and “imply.” In French, the noun “import” itself is generally left as it I (“import existentiel,” v. SENSE, Box 4, and cf. that’s unimportant, meaningless).  “Importer,” as used by Rabelais, 1536, “to necessitate, to entail,” forms via  It.“importare,” as used by Dante), from the Fr. “emporter,” “to entail, to have as a consequence,” dropped out of usage, and was brought back through Engl. “import.” The nature of the connection between the two primary usages of L. ‘implicare,’ It. ‘implicare,’ and Fr. ‘impliquer,’ “to entail IMPLICITitly” and “to lead to a consequence,” nonetheless remains obscure, but not to a Griceian, or Grecian. Another difficulty is understanding how the transition occurs from Fr. “impliquer,” “to lead to a consequence,” to “implication,” “a logical relation in which one statement necessarily supposes another one,” and how we can determine what in this precise case distinguishes “implication” from “PRAE-suppositio.” We therefore need to be attentive to what is implicit in Fr. “impliquer” and “implication,” to the dimension of Fr. “pli,” a pleat or fold, of Fr. “re-pli,” folding back, and of the Fr. “pliure,” folding, in order to separate out “imply,” “infer,” “lead to,” or “implication,” “inference,” “consequence”—which requires us to go back to Latin, and especially to medieval Latin. Once we clarify the relationship between the usage of “implication” and the medieval usage of “implicatio,” we will be able to examine certain derivations (as in Sidonius’s ‘implicatura,” and H. P. Grice’s “implicaturum,” after ‘temperature,’ from ‘temperare,’) or substitutes (“entailment”) of terms related to the generic field (for linguistic botanising) of “implicatio,” assuming that it is difficulties with the concept of implication (e. g., the ‘paradoxes,’ true but misleading, of material versus formal implication – ‘paradox of implication’ first used by Johnson 1921) that have given rise to this or that newly coined expression corresponding to this or that original attempt. This whole set of difficulties certainly becomes clearer as we leave Roman and go further upstream to Grecian, using the same vocabulary of implication, through the conflation of several heterogeneous gestures that come from the systematics in Aristotle and the Stoics. The Roman Vocabulary of Implication and the Implicatio has the necessary ‘gravitas,’ but Grice, being a Grecian at heart, found it had ‘too much gravitas,’ hence his ‘implicaturum,’ “which is like the old Roman ‘implicare,’ but for fun!” A number of different expressions in medieval Latin can express in a more or less equivalent manner the relationship between propositions and statements such that, from the truth-value of the antecedent (true or false), one can derive the truth-value of the consequent. There is “illatio,” and of course “illatum,” which Varro thought fell under ‘inferre.’ Then there’s the feminine noun, ‘inferentia,’ from the ‘participium praesens’ of ‘inferre,’ cf. ‘inferens’ and ‘ilatum.’ There is also ‘consequentia,’ which is a complex transliterating the Greek ‘syn-,’ in this case with ‘’sequentia,’ from the deponent verb. “I follow you.” Peter Abelard (Petrus Abelardus, v. Abelardus) makes no distinction in using the expression “consequentia” for the ‘propositio conditionalis,’ hypothetical. Si est homo, est animal. If Grice is a man, Grice is an animal (Dialectica, 473 – Abelardus uses ‘Greek man,’ not Grice.’ His implicaturum is ‘if a Greek man is a man, he is therefore also some sort of an animal’). But Abelardus also uses the expression “inferentia” for ‘same old same old’ (cf. “Implicaturum happens.”). Si non est iustus homo, est non iustus homo. Grice to Strawson on the examiner having given him a second. “If it is not the case that your examiner was a fair man, it follows thereby that your examiner was not a fair man, if that helps.” (Dialectica., 414).  For some reason, which Grice found obscure, ‘illatio” appears “almost always” in the context of commenting on Aristotle’s “Topics,” – “why people found the topic commenting escapes me” -- aand denotes more specifically a reasoning, or “argumentum,” in Boethius, allowing for a “consequentia” to be drawn from a given place. So Abelardus distinguishes: “illatio a causa.” But there is also “illatio a simili.” And there is “iillatio a pari.” And there is “illatio a partibus.” “Con-sequentia” sometimes has a very generic usage, even if not as generic as ‘sequentia.” “Consequentia est quaedam habitudo inter antecedens et consequens,” “Logica modernorum,” 2.1:38 – Cfr. Grice on Whitehead as a ‘modernist’! Grice draws his ‘habit’ from the scholastic ‘habitudo.’ Noe that ‘antededens’ and ‘consequens.’ The point is a tautological formula, in terms of formation. Surely ‘consequentia’ relates to a ‘consequens,’ where the ‘consequens’ is the ‘participium praesens’ of the verb from which ‘consequentia’ derives. It’s like deving ‘love’ by ‘to have a beloved.’ “Consequentia” is in any case present, in some way, without the intensifier ‘syn,’ which the Roman gravitas added to transliterate the Greek ‘syn,’ i. e. ‘cum.’ -- in the expression “sequitur” and in the expression “con-sequitur,” literally, ‘to follow,’ ‘to ensue,’ ‘to result in’). Keenan told Grice that this irritated him. “If there is an order between a premise and a conclusion, I will stop using ‘follow,’ because that reverts the order. I’ll use ‘… yields …’ and write that ‘p yields q.’” “Inferentia,” which is cognate (in the Roman way of using this expression broadly) with ‘illatio,’ and ‘illatum,’ -- frequently appears, by contrast, and “for another Grecian reason,” as Grice would put it -- in the context of the Aristotle’s “De Interpretatione,” on which Grice lectures only with J. L. Austin (Grice lectured with Strawson on “Categoriae,” only – but with Austin, from whom Grice learned – Grice lectured on both “Categoriae’ AND “De Interpretatione.” --  whether it is as part of a commentarium on Apuleius’s Isagoge and the Square of Oppositions (‘figura quadrata spectare”), in order to explain this or that “law” underlying any of the four sides of the square. So, between A and E we have ‘propositio opposita.’ Between A and I, and between E and O, we have propositio sub-alterna. Between A and O, and between E and I, we have propositio contradictoria. And between I and O, we have “propositio sub-alterna.” -- Logica modernorum, 2.1:115. This was irritatingly explored by P. F. Strawson and brought to H. P. Grice’s attention, who refused to accept Strawson’s changes and restrictions of the ‘classical’ validities (or “laws”) because Strawson felt that the ‘implication’ violated some ‘pragmatic rule,’ while still yielding a true statement. Then there’s the odd use of “inferentia” to apply to the different ‘laws’ of ‘conversio’ -- from ‘convertire,’ converting one proposition into another (Logica modernorum 131–39). Nevertheless, “inferentia” is used for the dyadic (or triadic, alla Peirce) relationship of ‘implicatio,’ which for some reason, the grave Romans were using for less entertaining things, and not this or that expressions from the “implication” family, or sub-field.  Surprisingly, a philosopher without a classical Graeco-Roman background could well be mislead into thinking that “implicatio” and “implication” are disparate! A number of treatises, usually written by monks – St. John’s, were Grice teaches, is a Cicercian monastery -- explore the “implicits.” Such a “tractatus” is not called ‘logico-philosophicus,’ but a “tractatus implicitarum,” literally a treatise on this or that  ‘semantic’ property of the proposition said to be an ‘implicaturum’ or an ‘implication,’ or ‘propositio re-lativa.’ This is Grice’s reference to the conversational category of ‘re-lation.’ “Re-latio” and “Il-latio” are surely cognate. The ‘referre’ is a bring back; while the ‘inferre’ is the bring in. The propositio is not just ‘brought’ (latum, or lata) it is brought back. Proposition Q is brought back (relata) to Proposition P. P and Q become ‘co-relative.’ This is the terminology behind the idea of a ‘relative clause,’ or ‘oratio relativa.’ E.g. “Si Plato tutee Socrates est, Socratos tutor Platonis est,” translated by Grice, “If Strawson was my tutee, it didn’t show!”. Now, closer to Grice “implicitus,” with an “i” following the ‘implic-‘ rather than the expected ‘a’ (implica), “implicita,” and “implicitum,” is an alternative “participium passatum” from “im-plic-are,” in Roman is used for “to be joined, mixed, enveloped.” implĭco (inpl- ), āvi, ātum, or (twice in Cic., and freq. since the Aug. per.) ŭi, ĭtum (v. Neue, Formenl. 2, 550 sq.), 1, v. a. in-plico, to fold into; hence, I.to infold, involve, entangle, entwine, inwrap, envelop, encircle, embrace, clasp, grasp (freq. and class.; cf.: irretio, impedio). I. Lit.: “involvulus in pampini folio se,” Plaut. Cist. 4, 2, 64: “ut tenax hedera huc et illuc Arborem implicat errans,” Cat. 61, 35; cf. id. ib. 107 sq.: “et nunc huc inde huc incertos implicat orbes,” Verg. A. 12, 743: “dextrae se parvus Iulus Implicuit,” id. ib. 2, 724; cf.: “implicuit materno bracchia collo,” Ov. M. 1, 762: “implicuitque suos circum mea colla lacertos,” id. Am. 2, 18, 9: “implicuitque comam laevā,” grasped, Verg. A. 2, 552: “sertis comas,” Tib. 3, 6, 64: “crinem auro,” Verg. A. 4, 148: “frondenti tempora ramo,” id. ib. 7, 136; cf. Ov. F. 5, 220: in parte inferiore hic implicabatur caput, Afran. ap. Non. 123, 16 (implicare positum pro ornare, Non.): “aquila implicuit pedes atque unguibus haesit,” Verg. A. 11, 752: “effusumque equitem super ipse (equus) secutus Implicat,” id. ib. 10, 894: “congressi in proelia totas Implicuere inter se acies,” id. ib. 11, 632: “implicare ac perturbare aciem,” Sall. J. 59, 3: “(lues) ossibus implicat ignem,” Verg. A. 7, 355.—In part. perf.: “quini erant ordines conjuncti inter se atque implicati,” Caes. B. G. 7, 73, 4: “Canidia brevibus implicatura viperis Crines,” Hor. Epod. 5, 15: “folium implicaturum,” Plin. 21, 17, 65, § 105: “intestinum implicaturum,” id. 11, 4, 3, § 9: “impliciti laqueis,” Ov. A. A. 2, 580: “Cerberos implicitis angue minante comis,” id. H. 9, 94: “implicitamque sinu absstulit,” id. A. A. 1, 561: “impliciti Peleus rapit oscula nati,” held in his arms, Val. Fl. 1, 264. II. Trop. A. In gen., to entangle, implicate, involve, envelop, engage: “di immortales vim suam ... tum terrae cavernis includunt, tum hominum naturis implicant,” Cic. Div. 1, 36, 79: “contrahendis negotiis implicari,” id. Off. 2, 11, 40: “alienis (rebus) nimis implicari molestum esse,” id. Lael. 13, 45: “implicari aliquo certo genere cursuque vivendi,” id. Off. 1, 32, 117: “implicari negotio,” id. Leg. 1, 3: “ipse te impedies, ipse tua defensione implicabere,” Cic. Verr. 2, 2, 18, § 44; cf.: multis implicari erroribus, id. Tusc. 4, 27, 58: “bello,” Verg. A. 11, 109: “eum primo incertis implicantes responsis,” Liv. 27, 43, 3: “nisi forte implacabiles irae vestrae implicaverint animos vestros,” perplexed, confounded, id. 40, 46, 6: “paucitas in partitione servatur, si genera ipsa rerum ponuntur, neque permixte cum partibus implicantur,” are mingled, mixed up, Cic. Inv. 1, 22, 32: ut omnibus copiis conductis te implicet, ne ad me iter tibi expeditum sit, Pompei. ap. Cic. Att. 8, 12, D, 1: “tanti errores implicant temporum, ut nec qui consules nec quid quoque anno actum sit digerere possis,” Liv. 2, 21, 4.—In part. perf.: “dum rei publicae quaedam procuratio multis officiis implicaturum et constrictum tenebat,” Cic. Ac. 1, 3, 11: “Deus nullis occupationibus est implicatus,” id. N. D. 1, 19, 51; cf.: “implicatus molestis negotiis et operosis,” id. ib. 1, 20, 52: “animos dederit suis angoribus et molestiis implicatos,” id. Tusc. 5, 1, 3: “Agrippina morbo corporis implicatura,” Tac. A. 4, 53: “inconstantia tua cum levitate, tum etiam perjurio implicatura,” Cic. Vatin. 1, 3; cf. id. Phil. 2, 32, 81: “intervalla, quibus implicatura atque permixta oratio est,” id. Or. 56, 187: “(voluptas) penitus in omni sensu implicatura insidet,” id. Leg. 1, 17, 47: “quae quatuor inter se colligata atque implicatura,” id. Off. 1, 5, 15: “natura non tam propensus ad misericordiam quam implicatus ad severitatem videbatur,” id. Rosc. Am. 30, 85; “and in the form implicitus, esp. with morbo (in morbum): quies necessaria morbo implicitum exercitum tenuit,” Liv. 3, 2, 1; 7, 23, 2; 23, 40, 1: “ubi se quisque videbat Implicitum morbo,” Lucr. 6, 1232: “graviore morbo implicitus,” Caes. B. C. 3, 18, 1; cf.: “implicitus in morbum,” Nep. Ages. 8, 6; Liv. 23, 34, 11: “implicitus suspicionibus,” Plin. Ep. 3, 9, 19; cf.: “implicitus terrore,” Luc. 3, 432: “litibus implicitus,” Hor. A. P. 424: “implicitam sinu abstulit,” Ov. A. A. 1, 562: “(vinum) jam sanos implicitos facit,” Cael. Aur. Acut. 3, 8, 87.— B. In partic., to attach closely, connect intimately, to unite, join; in pass., to be intimately connected, associated, or related: “(homo) profectus a caritate domesticorum ac suorum serpat longius et se implicet primum civium, deinde mortalium omnium societate,” Cic. Fin. 2, 14, 45: “omnes qui nostris familiaritatibus implicantur,” id. Balb. 27, 60: “(L. Gellius) ita diu vixit, ut multarum aetatum oratoribus implicaretur,” id. Brut. 47, 174: “quibus applicari expediet, non implicari,” Sen. Ep. 105, 5.— In part. perf.: “aliquos habere implicatos consuetudine et benevolentia,” Cic. Fam. 6, 12, 2: “implicatus amicitiis,” id. Att. 1, 19, 8: “familiaritate,” id. Pis. 29, 70: “implicati ultro et citro vel usu diuturno vel etiam officiis,” id. Lael. 22, 85. —Hence, 1. implĭcātus (inpl- ), a, um, P. a., entangled, perplexed, confused, intricate: “nec in Torquati sermone quicquam implicaturum aut tortuosum fuit,” Cic. Fin. 3, 1, 3: “reliquae (partes orationis) sunt magnae, implicaturae, variae, graves, etc.,” id. de Or. 3, 14, 52: vox rauca et implicatura, Sen. Apocol. med. — Comp.: “implicatior ad loquendum,” Amm. 26, 6, 18. — Sup.: “obscurissima et implicatissima quaestio,” Gell. 6, 2, 15: “ista tortuosissima et implicatissima nodositas,” Aug. Conf. 2, 10 init.— 2. im-plĭcĭtē (inpl- ), adv., intricately (rare): “non implicite et abscondite, sed patentius et expeditius,” Cic. Inv. 2, 23, 69. -- “Implicare” adds to these usages the idea of an unforeseen difficulty, i. e. a hint of “impedire,” and even of deceit, i. e. a hint of “fallere.” Why imply what you can exply? Cf. subreptitious. subreption (n.)"act of obtaining a favor by fraudulent suppression of facts," c. 1600, from Latin subreptionem (nominative subreptio), noun of action from past-participle stem of subripere, surripere (see surreptitious). Related: Subreptitious. surreptitious (adj.)mid-15c., from Latin surrepticius "stolen, furtive, clandestine," from surreptus, past participle of surripere "seize secretly, take away, steal, plagiarize," from assimilated form of sub "from under" (hence, "secretly;" see sub-) + rapere "to snatch" (see rapid). Related: Surreptitiously. The source of the philosophers’s usage of ‘implicare’ is a passage from Aristotle’s “De Int.” on the contrariety of proposition A and E (14.23b25–27), in which “implicita” (that sould be ‘com-plicita,’ and ‘the emissor complicates that p”) renders Gk. “sum-pepleg-menê,” “συμ-πεπλεγμένη,” f. “sum-plek-ein,” “συμ-πλέϰein,” “to bind together,” as in ‘com-plicatio,’ complication, and Sidonius’s ‘complicature,’ and Grice’s ‘complicature,’ as in ‘temperature,’ from ‘temperare.’ “One problem with P. F. Strawson’s exegesis of J. L. Austin is the complicature is brings.” This is from the same family or field as “sum-plokê,” “συμ-πλοϰή,” which Plato (Pol. 278b; Soph. 262c) uses for the ‘second articulation,’ the “com-bination” of sounds (phone) that make up a word (logos), and, more philosophically interesting, for ‘praedicatio,’ viz., the interrelation within a ‘logos’ or ‘oratio’ of a noun, or onoma or nomen, as in “the dog,” and a verb, or rhema, or verbum, -- as in ‘shaggisising’ -- that makes up a propositional complex, as “The dog is shaggy,” or “The dog shaggisises.” (H. P. Grice, “Verbing from adjectiving.”). In De Int. 23b25-27, referring to the contrariety of A and O, Aristotle, “let’s grant it” – as Grice puts it – “is hardly clear.” Aristotle writes: “hê de tou hoti kakon to agathon SUM-PEPLEG-MENÊ estin.” “Kai gar hoti ouk agathon anagkê isôs hupolambanein ton auton.”“ἡ δὲ τοῦ ὅτι ϰαϰὸν τὸ ἀγαθὸν συμπεπλεγμένη ἐστίν.”“ϰαὶ γὰϱ ὅτι οὐϰ ἀγαθὸν ἀνάγϰη ἴσως ὑπολαμϐάνειν τὸν αὐτόν.” Back in Rome, Boethius thought of bring some gravitas to this. “Illa vero quae est,” Boethius goes,” Quoniam malum est quod est bonum, IMPLICATURA est. Et enim: “Quoniam non bonum est.” necesse est idem ipsum opinari (repr. in Aristoteles latinus, 2.1–2.4–6. In a later vulgar Romance, we have J. Tricot). “Quant au jugement, “Le bon est mal” ce n’est en réalité qu’une COMBINAISON de jugements, cars sans doute est-il nécessaire de sous-entendre en même temps “le bon n’est pas le bon.” Cf. Mill on ‘sous-entendu’ of conversation. This was discussed by H. P. Grice in a tutorial with Reading-born English philosopher J. L. Ackrill at St. John’s.  With the help of H. P. Grice, J. L. Ackrill tries to render Boethius into the vernacular (just to please Austin) as follows. “Hê de tou hoti kakon to agathon SUM-PEPLEG-MENÊ estin, kai gar hoti OUK agathon ANAGKê isôs hupo-lambanein ton auton” “Illa vero quae est, ‘Quoniam malum est quod est bonum,’ IMPLICATURA est, et enim, ‘Quoniam non bonum est,’ necesse est idem ipsum OPINARI. In the vernacular: “The belief expressed by the proposition, ‘The good is bad,’ is COM-PLICATED or com-plex, for the same person MUST, perhaps, suppose also the proposition, ‘The good it is not good.’” Aristotle goes on, “For what kind of utterance is “The good is not good,” or as they say in Sparta, “The good is no good”? Surely otiose. “The good” is a Platonic ideal, a universal, separate from this or that good thing. So surely, ‘the good,’ qua idea ain’t good in the sense that playing cricket is good. But playing cricket is NOT “THE” good: philosophising is.” H. P. Grice found Boethius’s commentary “perfectly elucidatory,” but Ackrill was perplexed, and Grice intended Ackrill’s perplexity to go ‘unnoticed’ (“He is trying to communicate his perplexity, but I keep ignoring it.” For Ackrill was surreptitiously trying to ‘correct’ his tutor. Aristotle, Acrkill thought, is wishing to define the ‘contrariety’ between two statements or opinions, or not to use a metalanguage second order, that what is expressed by ‘The good is bad’ is a contrarium of what is expressed by ‘The good is no good.’” Aristotle starts, surely, from a principle. The principle states that a maximally false proposition, set in opposition to a maximally true proposition (such as “The good is good”), deserves the name “contraria” – and ‘contrarium’ to what is expressed by it. In a second phase, Aristotle then tries to demonstrate, in a succession of this or that stage, that ‘The good is good’ understood as a propositio universalis dedicativa – for all x, if x is (the) good, x is good (To agathon agathon estin,’ “Bonum est bonum”) is a maximally true proposition.” And the reason for this is that “To agathon agathon estin,” or “Bonum bonum est,” applies to the essence (essentia) of “good,” and ‘predicates’ “the same of the same,” tautologically. Now consider Aristotle’s other proposition “The good is the not-bad,” the correlative E form, For all x, if x is good, x is not bad. This does not do. This is not a maximally true proposition. Unlike “The good is good,” The good is not bad” does not apply to the essence of ‘the good,’ and it does not predicate ‘the same of the same’ tautologically. Rather, ‘The good is not bad,’ unless you bring one of those ‘meaning postulates’ that Grice rightly defends against Quine in “In defense of a dogma,” – in this case, (x)(Bx iff ~Gx) – we stipulate something ‘bad’ if it ain’t good -- is only true notably NOT by virtue of a necessary logical implication, but, to echo my tutor, by implicaturum, viz. by accident, and not by essence (or essential) involved in the ‘sense’ of either ‘good’ or ‘bad,’ or ‘not’ for that matter. Surely Aristotle equivocates slightly when he convinced Grice that an allegedly maximally false proposition (‘the good is bad’) entails or yields the negation of the same attribute, viz., ‘The good is not good,’ or more correctly, ‘It is not the case that the good is good,’ for this is axiomatically contradictory, or tautologically and necessarily false without appeal to any meaning postulate. For any predicate, Fx and ~Fx. The question then is one of knowing whether ‘The good is bad’ deserves to be called the contrary proposition (propositio contraria) of ‘The good is good.’ Aristotle notes that the proposition, ‘The good is bad,’ “To agathon kakon estin,” “Bonum malum est,” is NOT the maximally false proposition opposed to the maximally true, tautological, and empty, proposition, “The good is good,” ‘To agathon agathon estin,’ “Bonum bonum est.” “Indeed, “the good is bad” is sumpeplegmenê, or COMPLICATA. What the emissor means is a complicatum, or as Grice preferred, a ‘complicature. Grice’s complicature (roughly rendered as ‘complification’) condenses all of the moments of the transition from the simple idea of a container (cum-tainer) to the “modern” ideas of implication, Grice’s implicaturum, and prae-suppositio. The ‘propositio complicate,’ is, as Boethius puts it, duplex, or equivocal. The proposition  has a double meaning – one explicit, the other implicit. “A ‘propositio complicata’ contains within itself [“continet in se, intra se”]: bonum non est.” Boethius then goes rightly to conclude (or infer), or stipulate, that only a “simplex” proposition, not a propositio complicata, involving some ‘relative clause,’ can be said to be contrary to another -- Commentarii in librum Aristotelis Peri hermêneais, 219. Boethius’s exegesis thesis is faithful to Aristotle. For Aristotle, nothing like “the good is not bad,” but only the tautologically false “the good is not good,” or it is not the case that the good is good, (to agathon agathon esti, bonum bonum est), a propositio simplex, and not a propositio complicate, is the opposite (oppositum, -- as per the ‘figura quadrata’ of ‘oppoista’ -- of “the good is good,” another propositio simplex. Boethius’s analysis of “the good is bad,” a proposition that Boethius calls ‘propositio complicate or ‘propositio implicita’ are manifestly NOT the same as Aristotle’s. For Aristotle, the “doxa hoti kakon to agathon [δόξα ὅτι ϰαϰὸν τὸ ἀγαθόν],” the opinion according to which the good is bad, is only ‘contrary’ to “the good is good” to the extent that it “con-tains” (in Boethius’s jargon) the tautologically false ‘The good is not good.’ For Boethius, ‘The good is bad’ is contrary to ‘the good is good’ is to the extent that ‘the good is bad’ contains, implicitly, the belief which Boethius expresses as ‘Bonum NON est —“ cf. Grice on ‘love that never told can be” – Featuring “it is not the case that,” the proposition ‘bonum non est’ is a remarkably complicated expression in Latin, a proposition complicata indeed. ‘Bonum non est’ can mean, in the vernacular, “the good is not.” “Bonum non est” can only be rendered as “there is nothing good.’ “Bonum non est’ may also be rendered, when expanded with a repeated property, the tautologically false ‘The good is not good” (Bonum non bonum est). Strangely, Abelard goes in the same direction as Aristotle, contra Boethius. “The good is bad” (Bonum malum est)  is “implicit” (propositio implicita or complicate) with respect to the tautologically false ‘Bonum bonum non est’ “the good is not good.”Abelardus, having read Grice – vide Strawson, “The influence of Grice on Abelardus” -- explains clearly the meaning of “propositio implicita”: “IMPLYING implicitly ‘bonum non bonum est,’ ‘the good is not good’ within itself, and in a certain wa containing it [“IM-PLICANS eam in se, et quodammodo continens.” Glossa super Periermeneias, 99–100. But Abelard expands on Aristotle. “Whoever thinks ‘bonum malum est,’ ‘the good is bad’ also thinks ‘bonum non bonum est,’ ‘the good is not good,’ whereas the reverse does not hold true, i. e. it is not the case that whoever thinks the tautologically false ‘the good is not good’ (“bonum bonum non est”) also think ‘the good is bad’ (‘bonum malum est’). He may refuse to even ‘pronounce’ ‘malum’ (‘malum malum est’) -- “sed non convertitur.” Abelard’s explanation is decisive for the natural history of Grice’s implication. One can certainly express in terms of “implication” what Abelard expresses when he notes the non-reciprocity or non-convertibility of the two propositions. ‘The good is bad,’ or ‘Bonum malum est’ implies or presupposes the tautologically true “the good is not good;’It is not the case that the tautologically false “the good is not good” (‘Bonum bonum non est’) implies ridiculous “the good is bad.” Followers of Aristotle inherit these difficulties.  Boethius and Abelard bequeath to posterity an interpretation of the passage in Aristotle’s “De Interpretatione” according to which “bonum malum est” “the good is bad” can only be considered the ‘propositio opposita’ of the tautologically true ‘bonum bonum est’ (“the good is good”) insofar as, a ‘propositio implicita’ or ‘relativa’ or ‘complicata,’ it contains the ‘propositio contradictoria, viz. ‘the good is not good,’ the tautologically false ‘Bonum non bonum est,’ of the tautologically true ‘Bonum bonum est’ “the good is good.” It is this meaning of “to contain a contradiction” that, in a still rather obscure way, takes up this analysis by specifying a usage of “impliquer.” The first attested use in French of the verb “impliquer” is in 1377 in Oresme, in the syntagm “impliquer contradiction” (RT: DHLF, 1793). These same texts give rise to another analysis. A propositio implicita or pregnant, or complicate, is a proposition that “implies,” that is, that in fact contains two propositions, one principalis, and the other relative, each a ‘propositio explicita,’ and that are equivalent or equipollent to the ‘propositio complicata’ when paraphrased. Consider. “Homo qui est albus est animal quod currit,” “A man who is white is an animal who runs.” This ‘propositio complicate contains the the propositio implicita, “homo est albus” (“a man is white”) and the propositio implicita, “animal currit” (“an animal  runs.”). Only by “exposing” or “resolving” (via ex-positio, or via re-solutio) such an ‘propositio complicata’ can one assign it a truth-value. “Omnis proposition implicita habet duas propositiones explicitas.” “A proposition implicita “P-im” has (at least) a proposition implicita P-im-1 and a different proposition implicita P-im-2.” “Verbi gratia.” “Socrates est id quod est homo.” “Haec propositio IMplicita aequivalet huic copulativae constanti ex duis propositionis explicitis. Socrates est aliquid est illud est homo. Haec proposition est vera, quare et propositio implicita vera. Every “implicit proposition” has two explicit propositions.” “Socrates is something (aliquid) which is a man.” This implicit proposition, “Socrates is something shich is a man,” is equivalent or equipoent to the following conjunctive proposition made up of two now EXplicit propositions, to wit, “Socrates is something,” and “That something is a man.” This latter conjunctive proposition of the two explicit propositions is true. Therefore, the “implicit” proposition is also true” (Tractatus implicitarum, in Giusberti – Materiale per studum, 43). The two “contained” propositions are usually relative propositions. Each is called an ‘implicatio.’ ‘Implicatio’ (rather than ‘implicitio’) becomes shorthand for “PROPOSITIO implicita.” An ‘implicatio’ becomes one type of  ‘propositio exponibilis,’ i. e. a proposition that is to be “exposed” or paraphrased for its form or structure to be understood.  In the treatises of Terminist logic, one chapter is by custom devoted to the phenomenon of “restrictio,” viz. a restriction in the denotation or the suppositio of the noun (v. SUPPOSITION). A relative expression (an implication), along with others, has a restrictive function (viz., “officium implicandi”), just like a sub-propositional expression like an adjective or a participle. Consider.  “A man, Grice, who argues, runs to the second base.”  “Man,” because of the relative expression or clause “who runs,” is restricted to denoting the present time (it is not Grice, who argues NOW but ran YESTERDAY). Moreover there is an equivalence or equipolence between the relative expression “qui currit” and the present participle “currens.” Running Grice argues. Grice who runs argues. Summe metenses, Logica modernorum, 2.1:464. In the case in which a relative expression is restrictive, its function is to “leave something that is constant,” “aliquid pro constanti relinquere,” viz., to produce a pre-assertion that conditions the truth of the main super-ordinate assertion without being its primary object or topic or signification or intentio. “Implicare est pro constanti et involute aliquid significare.” “Ut cum dicitur homo qui est albus currit.”  “Pro constanti” dico, quia praeter hoc quod assertitur ibi cursus de homine, aliquid datur intelligi, scilicet hominem album; “involute” dico quia praeter hoc quod ibi proprie et principaliter significatur hominem currere, aliquid intus intelligitur, scilicet hominem esse album. Per hoc patet quod implicare est intus plicare. Id enim quod intus “plicamus” sive “ponimus,” pro constanti relinquimus. Unde implicare nil aliud est quam subiectum sub aliqua dispositione pro constanti relinquere et de illo sic disposito aliquid affirmare. Ackrill translates to Grice: “To imply” is to signify something by stating it as constant, and in a pretty ‘hidden’ manner – “involute.” When I state that the man runs, I state, stating it as constant, because, beyond (“praeter”) the main supra-ordinate assertion or proposition that predicates the running of the man, my addressee is given to understand something else (“aliquid intus intelligitur”), viz. that the man is white; This is communicated in a hidden manner (“involute”) because, beyond (“praeter”) what is communicated (“significatur”) primarily, principally (“principaliter”) properly (“proprie”), literally, and explicitly, viz. that the man is running, we are given to understand something else (“aliquid intus intelligutur”) within (“intus”), viz.  that the man is white.  It follows from this that implicare is nothing other than what the form of the expression literally conveys, intus plicare (“folded within”).  What we fold or state within, we leave as a constant.  It follows from this that “to imply” is nothing other than leaving something as a constant in the subject (‘subjectum’), such that the subject (subjectum, ‘homo qui est albus”) is under a certain disposition, and that it is only under this disposition that something about the subjectum is affirmed” -- De implicationibus, Nota, 100) For the record: while Giusberti (“Materiale per studio,” 31) always reads “pro constanti,” the MSS occasionally has the pretty Griciean “precontenti.” This is a case of what the “Logique du Port-Royal” describes as an “in-cidental” assertion. The situation is even more complex, however, insofar as this operation only relates to one usage of a relative proposition, viz. when the proposition is restrictive. A restriction can sometimes be blocked, or cancelled, and the reinscriptions are then different for a  nonrestrictive and a restrictive relative proposition. One such case of a blockage is that of “false implication” (Johnson’s ‘paradox of ‘implicatio’) as in “a [or the] man who is a donkey runs,” (but cf. the centaur, the man who is a horse, runs) where there is a conflict (“repugnantia”) between what the determinate term itself denotes (homo, man) and the determination (ansinus, donkey). The truth-values of a proposition containing a relative clause or propositio thus varies according to whether it is restrictive, and of composite meaning, as in “homo, qui est albus, currit” (A man, who is white, runs), or non-restrictive, and of divided meaning, as in “Homo currit qui est albus” (Rendered in the vernacular in the same way, the Germanic languages not having the syntactic freedom the classical languages do: A man, who is white, is running. When the relative is restrictive, as in “Homo, qui est albus, curris”, the propositio implicits only produces one single assertion, since the relative corresponds to a pre-assertion. Thus, it is the equivalent, at the level of the underlying form, to a proposition conditionalis or hypothetical. Only in the second case can there be a “resolution” of the proposition implicita into the pair of this and that ‘propositio explicita, to wit, “homo currit,”  “homo est albus.”—and an equipolence between the complex proposition implicita and the conjunction of the first proposition explicita and the second proposition explicitta. Homo currit et ille est albus. So it is only in this second case of proposition irrestrictiva  that one can say that “Homo currit, qui est albus implies “Homo currit,” and “Homo est albus” and therefore, “Homo qui est albus currit.” The poor grave Romans are having trouble with Grecisms. The Grecist vocabulary of implication is both disparate and systematic, in a Griceian oxymoronic way. The grave Latin “implicare” covers and translates an extremely varied Grecian field of expressions ready to be botanized, that bears the mark of heterogeneous rather than systematic operations, whether one is dealing Aristotle or the Stoics. The passage through grave Roman allows us to understand retrospectively the connection in Aristotle’s jargon between the “implicatio” of the “propositio implicita,” sum-pepleg-menê, as an interweaving or interlacing, and conclusive or con-sequential implicatio, sumperasma, “συμπέϱασμα,” or “sumpeperasmenon,” “συμπεπεϱασμένον,” “sumpeperasmenê,” “συμπεπεϱασμένη,” f. perainein, “πεϱαίνein, “to limit,” which is the jargon Aristotle uses in the Organon to denote the conclusion of a syllogism (Pr. Anal. 1.15.34a21–24). If one designates as A the premise, tas protaseis, “τὰς πϱοτάσεις,” and as B the con-clusion, “to sumperasma,” συμπέϱασμα.” Cf. the Germanic puns with ‘closure,’ etc.  When translating Aristotle’s definition of the syllogism at Prior Analytics 1.1.24b18–21, Tricot chooses to render as the “con-sequence” Aristotle’s verb “sum-bainei,” “συμ-ϐαίνει,” that which “goes with” the premise and results from it. A syllogism is a discourse, “logos,” “λόγος,” in which, certain things being stated, something other than what is stated necessarily results simply from the fact of what is stated. Simply from the fact of what is stated, I mean that it is because of this that the consequence is obtained, “legô de tôi tauta einai to dia tauta sumbainei,” “λέγω δὲ τῷ ταῦτα εἶναι τὸ διὰ ταῦτα συμϐαίνει.” (Pr. Anal. 1.1, 24b18–21). To make the connection with “implication,” though, we also have to take into account, as is most often the case, the Stoics’ own jargon. What the Stoics call “sumpeplegmenon,” “συμπεπλεγμένον,” is a “conjunctive” proposition; e. g. “It is daytime, and it is light” (it is true both that A and that B). The conjunctive is a type of molecular proposition, along with the “conditional” (sunêmmenon [συνημμένον] -- “If it is daytime, it is light”) and the “subconditional” (para-sunêmmenon [παϱασυνημμένον]; “SINCE it is daytime, it is light”), and the “disjunctive” (diezeugmenon [διεζευγμένον] --  “It is daytime, or it is night.” Diog. Laert. 7.71–72; cf. RT: Long and Sedley, A35, 2:209 and 1:208). One can see that there is no ‘implicatio’ in the conjunctive, whereas there is one in the ‘sunêmmenon’ (“if p, q”), which constitutes the Stoic expression par excellence, as distinct from the Aristotelian categoric syllogism.Indeed, it is around the propositio conditionalis that the question and the vocabulary of ‘implicatio’ re-opens. The Aristotelian sumbainein [συμϐαίνειν], which denotes the accidental nature of a result, however clearly it has been demonstrated (and we should not forget that sumbebêkos [συμϐεϐηϰός] denotes accident; see SUBJECT, I), is replaced by “akolouthein” [ἀϰολουθεῖν] (from the copulative a- and keleuthos [ϰέλευθος], “path” [RT: Chantraine, Dictionnaire étymologique de la langue grecque, s.v. ἀϰόλουθος]), which denotes instead being accompanied by a consequent conformity. This connector, i. e. the “if” (ei, si) indicates that the second proposition, the con-sequens (“it is light”) follows (akolouthei [ἀϰολουθεῖ]) from the first (“it is daytime”) (Diog. Laert, 7.71). Attempts, beginning with Philo or Diodorus Cronus up to Grice and Strawson to determine the criteria of a “valid” conditional (to hugies sunêmmenon [τὸ ὑγιὲς συνημμένον] offer, among other possibilities, the notion of emphasis [ἔμφασις], which Long and Sedley translate as “G. E. Moore’s entailment” and Brunschwig and Pellegrin as “implication” (Sextus Empiricus, The Skeptic Way, in RT: Long and Sedley, The Hellenistic Philosophers, 35B, 2:211 and 1:209), a term that is normally used to refer to a reflected image and to the force, including rhetorical force, of an impression. Elsewhere, this “emphasis” is explained in terms of dunamis [δύναμις], of “virtual” content (“When we have the premise which results in a certain conclusion, we also have this conclusion virtually [dunamei (δυνάμει)] in the premise, even if it is not explicitly indicated [kan kat’ ekphoran mê legetai (ϰἂν ϰατ̕ ἐϰφοϱὰν μὴ λέγεται)], Sextus Empiricus, Against the Grammarians 8.229ff., D. L. Blank, 49 = RT: Long and Sedley, G36 (4), 2:219 and 1:209)—where connecting the different usages of “implication” creates new problems. One has to understand that the type of implicatio represented by the proposition conditionalis implies, in the double usage of “contains implicitly” and “has as its consequence,” the entire Stoic system. It is a matter of to akolouthon en zôêi [τὸ ἀϰόλουθον ἐν ζωῇ], “consequentiality in life,” or ‘rational life, as Grice prefers, as Long and Sedley translate it (Stobeus 2.85.13 = RT: Long and Sedley, 59B, 2:356; Cicero prefers “congruere,” (congruential) De finibus 3.17 = RT: Long and Sedley, 59D, 2:356). It is akolouthia [ἀϰολουθία] that refers to the conduct con-sequent upon itself that is the conduct of the wise man, the chain of causes defining will or fate, and finally the relationship that joins the antecedent to the con-sequent in a true proposition. Goldschmidt, having cited Bréhier (Le système stoïcien), puts the emphasis on antakolouthia [ἀνταϰολουθία], a Stoic neologism that may be translated as “reciprocal” implicatio,” and that refers specifically to the solidarity of virtues (antakolouthia tôn aretôn [ἀνταϰολουθία τῶν ἀϱετῶν], Diog. Laert. 7.125; Goldschmidt, as a group that would be encompassed by dialectical virtue, immobilizing akolouthia in the absolute present of the wise man. “Implicatio” is, in the final analysis, from then on, the most literal name of the Stoic system. Refs.: Aristotle.  Anal. Pr.. ed. H. Tredennick,  in Organon, Harvard; Goldschmidt, Le système stoïcien et l’idée de temps. Paris: Vrin, Sextus Empiricus. Against the Grammarians, ed. D. L. Blank. Oxford: Oxford. END OF INTERLUDE. Now for “Implication”/“Implicaturum.” Implicatura was used by Sidonius in a letter (that Grice found funny) and used by Grice in seminars on conversational helpfulness at Oxford. Grice sets out the basis of a systematic approach to communication, viz, concerning the relation between a proposition p and a proposition q in a conversational context. The need is felt by Sidonius and Grice for ‘implicaturum,’ tdistinct from “implication,” insofar as “implication” is used for a relation between a proposition p and a proposition q, whereas an “implicaturum” is a relation between this or that statement, within a given context, that results from an EMISSOR having utterered an utterance (thereby explicitly conveying that p) and thereby implicitly conveying and implicating that q. Grice thought the distinction was ‘frequently ignored by Austin,’ and Grice thought it solved a few problems, initially in G. A. Paul’s neo-Wttigensteinian objections to Price’s causal theory of perception (“The pillar box seems red to me; which does not surprise me, seeing that it is red”).  An “implication” is a relation bearing on the truth or falsity of this or that proposition (e. g. “The pillar box seems red” and, say, “The pillar box MAY NOT be red”) whereas an “implicaturum” brings an extra meaning to this or that statement it governs (By uttering “The pillar box seems red” thereby explicitly conveying that the pillar box seems red, the emissor implicates in a cancellable way that the pillar box MAY NOT be red.”). Whenever “implicaturum” is determined according to its context (as at Collections, “Strawson has beautiful handwriting; a mark of his character. And he learned quite a bit in spite of the not precisely angelic temperament of his tutor Mabbott”) it enters the field of pragmatics, and therefore has to be distinguished from a presupposition. Implicatio simpliciter is a relation between two propositions, one of which is the consequence of the other (Quine’s example: “My father is a bachelor; therefore, he is male”). An equivalent of “implication” is “entailment,” as used by Moore. Now, Moore was being witty. ‘Entail’ is derived from “tail” (Fr. taille; ME entaill or entailen = en + tail), and prior to its logical use, the meaning of “entailment” is “restriction,” “tail” having the sense of “limitation.” As Moore explains in his lecture: “An entailment is a limitation on the transfer or handing down of a property or an inheritance. *My* use of ‘entailment’ has two features in common with the Legalese that Father used to use; to wit: the handing down of a property; and; the limitation on one of the poles of this transfer. As I stipulate we should use “entailment” (at Cambridge, but also at Oxford), a PROPERTY is transferred from the antecedent to the con-sequent. And also, normally in semantics, some LIMITATION (or restriction, or ‘stricting,’ or ‘relevancing’) on the antecedent is stressed.” The mutation from the legalese to Moore’s usage explicitly occurs by analogy on the basis of these two shared common elements. Now, Whitehead had made a distinction between a material (involving a truth-value) implication and formal (empty) implication. A material implication (“if,” symbolized by the horseshoe “⊃,” because “it resembles an arrow,” Whitehead said – “Some arrow!” was Russell’s response) is a Philonian implication as defined semantically in terms of a truth-table by Philo of Megara. “If p, q” is false only when the antecedent is true and the con-sequent false. In terms of a formalization of communication, this has the flaw of bringing with it a counter-intuitive feeling of ‘baffleness’ (cf. “The pillar box seems red, because it is”), since a false proposition implies materially any proposition: If the moon is made of green cheese, 2 + 2 = 4. This “ex falso quodlibet sequitur” has a pedigreed history. For the Stoics and the Megarian philosophers, “ex falso quodlibet sequitur” is what distinguishes Philonian implication and Diodorean implication. It traverses the theory of consequence and is ONE of the paradoxes of material implication that is perfectly summed up in these two rules of Buridan: First, if P is false, Q follows from P; Second, if P is true, P follows from Q (Bochenski, History of Formal Logic). A formal (empty) implication (see Russell, Principles of Mathematics, 36–41) is a universal conditional implication: Ɐx (Ax ⊃ Bx), for any x, if Ax, then Bx. Different means of resolving the paradoxes of implication have been proposed. All failed except Grice’s. An American, C. I. Lewis’s “strict” implication (Lewis and Langford, Symbolic Logic) is defined as an implication that is ‘reinforced’ such that it is impossible for the antecedent to be true and the con-sequent false. Unfortunately, as Grice tells Lewis in a correspondence, “your strict implication, I regret to prove, has the same alleged flaw as the ‘material’ implication that your strict implication was meant to improve on. (an impossible—viz., necessarily false—proposition strictly implies any proposition). The relation of entailment introduced by Moore in 1923 is a relation that seems to avoid this or that paradox (but cf. Grice, “Paradoxes of entailment, followed by paradoxes of implication – all conversationally resolved”) by requiring a derivation of the antecedent from the con-sequent. In this case, “If 2 + 2 = 5, 2 + 3 = 5” is false, since the con-sequent is stipulated not be derivable from the antecedent. Occasionally, one has to call upon the pair “entailment”/“implication” in order to distinguish between an implication in qua material implication and an implication in Moore’s usage (metalinguistic – the associated material implication is a theorem), which is also sometimes called “relevant” if not strictc implication (Anderson and Belnap, Entailment), to ensure that the entire network of expressions is covered. Along with this first series of expressions in which “entailment” and “implication” alternate with one another, there is a second series of expressions that contrasts two kinds of “implicaturum,” or ‘implicatura.’ “Implicaturum” (Fr. implicaturum, G. Implikatur) is formed from “implicatio” and the suffix –ture, which expresses, as Grice knew since his Clifton days, a ‘resultant aspect,’ ‘aspectum resultativus’ (as in “signature”; cf. L. temperatura, from temperare).  “Implicatio” may be thought as derived from “to imply” (if not ‘employ’) and “implicaturum” may be thought as deriving from “imply”’s doulet, “to implicate” (from L. “in-“ + “plicare,” from plex; cf. the IE. plek), which has the same meaning. Some mistakenly see Grice’s “implicaturum” as an extension and modification of the concept of presupposition, which differs from ‘material’ implication in that the negation of the antecedent implies the consequent (the question “Have you stopped beating your wife?” presupposes the existence of a wife in both cases). An implicaturum escapes the paradoxes of material implication from the outset. In fact, Grice, the ever Oxonian, distinguishes “at least” two kinds of implicaturum, conventional and non-conventional, the latter sub-divided into non-conventional non-converastional, and non-conventional conversational. A non-conventional non-conversational implicaturum may occur in a one-off predicament. A Conventional implicaturum and a conventional implicaturum is practically equivalent, Strawson wrongly thought, to presupposition prae-suppositum, since it refers to the presuppositions attached by linguistic convention to a lexical item or expression.  E. g. “Mary EVEN loves Peter” has a relation of conventional implicaturum to “Mary loves other entities than Peter.” This is equivalent to: “ ‘Mary EVEN loves Peter’ presupposes ‘Mary loves other entities than Peter.’ With this kind of implicaturum, we remain within the expression, and thus the semantic, field. A conventional implicaturum, however, is surely different from a material implicatio. It does not concern the truth-values. With conversational implicaturum, we are no longer dependent on this or that emissum, but move into pragmatics (the area that covers the relation between statements and contexts. Grice gives the following example: If, in answer to A’s question about how C is getting on in his new job at a bank, B utters, “Well, he likes his colleagues, and he hasn’t been to in prison yet,” what B implicates by the proposition that it is not the case that C has been to prison yet depends on the context. It compatible with two very different contexts: one in which C, naïve as he is, is expected to be entrapped by unscrupulous colleagues in some shady deal, or, more likely, C is well-known by A and B to tend towards dishonesty (hence the initial question). References: Abelard, Peter. Dialectica. Edited by L. M. De Rijk. Assen, Neth.: Van Gorcum, 1956. 2nd rev. ed., 1970. Glossae super Periermeneias. Edited by Lorenzo Minio-Paluello. In TwelfthCentury Logic: Texts and Studies, vol. 2, Abelaerdiana inedita. Rome: Edizioni di Storia e Letteratura, 1958. Anderson, Allan Ross, and Nuel Belnap. Entailment: The Logic of Relevance and Necessity. Vol. 1. Princeton, NJ: Princeton University Press, 1975. Aristotle. De interpretatione. English translation by J. L. Ackrill: Aristotle’s Categories and De interpretatione. Notes by J. L. Ackrill. Oxford: Clarendon, 1963. French translation by J. Tricot: Organon. Paris: Vrin, 1966. Auroux, Sylvain, and Irène Rosier. “Les sources historiques de la conception des deux types de relatives.” Langages 88 (1987): 9–29. Bochenski, Joseph M. A History of Formal Logic. Translated by Ivo Thomas. New York: Chelsea, 1961. Boethius. Aristoteles latinus. Edited by Lorenzo Minio-Paluello. Paris: Descleé de Brouwer, 1965. Translation by Lorenzo Minio-Paluello: The Latin Aristotle. Toronto: Hakkert, 1972. Commentarii in librum Aristotelis Peri hermêneias. Edited by K. Meiser. Leipzig: Teubner, 1877. 2nd ed., 1880. De Rijk, Lambertus Marie. Logica modernorum: A Contribution to the History of Early Terminist Logic. 2 vols. Assen, Neth.: Van Gorcum, 1962–67.  “Some Notes on the Mediaeval Tract De insolubilibus, with the Edition of a Tract Dating from the End of the Twelfth-Century.” Vivarium 4 (1966): 100–103. Giusberti, Franco. Materials for a Study on Twelfth-Century Scholasticism. Naples, It.: Bibliopolis, 1982. Grice, H. P. “Logic and Conversation.” In Syntax and Semantics 3: Speech Acts, edited by P. Cole and J. Morgan, 41–58. New York: Academic Press, 1975. (Also in The Logic of Grammar, edited by D. Davidson and G. Harman, 64–74. Encino, CA: Dickenson, 1975.) Lewis, Clarence Irving, and Cooper Harold Langford. Symbolic Logic. New York: New York Century, 1932. Meggle, Georg. Grundbegriffe der Kommunikation. 2nd ed. Berlin: De Gruyter, 1997. Meggle, Georg, and Christian Plunze, eds. Saying, Meaning, Implicating. Leipzig: Leipziger Universitätsverlag, 2003. Moore, G. E.. Philosophical Studies. London: Kegan Paul, 1923. Rosier, I. “Relatifs et relatives dans les traits terministes des XIIe et XIIIe siècles: (2) Propositions relatives (implicationes), distinction entre restrictives et non restrictives.” Vivarium 24: 1 (1986): 1–21. Russell, Bertrand. The Principles of Mathematics. Cambridge: Cambridge University Press, 1903. implication, a relation that holds between two statements when the truth of the first ensures the truth of the second. A number of statements together imply Q if their joint truth ensures the truth of Q. An argument is deductively valid exactly when its premises imply its conclusion. Expressions of the following forms are often interchanged one for the other: ‘P implies Q’, ‘Q follows from P’, and ‘P entails Q’. (‘Entailment’ also has a more restricted meaning.) In ordinary discourse, ‘implication’ has wider meanings that are important for understanding reasoning and communication of all kinds. The sentence ‘Last Tuesday, the editor remained sober throughout lunch’ does not imply that the editor is not always sober. But one who asserted the sentence typically would imply this. The theory of conversational implicaturum explains how speakers often imply more than their sentences imply. The term ‘implication’ also applies to conditional statements. A material implication of the form ‘if P, then Q’ (often symbolized ‘P P Q’ or ‘P / Q’) is true so long as either the if-clause P is false or the main clause Q is true; it is false only if P is true and Q is false. A strict implication of the form ‘if P, then Q’ (often symbolized ‘P Q’) is true exactly when the corresponding material implication is necessarily true; i.e., when it is impossible for P to be true when Q is false. The following valid forms of argument are called paradoxes of material implication: Q. Therefore, P / Q. Not-P. Therefore, P / Q. The appearance of paradox here is due to using ‘implication’ as a name both for a relation between statements and for statements of conditional form. A conditional statement can be true even though there is no relation between its components. Consider the following valid inference: Butter floats in milk. Therefore, fish sleep at night / butter floats in milk. Since the simple premise is true, the conditional conclusion is also true despite the fact that the nocturnal activities of fish and the comparative densities of milk and butter are completely unreimmediate inference implication 419 4065h-l.qxd 08/02/1999 7:39 AM Page 419 lated. The statement ‘Fish sleep at night’ does not imply that butter floats in milk. It is better to call a conditional statement that is true just so long as it does not have a true if-clause and a false main clause a material conditional rather than a material implication. Strict conditional is similarly preferable to ‘strict implication’. Respecting this distinction, however, does not dissolve all the puzzlement of the so-called paradoxes of strict implication: Necessarily Q. Therefore, P Q. Impossible that P. Therefore, P Q. Here is an example of the first pattern: Necessarily, all rectangles are rectangles. Therefore, fish sleep at night all rectangles are rectangles. ‘All rectangles are rectangles’ is an example of a vacuous truth, so called because it is devoid of content. ‘All squares are rectangles’ and ‘5 is greater than 3’ are not so obviously vacuous truths, although they are necessary truths. Vacuity is not a sharply defined notion. Here is an example of the second pattern: It is impossible that butter always floats in milk yet sometimes does not float in milk. Therefore, butter always floats in milk yet sometimes does not float in milk fish sleep at night. Does the if-clause of the conclusion imply (or entail) the main clause? On one hand, what butter does in milk is, as before, irrelevant to whether fish sleep at night. On this ground, relevance logic denies there is a relation of implication or entailment. On the other hand, it is impossible for the if-clause to be true when the main clause is false, because it is impossible for the if-clause to be true in any circumstances whatever. Speranza, Luigi. Join the Grice Club! Strawson, P. F.. “On Referring.” Mind 59 (1950): 320–44.

implicaturum: a pragmatic relation different from, but easily confused with, the semantic relation of entailment. This concept was first identified, explained, and used by H. P. Grice (Studies in the Way of Words, 1989). Grice identified two main types of implicaturum, conventional and non-conventional (including conversational). An emisor is said to conversationally implicate that p in uttering x, provided that, although p is NOT logically implied by what the emisor explicitly communicates, the assumption that the emisor is attempting cooperative communication warrants inferring that the emisor is communicating that p. If Grice utters “There is a garage around the corner” in response to Strawson’s saying, “I am out of gas,” Grice conversationally implicates that the garage is open and has gas to sell. Grice identifies several conversational maxims to which cooperative conversationalists may be expected to conform, and which justify inferences about what the emisor implicates. In the above example, the implicaturums are due to the maxim of conversational relevance. Another important maxim is the maxim of conversational fortitude  (“Make your contribution as informatively strong as is required”). Among implicatura due to the Maxim of conversational fortitude is the scalar implicaturum, wherein the utterance contains an element that is part of a quantitative scale. Utterance of such a sentence conversationally implicates that the emisor does not believe related propositions higher on the scale of conversational fortitude or informativeness. E. g. an emisor who says, “Some of the zoo animals escaped,” implies that he does not believe that that most of the zoo animals escaped, or that every animal of the zoo animals escaped. Unlike a conversational implicaturum, a conventional implicaturum is due solely to the semantics of the expression. An emisor is said by Grice to conventionally imply that p, if the semantics of the expression commits the emisor to p, even though what the emisor explicitly communicates does not entail that p. Thus, uttering, as the Tommies did during the Great War, “She was poor but she was honest” a Tommy implicates, but does not explicitly convey, that there is a contrast between her poverty and her honesty.

impositum: a property of terms resulting from a convention to designate something. A term is not a mere noise but a significant sound. A term designating extralinguistic entities, such as ‘tree’, ‘stone’, ‘blue’, and the like, are classified by the tradition since Boethius as terms of “prima impositio,” first imposition. A term designating another term or other communicative items, such as ‘noun’, ‘declension’, and the like, is classified as terms of ‘secunda imposition,’ second imposition. The distinction between a terms of ‘prima impositio’ and ‘secunda impositio’ belongs to the realm of written and spoken language, while the parallel distinction between terms of first and second ‘intentio’ belongs to the realm of the soul. A ‘prima intentio’ (intentio re re), frst intention is, broadly, thoughts about trees, stones, colours, etc. A ‘seconda intention’ (intention de sensu), second intention, is a thought about a first intention. Refs.: H. P. Grice, “De sensu implicaturum.”

infinitum -- cantor, G. Grice thought that “I know there are infinitely many stars” is a stupid thing to say -- one of a number of late nineteenthcentury philosophers including Frege, Dedekind, Peano, Russell, and Hilbert who transformed both mathematics and the study of its philosophical foundations. The philosophical import of Cantor’s work is threefold. First, it was primarily Cantor who turned arbitrary collections into objects of mathematical study, sets. Second, he created a coherent mathematical theory of the infinite, in particular a theory of transfinite numbers. Third, linking these, he was the first to indicate that it might be possible to present mathematics as nothing but the theory of sets, thus making set theory foundational for mathematics. This contributed to the Camus, Albert Cantor, Georg 116   116 view that the foundations of mathematics should itself become an object of mathematical study. Cantor also held to a form of principle of plenitude, the belief that all the infinities given in his theory of transfinite numbers are represented not just in mathematical or “immanent” reality, but also in the “transient” reality of God’s created world. Cantor’s main, direct achievement is his theory of transfinite numbers and infinity. He characterized as did Frege sameness of size in terms of one-to-one correspondence, thus accepting the paradoxical results known to Galileo and others, e.g., that the collection of all natural numbers has the same cardinality or size as that of all even numbers. He added to these surprising results by showing 1874 that there is the same number of algebraic and thus rational numbers as there are natural numbers, but that there are more points on a continuous line than there are natural or rational or algebraic numbers, thus revealing that there are at least two different kinds of infinity present in ordinary mathematics, and consequently demonstrating the need for a mathematical treatment of these infinities. This latter result is often expressed by saying that the continuum is uncountable. Cantor’s theorem of 2 is a generalization of part of this, for it says that the set of all subsets the power-set of a given set must be cardinally greater than that set, thus giving rise to the possibility of indefinitely many different infinities. The collection of all real numbers has the same size as the power-set of natural numbers. Cantor’s theory of transfinite numbers 0 97 was his developed mathematical theory of infinity, with the infinite cardinal numbers the F-, or aleph-, numbers based on the infinite ordinal numbers that he introduced in 0 and 3. The F-numbers are in effect the cardinalities of infinite well-ordered sets. The theory thus generates two famous questions, whether all sets in particular the continuum can be well ordered, and if so which of the F-numbers represents the cardinality of the continuum. The former question was answered positively by Zermelo in 4, though at the expense of postulating one of the most controversial principles in the history of mathematics, the axiom of choice. The latter question is the celebrated continuum problem. Cantor’s famous continuum hypothesis CH is his conjecture that the cardinality of the continuum is represented by F1, the second aleph. CH was shown to be independent of the usual assumptions of set theory by Gödel 8 and Cohen 3. Extensions of Cohen’s methods show that it is consistent to assume that the cardinality of the continuum is given by almost any of the vast array of F-numbers. The continuum problem is now widely considered insoluble. Cantor’s conception of set is often taken to admit the whole universe of sets as a set, thus engendering contradiction, in particular in the form of Cantor’s paradox. For Cantor’s theorem would say that the power-set of the universe must be bigger than it, while, since this powerset is a set of sets, it must be contained in the universal set, and thus can be no bigger. However, it follows from Cantor’s early 3 considerations of what he called the “absolute infinite” that none of the collections discovered later to be at the base of the paradoxes can be proper sets. Moreover, correspondence with Hilbert in 7 and Dedekind in 9 see Cantor, Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, 2 shows clearly that Cantor was well aware that contradictions will arise if such collections are treated as ordinary sets. 

prædicatum: Grice on the praedicatum/impraedicatum distinction – an impredicative definition is the definition of a concept in terms of the totality to which it belongs. Whitehead and Russell, in their “Principia Mathematica” introduce ‘im-predicative’ (earlier, ‘non-predicative,’ which Grice prefers) prohibiting an impredicative definition from conceptual analysis, on the grounds that an impredicative definition entails (to use Moore’s jargon) a paradox – which Grice loves. An impredicative definition of the set R of all sets that are not members of themselves leads to the self-contradictory conclusion that R is a member of itself if and only if it is not a member of itself. In Grice’s rewrite: “Austin’s paradoxical dream was to create a ‘class’ each of whose member was such that his class had no other member.” To avoid an antinomy of this kind in the formalization of logic, Whitehead and Russell first implement in their ramified type theory the vicious circle principle, that no whole (totum) may contain parts (pars) that are definable only in terms of that whole (totum). The limitation of ramified type theory is that without use of an impredicative definition it is impossible to quantify over every item, but only over every item of a certain order or type. Without being able to quantify over every item generally, many of the most important definitions and theorems of classical philosophy cannot be formulated. Whitehead and Russell for this reason later abandoned ramified in favour of simple type theory, which avoids a logical paradox without outlawing an impredicative definition by forbidding the predication of terms of any type (object, property and relation, higher-order propertiy and relations of properties and relations, etc.) to terms of the same type.

correctum: there’s‘corrigibility’ (=  correctum) and ‘incorrigibility’ – “The implicaturum is that something is incorrigibile it cannot be corrected – but Chisholm never explies ‘by whom’”! (Grice uses ‘exply’ as opposite of ‘imply’).  Who is corrigible? The emissor. “I am sorry I have to tell you you are wrong.” On WoW: 142, Grice refers to the ‘authority’ of the utterer as a ‘rational being’ to DEEM that an M-intention is an antecedent condition for his act of meaning. Grice uses ‘privilege’ as synonym for ‘authority’ here. But not in the phrase ‘privileged access.’ His point is not so much about the TRUTH (which ‘incorrigibility’ suggests), but about the DEEMING. It is part of the authority or privilege of the utterer as rational to provide an ACCEPTABLE assignment of an M-intention behind his utterance.

commensuratum:  There’s commensurability and there’s incommensurability – “But Protagoras never explies what makes man commensurable – only implies it!” In the philosophy of science, the property exhibited by two scientific theories provided that, even though they may not logically contradict one another, they have reference to no common body of data. Positivist and logical empiricist philosophers of science like Carnap had long sought an adequate account of a theoryneutral language to serve as the basis for testing competing theories. The predicates of this language were thought to refer to observables; the observation language described the observable world or (in the case of theoretical terms) could do so in principle. This view is alleged to suffer from two major defects. First, observation is infected with theory – what else could specify the meanings of observation terms except the relevant theory? Even to perceive is to interpret, to conceptualize, what is perceived. And what about observations made by instruments? Are these not completely constrained by theory? Second, studies by Kuhn, Paul Feyerabend, and others argued that in periods of revolutionary change in science the adoption of a new theory includes acceptance of a completely new conceptual scheme that is incommensurable with the older, now rejected, theory. The two theories are incommensurable because their constituent terms cannot have reference to a theory-neutral set of observations; there is no overlap of observational meaning between the competitor theories; even the data to be explained are different. Thus, when Galileo overthrew the physics of Aristotle he replaced his conceptual scheme – his “paradigm” – with one that is not logically incompatible with Aristotle’s, but is incommensurable with it because in a sense it is about a different world (or the world conceived entirely differently). Aristotle’s account of the motion of bodies relied upon occult qualities like natural tendencies; Galileo’s relied heavily upon contrived experimental situations in which variable factors could be mathematically calculated. Feyerabend’s even more radical view is that unless scientists introduce new theories incommensurable with older ones, science cannot possibly progress, because falsehoods will never be uncovered. It is an important implication of these views about incommensurability that acceptance of theories has to do not only with observable evidence, but also with subjective factors, social pressures, and expectations of the scientific community. Such acceptance appears to threaten the very possibility of developing a coherent methodology for science.

consistens: “There’s consistens, and there’s inconsistens.” – H. P. Grice. The inconsistent triad, most generally, any three propositions such that it cannot be the case that all three of them are true. More narrowly, any three categorical propositions such that it cannot be the case that all three of them are true. A categorical syllogism is valid provided the three propositions that are its two premises and the negation (contradiction) of its conclusion are an inconsistent triad; this fact underlies a test for the validity of categorical syllogisms, which test are thus called by Grice the “method of” the inconsistent triad.

dependens – independens -- independence results, proofs of non-deducibility. Any of the following equivalent conditions may be called independence: (1) A is not deducible from B; (2) its negation - A is consistent with B; (3) there is a model of B that is not a model of A; e.g., the question of the non-deducibility of the parallel axiom from the other Euclidean axioms is equivalent to that of the consistency of its negation with them, i.e. of non-Euclidean geometry. Independence results may be not absolute but relative, of the form: if B is consistent (or has a model), then B together with - A is (or does); e.g. models of non-Euclidean geometry are built within Euclidean geometry. In another sense, a set B is said to be independent if it is irredundant, i.e., each hypothesis in B is independent of the others; in yet another sense, A is said to be independent of B if it is undecidable by B, i.e., both independent of and consistent with B. The incompleteness theorems of Gödel are independence results, prototypes for many further proofs of undecidability by subsystems of classical mathematics, or by classical mathematics as a whole, as formalized in ZermeloFraenkel set theory with the axiom of choice (ZF ! AC or ZFC). Most famous is the undecidability of the continuum hypothesis, proved consistent relative to ZFC by Gödel, using his method of constructible sets, and independent relative to ZFC by Paul J. Cohen, using his method of forcing. Rather than build models from scratch by such methods, independence (consistency) for A can also be established by showing A implies (is implied by ) some A* already known independent (consistent). Many suitable A* (Jensen’s Diamond, Martin’s Axiom, etc.) are now available. Philosophically, formalism takes A’s undecidability by ZFC to show the question of A’s truth meaningless; Platonism takes it to establish the need for new axioms, such as those of large cardinals. (Considerations related to the incompleteness theorems show that there is no hope even of a relative consistency proof for these axioms, yet they imply, by way of determinacy axioms, many important consequences about real numbers that are independent of ZFC.) With non-classical logics, e.g. second-order logic, (1)–(3) above may not be equivalent, so several senses of independence become distinguishable. The question of independence of one axiom from others may be raised also for formalizations of logic itself, where many-valued logics provide models.

determinatum: There’s the determinatum and there’s the indeeterminatum – “And then there’s ‘indeterminacy.”” “A determinatum is like a definitum, in that a ‘term’ is like the ‘end’ – “Thus, I am a Mercian, from Harborne.” “The Mericans were thus called because the lived at the end of England.” “Popper, who doesn’t know the first thing about this, prefers, ‘demarcatum’, which is cognate with “mercian.’” Grice was always cautious and self-apologetic. “I’m not expecting that you’ll find this to be a complete theory of implication, but that was not my goal, and the endeavour should be left for another day, etc.” But consider the detail into which he, like any other philosopher before, went when it came to what he called the ‘catalyst’ tests or ideas or tests or ideas for the implicaturum. In “Causal Theory” there are FOUR ideas. It is good to revise the treatment in “Causal.” He proposes two ideas with the first two examples and two further ideas with the two further examples. Surely his goal is to apply the FOUR ideas to his own example of the pillar box. Grice notes re: “You have not ceased eating iron” – the cxample is “a stock case of what is sometimes called " prcsupposition " and it is often held that here 1he truth of what is irnplicd is a necessary condition of the original statement's beirrg cither true or false.” So the first catalyst in the first published version concerns the value, or satisfactory value. This will be retained and sub-grouped in Essay II. “It is often held” Implicture: but often not, and trust me I won’t. “that here the truth of what is implied [implicated in the negative, entailed in the affirmative] is a necessary condition of the original statement's being either true or false.” So the first catalyst in the first published version concerns the value, or satisfactory value. This will be retained and sub-grouped in Essay II. “This might be disputed, but it is at least arguable that it is so, and its being arguable might be enough to distinguish this type of case from others.” So he is working on a ‘distinctive feature’ model. And ‘feature’ is exactly the expression he uses in Essay II. He is looking for ‘distinctive features’ for this or that implication. When phonologists speak of ‘distinctive feature’ they are being philosophical or semioticians.“I shall however for convenience assume that the common view mentioned is correct.”“This consideration clearly distinguishes “you have not ceased eating iron” from [a case of a conventional implicaturum] “poor BUT honest.”“Even if the implied proposition were false, i.e. if there were no reason in the world to contrast poverty with honesty either in general or in her case, the original statement COULD still be false.” “She [is]  poor but she [is] honest” would be false if for example she were rich and dishonest.”“One might perhaps be less comfortable about assenting to its TRUTH if the implied contrast did not in fact obtain; but the possibility of falsity is enough for the immediate purpose.”“My next experiment [test, litmus idea – that he’ll apply as one of the criteria to provide distinctive features for this or that implicaturum, with a view to identify the nature of the animal that a conversational implicaturum is] on these examples is to ask what it is in each case which could properly be said to be the vehicle of implication (to do the implying).”In Essay II, since he elaborates this at an earlier stage than when he is listing the distinctive features, he does not deal much. It is understood that in Essay II by the time he is listing the distinctive features, the vehicle is the UTTERER. But back in “Causal,” he notes: “There are AT LEAST FOUR candidates, not necessarily mutually exclusive.”“Supposing someone to have ‘uttered’ one or other of [the] sample sentences, we may ask whether the vehicle of implication would be (FIRST) WHAT the emissor communicated (or asserted or stated or explicitly conveyed), or (SECOND) the emissor himself ("Surely you’re not  implying that ….’ ) or (THIRD) the utterance  (FOURTH) his communicating, or explicitly conveying that (or again his explicitly conveying that in that way); or possibly some plurality of these items.”“As regards the first option for the vehicle, ‘what the emissor has explicitly conveyed,’ Grice takes it that “You have not ceased eating iron” and “Poor but honest” may differ.It seems correct for Grice to say in the case of “eating iron” that indeed it is the case that it is what he emissor explicitly conveys which implies that Smith has been eating iron.On the other hand, Grice feels it would be ‘incorrect,’ or improper, or bad, or unnatural or artificial, to say in the case of “poor but honest” that it is the case. Rather it is NOT the case that  it is WHAT the emissor explicitly conveys which implies that there is a contrast between, e. g., honesty and poverty.”“A sub-test on which Grice would rely is the following.If accepting that the conventional implicaturum holds (contrast between honesty and poverty) involves the emissor in accepting an hypothetical or conditional ‘if p, q,’ where 'p’ represents the original statement (“She [is] poor and she [is] honest) and 'q' represents what is implied (“There is a contrast between honesty and poverty”), it is the case that it is what the emissor explicitly conveys which is a (or the) vehicle of implication. If that chain of acceptances does not hold, it is not. To apply this rule to the “eat iron” and “poor but honest”, if the emissor accepts the implication alleged to hold in the case of “eat iron”, I should feel COMPELLED (forced, by the force of entailment) to accept the conditional or hypothetical "If you have not ceased eating iron, you may have never started.”[In “Causal,” Grice has yet not stressed the asymmetry between the affirmative and the negative in alleged cases of presupposition. When, due to the success of his implicaturum, he defines the presuppositum as a form of implicaturum, he does stress the asymmetry: the entailment holds for the affirmative, and the implicaturum for the negative). On the other hand, when it comes to a CONVENTIONAL implicaturum (“poor but honest”) if the emissor accepted the alleged implication in the case of “poor but honest”, I should NOT feel compelled to accept the conditional or hypothetical "If she was poor but honest, there is some contrast between poverty and honesty, or between her poverty and her honesty." Which would yield that in the presuppositum case, we have what is explicitly conveyed as a vehicle, but not in the case of the conventional implicaturum.The rest of the candidates (Grice lists four and allows for a combination) can be dealt with more cursorily.As regards OPTION II (second):Grice should be inclined to say with regard to both “eat iron” and “poor but honest” that the emissor could be said to have implied whatever it is that is irnplied.As regards Option III (third: the utterance): In the case of “poor but honest” it seems fairly clear that the utterance could be said, if metabolically, and animistically, to ‘imply’ a contrast.It is much less clear whether in the case of “eat iron” the utterance could be said to ‘imply’ that Smith has been eating iron.As for option IV, in neither case would it be evidently appropriate (correct, natural) to speak of the emissor’s explicitly conveying that, or of his explicitly conveying that in that way, as ‘implying’ what is implied. A third catalyst idea with which Grice wish to assail my two examples is really a TWIN idea, or catalyst, or test [That’s interesting – two sides of the same coin] that of the detachability or cancellability of the implication. Consider “eat iron.”One cannot find an alternative utterance which could be used to assert explicitly just what the utterance “Smith has not ceased from eating iron" might be used to convey explicitly, such that when this alternative utterance is used the implication that Smith never started eating iron is absent. Any way of (or any utterance uttered with a view to) conveying explicitly what is explicitly conveyed in (1) involves the implication in question. Grice expresses this fact – which he mentioned in seminars, but this is the first ‘popularisation’ -- by saying that in the case of (l) the implication is NOT detachable FROM what is asserted (or simpliciter, is not detachable). Furthermore, and here comes the twin of CANCELLABILITY: one cannot take any form of words for which both what is asserted and what is implied is the same as for (l), AND THEN ADD a further clause withholding commitment from what would otherwise be implied, with the idea of ANNULLING THE IMPLICATURUM *without* ANNULLING annulling the EXPLICITUM.  One cannot intelligibly say " Smith has left off beating his wife but I do not mean to imply that he has been beating her." But one surely can intelligibly say, “You have not ceased eating iron because you never started.”While Grice uses “Smith,” the sophisma (or Griceisma) was meant in the second person, to test the tutee’s intelligence (“Have you stopped beating your dog?”). The point is that the tutee will be offended – whereas he shouldn’t, and answer, “I never started, and I never will.”Grice expresses this fact by saying that in the case of ‘eat iron’ the implication is not cancellable or annullable (without cancelling or annulling the assertion). If we turn to “poor but honest” we find, Grice thinks, that there is quite a strong case for saying that here the implication IS detachable. Therc sccms quite a good case for maintaining that if, instead of saying " She is poor but she is honcst " I were to say, alla Frege, without any shade, " She is poor AND she is honcst", I would assert just what I would havc asscrtcct ii I had used thc original senterrce; but there would now be no irnplication of a contrast between e.g', povery and honesty. Of course, this is not a philosophical example, and it would be good to revise what Frege thought about ‘aber.’ By the time Grice is lecturing “Causal Theory” he had lectured for the Logic Paper for Strawson before the war, so Whitehead and Russell are in the air.Surely in Anglo-Saxon, the contrast is maintained, since ‘and’ means ‘versus.’“She is poor contra her being honest.”Oddly, the same contrariety is present in Deutsche, that Frege speaks, with ‘UND.”It’s different with Roman “et.” While Grecian ‘kai,’ even Plato thought barbaric!The etymology of ‘by-out’ yields ‘but.’So Grice is thinking that he can have a NEUTRAL conjoining – but ‘and’ has this echo of contrariety, which is still present in ‘an-swer, i. e. and-swear, to contradict. Perhaps a better neutral version would be. Let’s start with the past version and then the present tense version.“She was pooo-ooor, she was honest, and her parents were the same, till she met a city feller, and she lost her honest name.”In terms of the concepts CHOSEN, the emissor wants to start the ditty with pointing to the fact that she is poor – this is followed by stating that she is honest. There’s something suspicious about that.I’m sure a lady may feel offended without the ‘and’ OR ‘but’ – just the mere ‘succession’ or conjoining of ‘poor’ as pre-ceding the immediate ‘honest’ ‘triggers’ an element of contrast. The present tense seems similar: “She is poooor, she is honest, and her parents are the same, but she’ll meet a city feller, and she’ll lose her honest name.”The question whether, in thre case of ‘poor but honest,’ the implication is cancellable, is slightly more cornplex, which shouldn’t if the catalysts are thought of as twins.There is a way in which we may say that it is not cancellable, or annullable.Imagine a Tommy marching  and screaming: “She is poor but she is honest,”“HALT!” the sargent shouts.The Tommy catches the implicaturum:“though of course, sir, I do not mean to imply, sir, that there is any contrast, sir, between her poverty, sir, and her honesty, sir.”As Grice notes, this would be a puzzling and eccentric thing for a Tommy to engage in.And though the sargent might wish to quarrel with the tommy (Atkins – Tommy Atkins is the name”), an Oxonian philosopher should NOT go so far as to say that the tommy’s utterance is unintelligible – or as Vitters would say, ‘nunsense.’The sargent should rather suppose, or his lieutenant, since he knows more, that private Tommy Atkins has adopted a “most pecooliar” way of conveying the news that she was poor and honest.The sargent’s argument to the lieu-tenant:“Atkins says he means no disrespect, sir, but surely, sir, just conjoining poverty and honesty like that makes one wonder.”“Vitters: this is a Cockney song! You’re reading too much into it!”“Cockney? And why the citty feller, then – aren’t Cockneys citty fellers. I would rather, sir, think it is what Sharp would call a ‘sharp’ folk, sir, song, sir.’ The fourth and last test Grice imposes on his examples is to ask whether we would be inclined to regard the fact that the appropriate (or corresponding, since they are hardly appropriate – either of them! – Grice changes the tune as many Oxford philosophers of ordinary language do when some female joins the Union) implication is present as being a matter of the, if we may be metabolic and animistic, ‘meaning’ of some particular word or phrase occurring in the sentences in question. Grice is aware and thus grants that this may not be always a very clear or easy question to answer.Nevertheless, Grice risks the assertion that we would be fairly happy and contented to say that, as regards ‘poor but honest,’ the fact that the implication obtains is a matter of the ‘meaning’ of 'but ' – i. e. what Oxonians usually mean when they ‘but.’So far as “he has not ceased from…’ is concerned we should have at least some inclination to say that the presence of the implication is a matter of the, metabolically, ‘meaning’ of some of the words in the sentence, but we should be in some difficulty when it came to specifying precisely which this word, or words are, of which this is true. Well, it’s semantics. Why did Roman think that it was a good thing to create a lexeme, ‘cease.’“Cease” means “stop,” or ‘leave off.”It is not a natural verb, like ‘eat.’A rational creature felt the need to have this concept: ‘stop,’ ‘leave off,’ ‘cease.’The communication-function it serves is to indicate that SOMETHING has been taken place, and then this is no longer the case.“The fire ceased,” one caveman said to his wife.The wife snaps back – this is the Iron Age:“Have you ceased eating iron, by the way, daa:ling?”“I never started!”So it’s the ‘cease’ locution that does the trick – or equivalents, i.e. communication devices by which this or that emissor explicitly convey more or less the same thing: a halting of some activity.Surely the implication has nothing to do with the ‘beat’ and the ‘wife.’After third example (‘beautiful handwriting) introduced, Grice goes back to IDEA OR TEST No. 1 (the truth-value thing). Grice notes that it is plain that there is no case at all for regarding the truth of what is implied here (“Strawson is hopeless at philosophy”) as a pre-condition of the truth or falsity of what the tutor has asserted.A denial of the truth of what is implied would have no bearing at all on whether what I have asserted is true or false. So ‘beautiful handwring’ is much closer to ‘poor but honest’ than ‘cease eating iron’ in this respect. Next, as for the vehicle we have the at least four options and possible combinations.The emissor, the tutor, could certainly be said to have implied that Strawson is hopeless (provided that this is what the tutor intended to ‘get across’) and the emissor’s, the tutor’s explicitly saying that (at any rate the emissor’s saying that and no more) is also certainly a vehicle of implication. On the other hand the emissor’s words and what the emissor explicitly conveys are, Grice thinks, not naturally here characterised as the ‘vehicle’ of implication. “Beautiful handwriting” thus differs from BOTH “don’t cease eating iron” and “poor but honest” – so the idea is to have a table alla distinctive features, with YES/NO questions answered for each of the four implication, and the answers they get.As for the third twin, the result is as expected: The implication is cancellable but not detachable. And it looks as if Grice created the examples JUST to exemplify those criteria.If the tutor adds, 'I do not of course mean to imply that Strawson is no good at philosophy” the whole utterance is intelligible and linguistically impeccable, even though it may be extraordinary tutorial behaviour – at the other place, not Oxford --.The tutor can no longer be said to have, or be made responsible for having implied that Strawson was no good, even though perhaps that is what Grice’s colleagues might conclude to be the case if Grice had nothing else to say. The implication is not however, detachable.Any other way of making, in the same context of utterance, just the assertion I have made would involve the same implication.“His calligraphy is splendid and he is on time.”“Calligraphy splendid,” Ryle objected. “That’s slightly oxymoronic, Grice – ‘kallos agathos’”Finally, for TEST No. 4, ‘meaning’ of expression? The fact that the implication holds is surely NOT a matter of any particular word or phrase within the sentence which I have uttered.It is just the whole sentence. Had he gone tacit and say,“Beautiful handwriting!”Rather than“He has beautiful handwriting.”The implication SEEMS to be a matter of two particular words: the handwriting word, viz. ‘handwriting.’ And the ‘beautiful’ word, i. e. ‘beautiful.’Any lexeme expressing same concept, ‘Calligraphy unique!’would do the trick because this is damn by faint praise, or suggestio falsi, suppressio veri. So in this respect “Beautiful handwring” is certainly different from “Poor but honest” and, possibly different from “Don’t cease to eat iron!”One obvious fact should be mentioned before one passes to the fourth example (“kitchen or bedroom”).This case of implication is unlike the others in that the utterance of the sentence "Strawson has beautiful handwriting" does not really STANDARDLY involve the implication here attributed to it (but cf. “We should have lunch together sometime” meaning “Get lost” – as Grice said, “At Oxford, that’s the standard – that’s what the ‘expression’ “means”); it requires a special context (that it should be uttered at Collections) to attach the implication to its utterance. More generally: it requires a special scenario (one should avoid the structuralist Derrideian ‘context’ cf. Grice, “The general theory of context”). If back in the house, Mrs. Grice asks, “He has beautiful handwriting,” while not at Collections, the implicaturum would hold. Similarly at the “Lamb and Flag,” or “Bird and Baby.”But one gets Grice’s point. The scenario is one where Strawson is being assessed or evaluated AS A PHILOSOPHER. Spinoza’s handwriting was, Stuart Hampshire said, “terrible – which made me wonder at first whether I should actually waste my time with him.”After fourth and last example is introduced (“kitchen or bedroom”): in the case of the Test No. I (at least four possible vehicles) one can produce a strong argument in favour of holding that the fulfllment of the implication of the speaker's ignorance (or that he is introducing “or” on grounds other than Whitehead’s and Russell’s truth-functional ones) is not a precaution (or precondition) of the truth or falsity of the disjunctive statement. Suppose that the emissor KNOWS that his wife IS in the KITCHEN, that the house has only two rooms, and no passages. Even though the utterer knows that his wife is in the kitchen (as per given), the utterer can certainly still say truly (or rather truthfully) "She is IN THE HOUSE.”SCENARIOA: Where is your wife? ii. Where in your house is your wife?B: i. In the kitchen. ii. In the bedroom. iiia. She’s in the house, don’t worry – she’s in the house, last time I checked. iii. In the HOUSE (but inappropriate if mentioned in the question – unless answered: She’s not. iv. In the kitchen or in the bedroom (if it is common ground that the house only has two rooms there are more options) vi. v. I’m a bachelor.  vi. If she’s not in the bedroom, she is in the kitchen. vii. If she’s not in the kitchen, she’s in the bedroom. viii. Verbose but informative: “If she’s not in the bedroom she’s in the kitchen, and she’s not in the kitchen” Or consider By uttering “She is in the house,” the utterer is answering in a way that he is merely not being as informative as he could bc if need arose.  But the true proposition [cf. ‘propositional complex’] that his wife is IN THE HOUSE together with the true proposition that ‘THE HOUSE’ consists entirely of a ‘kitchen’ and a ‘bedroom,’ ENTAIL or yield the proposition that his wife is in the kitchen or in the bedroom. But IF to express the proposition p (“My wife is in the house, that much I can tell”) in certain circumstances (a house consisting entirely of a kitchen and a bedroom – an outback bathroom which actually belongs to the neighbour – cf. Blenheim) would be to speak truly, and p (“My wife is, do not worry, in the house”) togelher with another true proposition – assumed to be common ground, that the house consists entirely of a kitchen and a bedroom -- entails q (“My wife is in the kitchen OR in the bedroom”), surely to express what is entailed (“My wife is in the kitchen or in the bedroom”) in the same circvmstances must be, has to be to speak truly.  So we have to take it that the disjunctive statement – “kitchen or bedroom” -- does not fail to be TRUE or FALSE if the implied ignorance (or the implied consideration that the utterer is uttering ‘or’ on grounds other than the truth-functional ones that ‘introduce’ “or” for Gentzen) is in fact not realized, i. e. it is false. Secondly, as for Test No. 2 (the four or combo vehicles), Grice thinks it is fairly clear that in this case, as in the case of “beautiful handwriting”, we could say that the emissor had implies that he did not know (or that his ground is other than truth-functional – assuming that he takes the questioner to be interested in the specific location – i. e. to mean, “where IN THE HOUSE is your wife?”) and also that his conveying explicilty that (or his conveying explicitly that rather than something else, viz, in which room or where in the house she is, or ‘upstairs,’ or ‘downstairs,’ or ‘in the basement,’ or ‘in the attic,’ ‘went shopping,’ ‘at the greengrocer’ – ‘she’s been missing for three weeks’) implied that he did not know in which one of the two selected rooms his wife is ‘resident’ (and that he has grounds other than Gentzen’s truth-functional ones for the introduction of ‘or.’). Thirdly, the implication (‘kitchen or bedroom’) is in a way non-detachable, in that if in a given context the utterance of the disjunctive sentence would involve the implication that the emissor did not know in which room his his wife was (or strictly, that the emissor is proceeding along non-truth-functional grounds for the introduction of ‘or,’ or even more strictly still, that the emissor has grounds other than truth-functional for the uttering of the disjunction), this implication would also be involved in the utterance of any other form of words which would make the same disjunctive assertion (e.g., "Look, knowing her, the alternatives are she is either preparing some meal in the kitchen or snoozing in the bedroom;” “One of the following things is the case, I’m pretty confident. First thing: she is in the kitchen, since she enjoys watching the birds from the kitchen window. Second thing: she is in the bedroom, since she enjoys watching birds from the bedroom window.” Etymologically, “or” is short for ‘other,’ meaning second. So a third possibility: “I will be Anglo-Saxon: First, she is the kitchen. Second, she is in the bedroom.” “She is in the kitchen UNLESS she is in the bedroom”“She is in the kitchen IF SHE IS NOT in the bedroom.”“Well, it is not the case that she is in the KITCHEN *AND* in the bedroom, De Morgan!” She is in the kitchen, provided she is not in the bedroom” “If she is not in the kitchen, she is in the bedroom” “Bedroom, kitchen; one of the two.” “Kitchen, bedroom; check both just in case.”“Sleeping; alternatively, cooking – you do the maths.”“The choices are: bedroom and kitchen.”“My choices would be: bedroom and kitchen.”“I would think: bedroom? … kitchen?”“Disjunctively, bedroom – kitchen – kitchen – bedroom.”“In alternation: kitchen, bedroom, bedroom, kitchen – who cares?”“Exclusively, bedroom, kitchen.”ln another possible way, however, the implication could perhaps bc said to BE indeed detachable: for there will be some contexts of utterance (as Firth calls them) in which the ‘normal’ implication (that the utterer has grounds other than truth-functional for the utterance of a disjunction) will not hold.Here, for the first time, Grice brings a different scenario for ‘or’:“Thc Secretary of the Aristotelian Society, announcing ‘Our coming symposium will be in Oxford OR not take place at all” perhaps does not imply that he is has grounds other than truth-functional for the utterance of the disjunction. He is just being wicked, and making a bad-taste joke. This totally extraneous scenario points to the fact that the implication of a disjunction is cancellable.Once we re-apply it to the ‘Where in the hell in your house your wife is? I hear the noise, but can’t figure!’ Mutatis mutandi with the Secretary to The Aristotelian Socieety, a man could say, “My wife is in the kitchen or in the bedroorn.”in circumstances in which the implication (that the man has grounds other than truth-functional for the uttering of the disjunction) would normally be present, but he is not being co-operative – since one doesn’t HAVE to be co-operative (This may be odd, that one appeals to helpfulness everywhere but when it comes to the annulation!).So the man goes on, “Mind you, I am not saying that I do not know which.”This is why we love Grice. Why I love Grice. One would never think of finding that sort of wicked English humour in, say Strawson. Strawson yet says that Grice should ‘let go.’ But to many, Grice is ALWAYS humorous, and making philosophy fun, into the bargain, if that’s not the same thing. Everybody else at the Play Group (notably the ones Grice opposed to: Strawson, Austin, Hare, Hampshire, and Hart) would never play with him. Pears, Warnock, and Thomson would!“Mind you, I am not saying that I do not know which.”A: Where in the house is your wife? I need to talk to her.B: She is in the kitchen – or in the bedroom. I know where she is – but since you usually bring trouble, I will make you decide so that perhaps like Buridan’s ass, you find the choice impossible and refrain from ‘talking’ (i. e. bringing bad news) to her.A: Where is your wife? B: In the kitchen or in the bedroom. I know where she is. But I also know you are always saying that you know my wife so well. So, calculate, by the time of the day – it’s 4 a.m – where she could be. A: Where is your wife? B: In the bedroom or in the kitchen. I know where she is – but remember we were reading Heidegger yesterday? He says that a kitchen is where one cooks, and a bedroom is where one sleeps. So I’ll let you decide if Heidegger has been refuted, should you find her sleeping in the kitchen, or cooking in the bedroom.A: Where is your wife? B: In the kitchen or the bedroom. I know where she is. What you may NOT know, is that we demolished the separating wall. We have a loft now. So all I’ll say is that she may be in both!  All this might be unfriendly, unocooperative, and perhaps ungrammatical for Austen [Grice pronounced the surname so that the Aristotelian Society members might have a doubt] – if not Vitters, but, on the other hand, it would be a perfectly intelligible thing for a (married) man to say. We may not even GO to bachelors. Finally, the fact that the utterance of the disjunctive sentence normally or standardly or caeteris paribus involves the implication of the emissor's ignorance of the truth-values of the disjuncts (or more strictly, the implication of the emissor’s having grounds other than truth-functional for the uttering of the disjunctive) is, I should like to say, to be ‘explained’ – and Grice is being serious here, since Austin never cared to ‘explain,’ even if he could -- by reference to a general principle governing – or if that’s not too strong, guiding – conversation, at least of the cooperative kind the virtues of which we are supposed to be exulting to our tuttees. Exactly what this principle we should not go there. To explain why the implicaturum that the emissor is having grounds other than truth-functional ones for the utterance of a disjunction one may appeal to the emissor being rational, assuming his emissee to be rational, and abiding by something that Grice does NOT state in the imperative form, but using what he calls a Hampshire modal (Grice divides the modals as Hampshire: ‘should,’ the weakest, ‘ought’ the Hare modal, the medium, and ‘must,’ Grice, the stronges)"One, a man, a rational man, should not make conversational move communicating ‘p’ which may be characterised (in strict terms of entailment) as weaker (i.e. poor at conversational fortitude) rather than a stronger (better at conversational fortitude) one unless there is a good reason for so doing." So Gentzen is being crazey-basey if he thinks:p; therefore, p or q.For who will proceed like that?“Or” is complicated, but so is ‘if.’ The Gentzen differs from the evaluation assignemt:‘p or q’ is 1 iff p is 1 or q is 1. When we speak of ‘truth-functional’ grounds it is this assignment above we are referring to.Of courseif p, p or q [a formulation of the Gentzen introduction]is a TAUTOLOGY [which is what makes the introduction a rule of inference].In terms of entailment P Or Q (independently)  Is stronger than ‘p v q’ In that either p or q entail ‘p or q’ but the reverse is not true. Grice says that he first thought of the pragmatic rule in terms of the theory of perception, and Strawson hints at this when he says in the footnote to “Introduction to Logical theory” that the rule was pointed out by his tutor in the Logic Paper, Grice, “in a different connection.” The logic paper took place before the war, so this is early enough in Grice’s career – so the ghosts of Whitehead and Russell were there! We can call the above ‘the principle of conversational fortitude.’ This is certainly not an adequate formulation but will perhaps be good enough for Grice’s purpose in “Causal.” On the assumption that such a principle as this is of general application, one can DRAW or infer or explain the conclusion that the utterance of a disjunctive sentence would imply that the emissor has grounds other than truth-functional for the uttering of a disjunctum, given that, first, the obvious reason for not making a statemcnt which there is some call on one to make VALIDLY is that one is not in a position (or entitled) to make it, and given, second, the logical ‘fact’ that each disjunct entails the disjunctive, but not vice versa; which being so, each disjunct is stronger (bears more conversational ‘fortitude’) than the disjunctive. If the outline just given is on the right lines, Grice would wish to say, we have a reason for REFUSING (as Strawson would not!) in the case of “kitchen or bedroom” to regard the implication of the emissor having grounds other than truth-functional for the uttering of the disjunctive as being part of the ‘meaning’ (whatever that ‘means’) of 'or' – but I should doublecheck with O. P. Wood – he’s our man in ‘or’ – A man who knows about the logical relation between a disjunction and each disjunct, i. e. a man who has at least BROWSED Whitehead and Russell – and diregards Bradley’s exclusivist account -- and who also ‘knew,’ qua Kantian rational agent, about the alleged general principle or guiding conversational, could work out for hirnself, surely, that a disjunctive utterance would involve the implication which it does in fact involve. Grice insists, however, that his aim in discussing this last point – about the principle of conversational fortitude EXPLAING the generation of the implicaturum -- has been merelyto indicate the position I would wish to take up, and not to argue scriously in favour of it. Grice’s main purpose in the excursus on implication was to introduce four ideas or catalysts, or tesets – TEST No. I: truth-value; TEST No. 2: Vehicle out of four; Test No. 3/Twin Test: Annulation and Non-Detachment (is there a positive way to express this – non-detached twins as opposed to CONJOINT twins), and Test No. 4 – ‘Meaning’ of expression? -- of which Grice then goes to make some use re: the pillar box seeming red.; and to provide some conception of the ways in which each of the four tests apply or fail to apply to various types of implication. By the numbering of it, it seems that by the time of Essay II he has, typically, added an extra. It’s FIVE catalysts now, but actually, since he has two of the previous tests all rolled up in one, it is SIX CATALSTS. He’ll go back to them in Essay IV (“Indicative conditionals” with regard to ‘if’), and in Presupposition and Conversational (with regard to Example I here: “You have not ceased eating iron”). Implicaturum.He needs those catalysts. Why? It seems like he is always thinking that someone will challenge him! This is Grice: “We can now show that, it having been stipulated as being what it is, a conversational implicaturum must possess certain distinctive features, they are six. By using distinctive feature Grice is serious. He wants each of the six catalysts to apply to each type of ‘implicaturum’, so that a table can be constructed. With answers yes/no. Or rather here are some catalyst ideas which will help us to determine or individuate. Six tests for implicaturum as it were. SO THESE FEATURES – six of them – apply to three of the examples – not the ‘poor but honest’ – but the “you have not ceased eating iron,” “Beautiful handwriting,” and “Kitchen or bedroom.”First test – nothing about the ‘twin’ – it’s ANNULATION or CANCELLABILITY – as noted in “Causal Theory” – for two of the examples (‘beautiful handwriting’ and ‘kitchen or bedroom’ and NEGATIVE version of “You don’t cease to eat iron”) and the one of the pillar box – He adds a qualifier now: the annulation should best be IMPLICIT. But for the fastidious philosopher, he allows for an EXPLICITATION which may not sound grammatical enough to Austen (pronounced to rhyme with the playgroup master, or the kindergarten’s master). To assume the presence of a conversational implicaturum, the philosopher (and emissee) has to assume that the principle of conversational co-operation (and not just conversational fortitude) is being observed.However, it is mighty possible to opt out of this and most things at Oxford, i. e. the observation of this principle of conversational cooperation (or the earlier principle of conversational fortitude).It follows then that now we CAN EXPLAIN WHY CANCELLABILITY IS A DISTINCTIVE FEATURE. He left it to be understood in “Causal.”It follows then, deductively, that an implicaturum can be canceled (or annulled) in a particular case. The conversational implicaturum may be, drearily – but if that’s what the fastidious philosopher axes -- explicitly canceled, if need there be, by the addition of a clause by which the utterer states or implies that he opts out (e. g. “The pillar box seems red but it is.” “Where is your wife?” “My lips are sealed”). Then again the conversational implicaturum may be contextually (or implicitly) canceled, as Grice prefers (e. g. to a very honest person, who knows I disbelieve the examiner exists, “The loyalty examiner won’t be summoning you at any rate”). The utterance that usually would carry an implicaturum is used on an occasion that makes it clear or obvious that the utterer IS opting out without having to bore his addressee by making this obviousness explicit. SECOND DISTINCTIVE FEATURE: CONJOINING, i.e. non-detachability.There is a second litmus test or catalyst idea.Insofar as the calculation that a implicaturum is present requires, besides contextual and background information only an intuitive rational knowledge or understanding or processing of what has been explicitly conveyed (‘are you playing squash? B shows bandaged leg) (or the, shall we say, ‘conventional’ ‘arbitrary’ ‘commitment’ of the utterance), and insofar as the manner or style, of FORM, rather than MATTER, of expression should play at best absolutely no role in the calculation, it is NOT possible to find another way of explicitly conveying or putting forward the same thing, the same so-and-so (say that q follows from p) which simply ‘lacks’ the unnecessary implicaturum in question -- except [will his excluders never end?] where some special feature of the substituted version [this other way which he says is not conceivable] is itself relevant to the determination of the implicaturum (in virtue of this or that conversational maxims pertaining to the category of conversational mode. THIS BIG CAVEAT makes you wonder that Grice regretted making fun of Kant. By adopting jocularly the four conversational categories, he now finds himself in having to give an excuse or exception for those implicatura generated by a flout to what he earlier referred to as the ‘desideratum of conversational clarity,’ and which he jocularly rephrased as a self-defeating maxim, ‘be perspicuous [sic], never mind perspicacious!’If we call this feature, as Grice does in “Causal Theory,” ‘non-detachability’ (or conjoining)– in that the implicaturum cannot be detached or disjointed from any alternative expression that makes the same point -- one may expect the implicaturum carried by this or that locution to have a high degree of non-detachability. ALTERNATIVES FOR “NOT” Not, it is not the case, it is false that. There’s nothing unique about ‘not’.ALTERNATIVES FOR “AND” and, nothing, furthermore, but. There isnothing unique about ‘and’ALTERNATIVES FOR “OR”: One of the following is true. There is nothing unique about ‘or’ALTERNATIVES FOR “IF” Provided. ‘There is nothing unique about ‘if’ALTERNATIVES FOR “THE” – There is at least one and at most one. And it exists. (existence and uniqueness). There is nothing unique about ‘the’.THIS COVERS STRAWSON’S first problem.What about the other English philosophers?AUSTIN – on ‘voluntarily’ ALTERNATIVES to ‘voluntarily,’ with the will, willingly, intentionally. Nothing unique about ‘voluntarily.’STRAWSON on ‘true’ – it is the case, redundance theory, nothing. Nothing unique about ‘true’HART ON good. To say that ‘x is commendable’ is to recommend x. Nothing unique about ‘good.’HART on ‘carefully.’ Da Vinci painted Mona Lisa carefully, with caution, with precaution. Nothing unique about ‘carefully.’THIRD LITMUS TEST or idea and ATTENDING THIRD  DISTINCTIVE FEATURE. THIRD DISTINCTIVE FEATURE is in the protasis of the conditional.The implicaturum depends on the explicatum or explicitum, and a fortiori, the implicaturum cannot INVOLVE anything that the explicatum involves – There is nothing about what an emissor explicitly conveys about “or” or a disjunctum in general, which has to do with the emissor having grounds other than truth-functional for the utterance of a disjunctum.The calculation of the presence of an implicaturum presupposes an initial knowledge, or grasping, or understanding, or taking into account of the ‘conventional’ force (not in Austin’s sense, but translating Latin ‘vis’) of the expression the utterance of which carries the implicaturum.A conversational implicaturum will be a condition (but not a truth-condition), i. e. a condition that is NOT, be definition, on risk of circularity of otiosity, included in what the emissor explicitly conveys, i. e. the original specification of the expression's ‘conventional’ or arbitrary forceIf I’m saying that ‘seems’ INVOLVES, as per conventional force, ‘doubt or denial,’what’s my point? If Strawson is right that ‘if’ has the conventional force of conventionally committing the utterer with the belief that q follows from p, why bother? And if that were so, how come the implicaturum is still cancellable?Though it may not be impossible for what starts life, so to speak, as a conversational implicaturum to become conventionalized, to suppose that this is so in a given case would require special justification. (Asking Lewis). So, initially at least, a conversational implicaturum is, by definition and stipulation, not part of the sense, truth-condition, conventional force, or part of what is explicitly conveyed or put forward, or ‘meaning’ of the expression to the employment of which the impicatum attaches. FOURTH LITMUS TEST or catalyst idea. Mentioned in “Causal theory” YIELDS THE FOUTH DISICTINVE FEATURE and the FIFTH distinctive feature.FOURTH DISTINCTIVE FEATURE: in the protasis of the conditional – truth value.The alethic value – conjoined with the test about the VEHICLE --. He has these as two different tests – and correspondingly two distinctive features in “Causal”. The truth of a conversational implicaturum is not required by (is not a condition for) the truth of what is said or explicitly conveyed (what is said or explicated – the explicatum or explicitum, or what is explicitly conveyed or communicated) may be true -- what is implicated may be false – that he has beautiful handwriting, that q follows from p, that the utterer is ENDORSING what someone else said, that the utterer is recommending x, that the person who is said to act carefully has taken precaution), FIFTH DISTINCTIVE FEATURE: vehicle – this is the FOURTH vehicle of the four he mentions in “Causal”: ‘what the emissor explicitly conveys,’ ‘the emissor himself,’ the emissor’s utterance, and fourth, the emissor’s explicitly conveying, or explicitly conveying it that way --. The apodosis of the conditional – or inferrability schema, since he uses ‘since,’ rather than ‘if,’ i. e. ‘GIVEN THAT p, q. Or ‘p; therefore, q’. The implicaturum is NOT carried by what is said or the EXPLICATUM or EXPLICITUM, or is explicitly conveyed, but only by the ‘saying’ or EXPLICATING or EXPLICITING of what is said or of the explicatum or explicitum, or by 'putting it that way.’The fifth and last litmus test or catalyst idea YIELDS A SIXTH DISTINCTIVE FEATURE:Note that he never uses ‘first, second, etc.’ just the numerals, which in a lecture format, are not visible!SIXTH DISTINCTIVE FEATURE: INDETERMINACY. Due to the open character of the reasoning – and the choices available to fill the gap of the content of the propositional attitude that makes the conversational rational:“He is potentially dishonest.” “His colleagues are treacherous”Both implicatura possible for “He hasn’t been to prison at his new job at the bank – yet.”Since, to calculate a conversational implicaturum is to calculate what has to be supposed in order to preserve the supposition that the utterer is a rational, benevolent, altruist agent, and that the principle of conversational cooperation is being observed, and since there may be various possible specific explanations or alternatives that fill the gap here – as to what is the content of the psychological attitude to be ascribed to the utterer, a list of which may be open, or open-ended, the conversational implicaturum in such cases will technically be an open-ended disjunction of all such specific explanations, which may well be infinitely non-numerable. Since the list of these IS open, the implicaturum will have just the kind of INDETERMINACY or lack of determinacy that an implicaturum appears in most cases to possess. indeterminacy of translation, a pair of theses derived, originally, from a thought experiment regarding radical translation first propounded by Quine in Word and Object (1960) and developed in his Ontological Relativity (1969), Theories and Things (1981), and Pursuit of Truth (1990). Radical translation is an imaginary context in which a field linguist is faced with the challenge of translating a hitherto unknown language. Furthermore, it is stipulated that the linguist has no access to bilinguals and that the language to be translated is historically unrelated to that of the linguist. Presumably, the only data the linguist has to go on are the observable behaviors of incompleteness indeterminacy of translation 422 4065h-l.qxd 08/02/1999 7:39 AM Page 422 native speakers amid the publicly observable objects of their environment. (1) The strong thesis of indeterminacy, indeterminacy of translation of theoretical sentences as wholes, is the claim that in the context of radical translation a linguist (or linguists) could construct a number of manuals for translating the (natives’) source language into the (linguists’) target language such that each manual could be consistent with all possible behavior data and yet the manuals could diverge with one another in countless places in assigning different target-language sentences (holophrastically construed) as translations of the same source-language sentences (holophrastically construed), diverge even to the point where the sentences assigned have conflicting truth-values; and no further data, physical or mental, could single out one such translation manual as being the uniquely correct one. All such manuals, which are consistent with all the possible behavioral data, are correct. (2) The weak thesis of indeterminacy, indeterminacy of reference (or inscrutability of reference), is the claim that given all possible behavior data, divergent target-language interpretations of words within a source-language sentence could offset one another so as to sustain different targetlanguage translations of the same source-language sentence; and no further data, physical or mental, could single out one such interpretation as the uniquely correct one. All such interpretations, which are consistent with all the possible behavioral data, are correct. This weaker sort of indeterminacy takes two forms: an ontic form and a syntactic form. Quine’s famous example where the source-language term ‘gavagai’ could be construed either as ‘rabbit’, ‘undetached rabbit part’, ‘rabbithood’, etc. (see Word and Object), and his proxy function argument where different ontologies could be mapped onto one another (see Ontological Relativity, Theories and Things, and Pursuit of Truth), both exemplify the ontic form of indeterminacy of reference. On the other hand, his example of the Japanese classifier, where a particular three-word construction of Japanese can be translated into English such that the third word of the construction can be construed with equal justification either as a term of divided reference or as a mass term (see Ontological Relativity and Pursuit of Truth), exemplifies the syntactic form of indeterminacy of reference.

indexical: Bradley’s thisness, and whatness – “Grice is improving on Scotus: Aristotle’s tode ti is exactly Bradley’s thisness whatness – and more familiar to the English ear than Scotus feminine ‘haecceitas.’” “Russell, being pretentious, call Bradley’s “thisness” and “thatness,” but not “whatness” – as a class of the ‘egocentric particular’ --  a type of expression whose semantic value is in part determined by features of the context of utterance, and hence may vary with that context. Among indexicals are the personal pronouns, such as ‘I’, ‘you’, ‘he’, ‘she’, and ‘it’; demonstratives, such as ‘this’ and ‘that’; temporal expressions, such as ‘now’, ‘today’, ‘yesterday’; and locative expressions, such as ‘here’, ‘there’, etc. Although classical logic ignored indexicality, many recent practitioners, following Richard Montague, have provided rigorous theories of indexicals in the context of formal semantics. Perhaps the most plausible and thorough treatment of indexicals is by David Kaplan, a prominent philosopher of language and logic whose long-unpublished “Demonstratives” was especially influential; it eventually appeared in J. Almog, J. Perry, and H. Wettstein, eds., Themes from Kaplan. Kaplan argues persuasively that indexical singular terms are directly referential and a species of rigid designator. He also forcefully brings out a crucial lesson to be learned from indexicals, namely, that there are two types of meaning, which Kaplan calls “content” and “character.” A sentence containing an indexical, such as ‘I am hungry’, can be used to say different things in different contexts, in part because of the different semantic contributions made by ‘I’ in these contexts. Kaplan calls a term’s contribution to what is said in a context the term’s content. Though the content of an indexical like ‘I’ varies with its context, it will nevertheless have a single meaning in the language, which Kaplan calls the indexical’s character. This character may be conceived as a rule of function that assigns different contents to the indexical in different contexts.

implicaturum: in his Oxford seminars. Grice: “I distinguish between the ‘implicaturum’ and the ‘implicaturum.’” “The ‘implicaturum’ corresponds to Moore’s entailment.” “For the ‘pragmatic-type’ of thing, one should use ‘implicaturum.’” “The –aturum’ form is what at Clifton I learned as the future, and a ‘future’ twist it has, since it refers to the future.” “ ‘Implicaturum esse’ is, strictly, the infinitivum futurum, made out of the ‘esse’ plus the ‘indicaturum.’ We loved these things at Clifton!”

indicatum. “oριστική,” “oristike,” – The Roman ‘indicatum’ is a composite of ‘in’ plus ‘dicatum.’ The Romans were never sure about this. Literally for the Greeks it’s the ‘definitive’ – ‘horistike’ klesis, inclinatio or modus animae affectationem demonstrans indefinitivus – While indefinitivus is the transliteration, the Romans also used ‘finitivus’ ‘finitus,’ and ‘indicativus’ and ‘pronuntiativus’. ‘Grice distinguishes between the indicative mode and the informational mode. One can hardly inform oneself. Yet one can utter an utterance in the indicative mode without it being in what he calls the informational sub-mode. It’s interesting that Grice thinks he has to distinguish between the ‘informational’ and the mere ‘indicative.’ Oddly when he sets the goal to which ‘co-operation’ leads, it’s the informing/being informed, influencing/being influenced. Surely he could have simplified that by, as he later will, psi-transmission, whatever. So the emissor INDICATES, even in an imperative utterance, what his will is. All moves are primarily ‘exhibitive,’ (and the function of the mode is to EXPRESS the corresponding attitude). Only some moves are ‘protreptic.’ Grice was well aware, if perhaps not TOO aware, since Austin was so secretive, about Austin on the ‘perlocution.’ Because Austin wanted to deprieve the act from the cause of the act. Thus, Austin’s communicative act may have a causal intention, leading to this or that effect – but that would NOT be part of the philosopher’s interest. Suppose !p; whether the order is successful and Smith does get a job he is promised, it hardly matters to Kant, Austin, or Grice. Interestingly, ‘indicatum’ has the same root as ‘dic-‘, to say – but surely you don’t need to say to indicate, as in Grice’s favourite indicative mood: a hand wave signaling that the emissor knows the route or is about to leave the emissee.

directum. “Searle thought he was being witty when adapting my implicaturum to what he called an Indirect Austinian thing. Holdcroft was less obvious!” – Grice. – indirectum -- indirect discourse, also called oratio obliqua, the use of words to report what others say, but without direct quotation. When one says “John said, ‘Not every doctor is honest,’ “ one uses the words in one’s quotation directly – one uses direct discourseto make an assertion about what John said. Accurate direct discourse must get the exact words. But in indirect discourse one can use other words than John does to report what he said, e.g., “John said that some physicians are not honest.” The words quoted here capture the sense of John’s assertion (the proposition he asserted). By extension, ‘indirect discourse’ designates the use of words in reporting beliefs. One uses words to characterize the proposition believed rather than to make a direct assertion. When Alice says, “John believes that some doctors are not honest,” she uses the words ‘some doctors are not honest’ to present the proposition that John believes. She does not assert the proposition. By contrast, direct discourse, also called oratio recta, is the ordinary use of words to make assertions. Grice struggled for years as to what the ‘fundamentum distinctionis’ is between the central and the peripheric communicatum. He played with first-ground versus second-ground. He played with two different crtieria: formal/material, and dictive-non-dictive. Refs.: H. P. Grice, “Holdcroft on direct and indirect communication.”

discernibile – “There’s the discernible and the indiscernible, and Leibniz was a bit of a genius in focusing on the second!” – Grice. indiscernibility: of identicals, the principle that if A and B are identical, there is no difference between A and B: everything true of A is true of B, and everything true of B is true of A; A and B have just the same properties; there is no property such that A has it while B lacks it, or B has it while A lacks it. A tempting formulation of this principle, ‘Any two things that are identical have all their properties in common’, verges on nonsense; for two things are never identical. ‘A is numerically identical with B’ means that A and B are one and the same. A and B have just the same properties because A, that is, B, has just the properties that it has. This principle is sometimes called Leibniz’s law. It should be distinguished from its converse, Leibniz’s more controversial principle of the identity of indiscernibles. A contraposed form of the indiscernibility of identicals – call it the distinctness of discernibles – reveals its point in philosophic dialectic. If something is true of A that is not true of B, or (to say the same thing differently) if something is true of B that is not true of A, then A and B are not identical; they are distinct. One uses this principle to attack identity claims. Classical arguments for dualism attempt to find something true of the mind that is not true of anything physical. For example, the mind, unlike everything physical, is indivisible. Also, the existence of the mind, unlike the existence of everything physical, cannot be doubted. This last argument shows that the distinctness of discernibles requires great care of application in intentional contexts. Refs.: H. P. Grice, “Definite descriptions in Leibniz and in the vernacular.”

individuum: versus the dividuum – or divisum. Cicero’s attempt to translate ‘a-tomon.’ In metaphysics, a process whereby a universal, e.g., cat, becomes instantiated in an individual – also called a particular e.g., Minina; (2) in epistemology, a process whereby a knower discerns an individual, e.g., someone discerns Minina. The double understanding of individuation raises two distinct problems: identifying the causes of metaphysical individuation, and of epistemological individuation. In both cases the causes are referred to as the principle of individuation. Attempts to settle the metaphysical and epistemological problems of individuation presuppose an understanding of the nature of individuality. Individuality has been variously interpreted as involving one or more of the following: indivisibility, difference, division within a species, identity through time, impredicability, and non-instantiability. In general, theories of individuation try to account variously for one or more of these. Individuation may apply to both substances (e.g., Minina) and their features (e.g., Minina’s fur color), generating two different sorts of theories. The theories of the metaphysical individuation of substances most often proposed identify six types of principles: a bundle of features (Russell); space and/or time (Boethius); matter (Aristotle); form (Averroes); a decharacterized, sui generis component called bare particular (Bergmann) or haecceity (Duns Scotus); and existence (Avicenna). Sometimes several principles are combined. For example, for Aquinas the principle of individuation is matter under dimensions (materia signata). Two sorts of objections are often brought against these views of the metaphysical individuation of substances. One points out that some of these theories violate the principle of acquaintance,since they identify as individuators entities for which there is no empirical evidence. The second argues that some of these theories explain the individuation of substances in terms of accidents, thus contradicting the ontological precedence of substance over accident. The two most common theories of the epistemological individuation of substances identify spatiotemporal location and/or the features of substances as their individuators; we know a thing as an individual by its location in space and time or by its features. The objections that are brought to bear against these theories are generally based on the ineffectiveness of those principles in all situations to account for the discernment of all types of individuals. The theories of the metaphysical individuation of the features of substances fall into two groups. Some identify the substance itself as the principle of individuation; others identify some feature(s) of the substance as individuator(s). Most accounts of the epistemological individuation of the features of substances are similar to these views. The most common objections to the metaphysical theories of the individuation of features attempt to show that these theories are either incomplete or circular. It is argued, e.g., that an account of the individuation of features in terms of substance is incomplete because the individuation of the substance must also be accounted for: How would one know what tree one sees, apart from its features? However, if the substance is individuated by its features, one falls into a vicious circle. Similar points are made with respect to the epistemological theories of the individuation of features. Apart from the views mentioned, some philosophers hold that individuals are individual essentially (per se), and therefore that they do not undergo individuation. Under those conditions either there is no need for a metaphysical principle of individuation (Ockham), or else the principle of individuation is identified as the individual entity itself (Suárez).

inductum: in the narrow sense, inference to a generalization from its instances; (2) in the broad sense, any ampliative inference – i.e., any inference where the claim made by the conclusion goes beyond the claim jointly made by the premises. Induction in the broad sense includes, as cases of particular interest: argument by analogy, predictive inference, inference to causes from signs and symptoms, and confirmation of scientific laws and theories. The narrow sense covers one extreme case that is not ampliative. That is the case of mathematical induction, where the premises of the argument necessarily imply the generalization that is its conclusion. Inductive logic can be conceived most generally as the theory of the evaluation of ampliative inference. In this sense, much of probability theory, theoretical statistics, and the theory of computability are parts of inductive logic. In addition, studies of scientific method can be seen as addressing in a less formal way the question of the logic of inductive inference. The name ‘inductive logic’ has also, however, become associated with a specific approach to these issues deriving from the work of Bayes, Laplace, De Morgan, and Carnap. On this approach, one’s prior probabilities in a state of ignorance are determined or constrained by some principle for the quantification of ignorance and one learns by conditioning on the evidence. A recurrent difficulty with this line of attack is that the way in which ignorance is quantified depends on how the problem is described, with different logically equivalent descriptions leading to different prior probabilities. Carnap laid down as a postulate for the application of his inductive logic that one should always condition on one’s total evidence. This rule of total evidence is usually taken for granted, but what justification is there for it? Good pointed out that the standard Bayesian analysis of the expected value of new information provides such a justification. Pure cost-free information always has non-negative expected value, and if there is positive probability that it will affect a decision, its expected value is positive. Ramsey made the same point in an unpublished manuscript. The proof generalizes to various models of learning uncertain evidence. A deductive account is sometimes presented indubitability induction 425 4065h-l.qxd 08/02/1999 7:39 AM Page 425 where induction proceeds by elimination of possibilities that would make the conclusion false. Thus Mill’s methods of experimental inquiry are sometimes analyzed as proceeding by elimination of alternative possibilities. In a more general setting, the hypothetico-deductive account of science holds that theories are confirmed by their observational consequences – i.e., by elimination of the possibilities that this experiment or that observation falsifies the theory. Induction by elimination is sometimes put forth as an alternative to probabilistic accounts of induction, but at least one version of it is consistent with – and indeed a consequence of – probabilistic accounts. It is an elementary fact of probability that if F, the potential falsifier, is inconsistent with T and both have probability strictly between 0 and 1, then the probability of T conditional on not-F is higher than the unconditional probability of T. In a certain sense, inductive support of a universal generalization by its instances may be a special case of the foregoing, but this point must be treated with some care. In the first place, the universal generalization must have positive prior probability. (It is worth noting that Carnap’s systems of inductive logic do not satisfy this condition, although systems of Hintikka and Niiniluoto do.) In the second place, the notion of instance must be construed so the “instances” of a universal generalization are in fact logical consequences of it. Thus ‘If A is a swan then A is white’ is an instance of ‘All swans are white’ in the appropriate sense, but ‘A is a white swan’ is not. The latter statement is logically stronger than ‘If A is a swan then A is white’ and a complete report on species, weight, color, sex, etc., of individual A would be stronger still. Such statements are not logical consequences of the universal generalization, and the theorem does not hold for them. For example, the report of a man 7 feet 11¾ inches tall might actually reduce the probability of the generalization that all men are under 8 feet tall. Residual queasiness about the foregoing may be dispelled by a point made by Carnap apropos of Hempel’s discussion of paradoxes of confirmation. ‘Confirmation’ is ambiguous. ‘E confirms H’ may mean that the probability of H conditional on E is greater than the unconditional probability of H, in which case deductive consequences of H confirm H under the conditions set forth above. Or ‘E confirms H’ may mean that the probability of H conditional on E is high (e.g., greater than .95), in which case if E confirms H, then E confirms every logical consequence of H. Conflation of the two senses can lead one to the paradoxical conclusion that E confirms E & P and thus P for any statement, P.

inductivism: “A philosophy of science invented by Popper and P. K. Feyerabend as a foil for their own views. Why, I must just have well invented ‘sensism’ as a foil for my theory of implicaturum!” -- According to inductivism, a unique a priori inductive logic enables one to construct an algorithm that will compute from any input of data the best scientific theory accounting for that data.

inductum: Not deductum, -- nor abductum -- epapoge, Grecian term for ‘induction’. Especially in the logic of Aristotle, epagoge is opposed to argument by syllogism. Aristotle describes it as “a move from particulars to the universal.” E.g., premises that the skilled navigator is the best navigator, the skilled charioteer the best charioteer, and the skilled philosopher the best philosopher may support the conclusion by epagoge that those skilled in something are usually the best at it. Aristotle thought it more persuasive and clearer than the syllogistic method, since it relies on the senses and is available to all humans. The term was later applied to dialectical arguments intended to trap opponents. R.C. epicheirema, a polysyllogism in which each premise represents an enthymematic argument; e.g., ‘A lie creates disbelief, because it is an assertion that does not correspond to truth; flattery is a lie, because it is a conscious distortion of truth; therefore, flattery creates disbelief’. Each premise constitutes an enthymematic syllogism. Thus, the first premise could be expanded into the following full-fledged syllogism: ‘Every assertion that does not correspond to truth creates disbelief; a lie is an assertion that does not correspond to truth; therefore a lie creates disbelief’. We could likewise expand the second premise and offer a complete argument for it. Epicheirema can thus be a powerful tool in oral polemics, especially when one argues regressively, first stating the conclusion with a sketch of support in terms of enthymemes, and then  if challenged to do so  expanding any or all of these enthymemes into standard categorical syllogisms.

illatum: A form of the conjugation Grice enjoyed was “inferentia,” cf essentia, sententia, prudentia, etc.. – see illatum -- Cf. illatio. Consequentia. Implicatio. Grice’s implicaturum and what the emissor implicates as a variation on the logical usage.

infima species (Latin, ‘lowest species’), a species that is not a genus of any other species. According to the theory of classification, division, and definition that is part of traditional or Aristotelian logic, every individual is a specimen of some infima species. An infima species is a member of a genus that may in turn be a species of a more inclusive genus, and so on, until one reaches a summum genus, a genus that is not a species of a more inclusive genus. Socrates and Plato are specimens of the infima specis human being (mortal rational animal), which is a species of the genus rational animal, which is a species of the genus animal, and so on, up to the summum genus substance. Whereas two specimens of animal – e.g., an individual human and an individual horse – can differ partly in their essential characteristics, no two specimens of the infima species human being can differ in essence.

infinite-off predicament, or ∞-off predicament.

infinitum: “What is not finite.” “I know that there are infinitely many stars” – an example of a stupid thing to say by the man in the street. apeiron, Grecian term meaning ‘the boundless’ or ‘the unlimited’, which evolved to signify ‘the infinite’. Anaximander introduced the term to philosophy by saying that the source of all things was apeiron. There is some disagreement about whether he meant by this the spatially antinomy apeiron unbounded, the temporally unbounded, or the qualitatively indeterminate. It seems likely that he intended the term to convey the first meaning, but the other two senses also happen to apply to the spatially unbounded. After Anaximander, Anaximenes declared as his first principle that air is boundless, and Xenophanes made his flat earth extend downward without bounds, and probably outward horizontally without limit as well. Rejecting the tradition of boundless principles, Parmenides argued that “what-is” must be held within determinate boundaries. But his follower Melissus again argued that what-is must be boundless  in both time and space  for it can have no beginning or end. Another follower of Parmenides, Zeno of Elea, argued that if there are many substances, antinomies arise, including the consequences that substances are both limited and unlimited apeira in number, and that they are so small as not to have size and so large as to be unlimited in size. Rejecting monism, Anaxagoras argued for an indefinite number of elements that are each unlimited in size, and the Pythagorean Philolaus made limiters perainonta and unlimiteds apeira the principles from which all things are composed. The atomists Leucippus and Democritus conceived of a boundless universe, partly full of an infinite number of atoms and partly void; and in the universe are countless apeiroi worlds. Finally Aristotle arrived at an abstract understanding of the apeiron as “the infinite,” claiming to settle paradoxes about the boundless by allowing for real quantities to be infinitely divisible potentially, but not actually Physics III.48. The development of the notion of the apeiron shows how Grecian philosophers evolved ever more abstract philosophical ideas from relatively concrete conceptions.  Infinity -- Grice thougth that “There are infinitely many stars” was a stupid thing to say -- diagonal procedure, a method, originated by Cantor, for showing that there are infinite sets that cannot be put in one-to-one correspondence with the set of natural numbers i.e., enumerated. For example, the method can be used to show that the set of real numbers x in the interval 0 ‹ x m 1 is not enumerable. Suppose x0, x1, x2, . . . were such an enumeration x0 is the real correlated with 0; x1, the real correlated with 1; and so on. Then consider the list formed by replacing each real in the enumeration with the unique non-terminating decimal fraction representing it: The first decimal fraction represents x0; the second, x1; and so on. By diagonalization we select the decimal fraction shown by the arrows: and change each digit xnn, taking care to avoid a terminating decimal. This fraction is not on our list. For it differs from the first in the tenths place, from the second in the hundredths place, and from the third in the thousandths place, and so on. Thus the real it represents is not in the supposed enumeration. This contradicts the original assumption. The idea can be put more elegantly. Let f be any function such that, for each natural number n, fn is a set of natural numbers. Then there is a set S of natural numbers such that n 1 S S n 2 fn. It is obvious that, for each n, fn & S.  Infinity -- eternal return, the doctrine that the same events, occurring in the same sequence and involving the same things, have occurred infinitely many times in the past and will occur infinitely many times in the future. Attributed most notably to the Stoics and Nietzsche, the doctrine is antithetical to philosophical and religious viewpoints that claim that the world order is unique, contingent in part, and directed toward some goal. The Stoics interpret eternal return as the consequence of perpetual divine activity imposing exceptionless causal principles on the world in a supremely rational, providential way. The world, being the best possible, can only be repeated endlessly. The Stoics do not explain why the best world cannot be everlasting, making repetition unnecessary. It is not clear whether Nietzsche asserted eternal return as a cosmological doctrine or only as a thought experiment designed to confront one with the authenticity of one’s life: would one affirm that life even if one were consigned to live it over again without end? On either interpretation, Nietzsche’s version, like the Stoic version, stresses the inexorability and necessary interconnectedness of all things and events, although unlike the Stoic version, it rejects divine providence.  infinitary logic, the logic of expressions of infinite length. Quine has advanced the claim that firstorder logic (FOL) is the language of science, a position accepted by many of his followers. Howinferential justification infinitary logic 428 4065h-l.qxd 08/02/1999 7:39 AM Page 428 ever, many important notions of mathematics and science are not expressible in FOL. The notion of finiteness, e.g., is central in mathematics but cannot be expressed within FOL. There is no way to express such a simple, precise claim as ‘There are only finitely many stars’ in FOL. This and related expressive limitations in FOL seriously hamper its applicability to the study of mathematics and have led to the study of stronger logics. There have been various approaches to getting around the limitations by the study of so-called strong logics, including second-order logic (where one quantifies over sets or properties, not just individuals), generalized quantifiers (where one adds quantifiers in addition to the usual ‘for all’ and ‘there exists’), and branching quantifiers (where notions of independence of variables is introduced). One of the most fruitful methods has been the introduction of idealized “infinitely long” statements. For example, the above statement about the stars would be formalized as an infinite disjunction: there is at most one star, or there are at most two stars, or there are at most three stars, etc. Each of these disjuncts is expressible in FOL. The expressive limitations in FOL are closely linked with Gödel’s famous completeness and incompleteness theorems. These results show, among other things, that any attempt to systematize the laws of logic is going to be inadequate, one way or another. Either it will be confined to a language with expressive limitations, so that these notions cannot even be expressed, or else, if they can be expressed, then an attempt at giving an effective listing of axioms and rules of inference for the language will fall short. In infinitary logic, the rules of inference can have infinitely many premises, and so are not effectively presentable. Early work in infinitary logic used cardinality as a guide: whether or not a disjunction, conjunction, or quantifier string was permitted had to do only with the cardinality of the set in question. It turned out that the most fruitful of these logics was the language with countable conjunctions and finite strings of first-order quantifiers. This language had further refinements to socalled admissible languages, where more refined set-theoretic considerations play a role in determining what counts as a formula. Infinitary languages are also connected with strong axioms of infinity, statements that do not follow from the usual axioms of set theory but for which one has other evidence that they might well be true, or at least consistent. In particular, compact cardinals are infinite cardinal numbers where the analogue of the compactness theorem of FOL generalizes to the associated infinitary language. These cardinals have proven to be very important in modern set theory. During the 1990s, some infinitary logics played a surprising role in computer science. By allowing arbitrarily long conjunctions and disjunctions, but only finitely many variables (free or bound) in any formula, languages with attractive closure properties were found that allowed the kinds of inductive procedures of computer science, procedures not expressible in FOL. -- infinite regress argument, a distinctively philosophical kind of argument purporting to show that a thesis is defective because it generates an infinite series when either (form A) no such series exists or (form B) were it to exist, the thesis would lack the role (e.g., of justification) that it is supposed to play. The mere generation of an infinite series is not objectionable. It is misleading therefore to use ‘infinite regress’ (or ‘regress’) and ‘infinite series’ equivalently. For instance, both of the following claims generate an infinite series: (1) every natural number has a successor that itself is a natural number, and (2) every event has a causal predecessor that itself is an event. Yet (1) is true (arguably, necessarily true), and (2) may be true for all that logic can say about the matter. Likewise, there is nothing contrary to logic about any of the infinite series generated by the suppositions that (3) every free act is the consequence of a free act of choice; (4) every intelligent operation is the result of an intelligent mental operation; (5) whenever individuals x and y share a property F there exists a third individual z which paradigmatically has F and to which x and y are somehow related (as copies, by participation, or whatnot); or (6) every generalization from experience is inductively inferable from experience by appeal to some other generalization from experience. What Locke (in the Essay concerning Human Understanding) objects to about the theory of free will embodied in (3) and Ryle (in The Concept of Mind) objects to about the “intellectualist leginfinite, actual infinite regress argument 429 4065h-l.qxd 08/02/1999 7:39 AM Page 429 end” embodied in (4) can therefore be only that it is just plain false as a matter of fact that we perform an infinite number of acts of choice or operations of the requisite kinds. In effect their infinite regress arguments are of form A: they argue that the theories concerned must be rejected because they falsely imply that such infinite series exist. Arguably the infinite regress arguments employed by Plato (in the Parmenides) regarding his own theory of Forms and by Popper (in the Logic of Scientific Discovery) regarding the principle of induction proposed by Mill, are best construed as having form B, their objections being less to (5) or (6) than to their epistemic versions: (5*) that we can understand how x and y can share a property F only if we understand that there exists a third individual (the “Form” z) which paradigmatically has F and to which x and y are related; and (6*) that since the principle of induction must itself be a generalization from experience, we are justified in accepting it only if it can be inferred from experience by appeal to a higherorder, and justified, inductive principle. They are arguing that because the series generated by (5) and (6) are infinite, the epistemic enlightenment promised by (5*) and (6*) will forever elude us. When successful, infinite regress arguments can show us that certain sorts of explanation, understanding, or justification are will-o’-thewisps. As Passmore has observed (in Philosophical Reasoning) there is an important sense of ‘explain’ in which it is impossible to explain predication. We cannot explain x’s and y’s possession of the common property F by saying that they are called by the same name (nominalism) or fall under the same concept (conceptualism) any more than we can by saying that they are related to the same form (Platonic realism), since each of these is itself a property that x and y are supposed to have in common. Likewise, it makes no sense to try to explain why anything at all exists by invoking the existence of something else (such as the theist’s God). The general truths that things exist, and that things may have properties in common, are “brute facts” about the way the world is. Some infinite regress objections fail because they are directed at “straw men.” Bradley’s regress argument against the pluralist’s “arrangement of given facts into relations and qualities,” from which he concludes that monism is true, is a case in point. He correctly argues that if one posits the existence of two or more things, then there must be relations of some sort between them, and then (given his covert assumption that these relations are things) concludes that there must be further relations between these relations ad infinitum. Bradley’s regress misfires because a pluralist would reject his assumption. Again, some regress arguments fail because they presume that any infinite series is vicious. Aquinas’s regress objection to an infinite series of movers, from which he concludes that there must be a prime mover, involves this sort of confusion. -- infinity, in set theory, the property of a set whereby it has a proper subset whose members can be placed in one-to-one correspondence with all the members of the set, as the even integers can be so arranged in respect to the natural numbers by the function f(x) = x/2, namely: Devised by Richard Dedekind in defiance of the age-old intuition that no part of a thing can be as large as the thing, this set-theoretical definition of ‘infinity’, having been much acclaimed by philosophers like Russell as a model of conceptual analysis that philosophers were urged to emulate, can elucidate the putative infinity of space, time, and even God, his power, wisdom, etc. If a set’s being denumerable – i.e., capable of having its members placed in one-to-one correspondence with the natural numbers – can well appear to define much more simply what the infinity of an infinite set is, Cantor exhibited the real numbers (as expressed by unending decimal expansions) as a counterexample, showing them to be indenumerable by means of his famous diagonal argument. Suppose all the real numbers between 0 and 1 are placed in one-to-one correspondence with the natural numbers, thus: Going down the principal diagonal, we can construct a new real number, e.g., .954 . . . , not found in the infinite “square array.” The most important result in set theory, Cantor’s theorem, is denied its full force by the maverick followers infinity infinity 430 4065h-l.qxd 08/02/1999 7:39 AM Page 430 of Skolem, who appeal to the fact that, though the real numbers constructible in any standard axiomatic system will be indenumerable relative to the resources of the system, they can be seen to be denumerable when viewed from outside it. Refusing to accept the absolute indenumerability of any set, the Skolemites, in relativizing the notion to some system, provide one further instance of the allure of relativism. More radical still are the nominalists who, rejecting all abstract entities and sets in particular, might be supposed to have no use for Cantor’s theorem. Not so. Assume with Democritus that there are infinitely many of his atoms, made of adamant. Corresponding to each infinite subset of these atoms will be their mereological sum or “fusion,” namely a certain quantity of adamant. Concrete entities acceptable to the nominalist, these quantities can be readily shown to be indenumerable. Whether Cantor’s still higher infinities beyond F1 admit of any such nominalistic realization remains a largely unexplored area. Aleph-zero or F0 being taken to be the transfinite number of the natural numbers, there are then F1 real numbers (assuming the continuum hypothesis), while the power set of the reals has F2 members, and the power set of that F3 members, etc. In general, K2 will be said to have a greater number (finite or transfinite) of members than K1 provided the members of K1 can be put in one-to-one correspondence with some proper subset of K2 but not vice versa. Skepticism regarding the higher infinities can trickle down even to F0, and if both Aristotle and Kant, the former in his critique of Zeno’s paradoxes, the latter in his treatment of cosmological antinomies, reject any actual, i.e. completed, infinite, in our time Dummett’s return to verificationism, as associated with the mathematical intuitionism of Brouwer, poses the keenest challenge. Recognition-transcendent sentences like ‘The total number of stars is infinite’ are charged with violating the intersubjective conditions required for a speaker of a language to manifest a grasp of their meaning.  Strawson, or Grice’s favourite informalist: THE INFORMALISTS – A Group under which Grice situated his post-generational Strawson and his pre-generational Ryle. informal fallacy, an error of reasoning or tactic of argument that can be used to persuade someone with whom you are reasoning that your argument is correct when really it is not. The standard treatment of the informal fallacies in logic textbooks draws heavily on Aristotle’s list, but there are many variants, and new fallacies have often been added, some of which have gained strong footholds in the textbooks. The word ‘informal’ indicates that these fallacies are not simply localized faults or failures in the given propositions (premises and conclusion) of an argument to conform to a standard of semantic correctness (like that of deductive logic), but are misuses of the argument in relation to a context of reasoning or type of dialogue that an arguer is supposed to be engaged in. Informal logic is the subfield of logical inquiry that deals with these fallacies. Typically, informal fallacies have a pragmatic (practical) aspect relating to how an argument is being used, and also a dialectical aspect, pertaining to a context of dialogue – normally an exchange between two participants in a discussion. Both aspects are major concerns of informal logic. Logic textbooks classify informal fallacies in various ways, but no clear and widely accepted system of classification has yet become established. Some textbooks are very inventive and prolific, citing many different fallacies, including novel and exotic ones. Others are more conservative, sticking with the twenty or so mainly featured in or derived from Aristotle’s original treatment, with a few widely accepted additions. The paragraphs below cover most of these “major” or widely featured fallacies, the ones most likely to be encountered by name in the language of everyday educated conversation. The genetic fallacy is the error of drawing an inappropriate conclusion about the goodness or badness of some property of a thing from the goodness or badness of some property of the origin of that thing. For example, ‘This medication was derived from a plant that is poisonous; therefore, even though my physician advises me to take it, I conclude that it would be very bad for me if I took it.’ The error is inappropriately arguing from the origin of the medication to the conclusion that it must be poisonous in any form or situation. The genetic fallacy is often construed very broadly making it coextensive with the personal attack type of argument (see the description of argumentum ad hominem below) that condemns a prior argument by condemning its source or proponent. Argumentum ad populum (argument to the people) is a kind of argument that uses appeal to popular sentiments to support a conclusion. Sometimes called “appeal to the gallery” or “appeal to popular pieties” or even “mob appeal,” this kind of argument has traditionally been portrayed as fallacious. However, there infinity, axiom of informal fallacy 431 4065h-l.qxd 08/02/1999 7:39 AM Page 431 need be nothing wrong with appealing to popular sentiments in argument, so long as their evidential value is not exaggerated. Even so, such a tactic can be fallacious when the attempt to arouse mass enthusiasms is used as a substitute to cover for a failure to bring forward the kind of evidence that is properly required to support one’s conclusion. Argumentum ad misericordiam (argument to pity) is a kind of argument that uses an appeal to pity, sympathy, or compassion to support its conclusion. Such arguments can have a legitimate place in some discussions – e.g., in appeals for charitable donations. But they can also put emotional pressure on a respondent in argument to try to cover up a weak case. For example, a student who does not have a legitimate reason for a late assignment might argue that if he doesn’t get a high grade, his disappointed mother might have a heart attack. The fallacy of composition is the error of arguing from a property of parts of a whole to a property of the whole – e.g., ‘The important parts of this machine are light; therefore this machine is light.’ But a property of the parts cannot always be transferred to the whole. In some cases, examples of the fallacy of composition are arguments from all the parts to a whole, e.g. ‘Everybody in the country pays her debts. Therefore the country pays its debts.’ The fallacy of division is the converse of that of composition: the error of arguing from a property of the whole to a property of its parts – e.g., ‘This machine is heavy; therefore all the parts of this machine are heavy.’ The problem is that the property possessed by the whole need not transfer to the parts. The fallacy of false cause, sometimes called post hoc, ergo propter hoc (after this, therefore because of this), is the error of arguing that because two events are correlated with one another, especially when they vary together, the one is the cause of the other. For example, there might be a genuine correlation between the stork population in certain areas of Europe and the human birth rate. But it would be an error to conclude, on that basis alone, that the presence of storks causes babies to be born. In general, however, correlation is good, if sometimes weak, evidence for causation. The problem comes in when the evidential strength of the correlation is exaggerated as causal evidence. The apparent connection could just be coincidence, or due to other factors that have not been taken into account, e.g., some third factor that causes both the events that are correlated with each other. The fallacy of secundum quid (neglecting qualifications) occurs where someone is arguing from a general rule to a particular case, or vice versa. One version of it is arguing from a general rule while overlooking or suppressing legitimate exceptions. This kind of error has also often been called the fallacy of accident. An example would be the argument ‘Everyone has the right to freedom of speech; therefore it is my right to shout “Fire” in this crowded theater if I want to.’ The other version of secundum quid, sometimes also called the fallacy of converse accident, or the fallacy of hasty generalization, is the error of trying to argue from a particular case to a general rule that does not properly fit that case. An example would be the argument ‘Tweetie [an ostrich] is a bird that does not fly; therefore birds do not fly’. The fault is the failure to recognize or acknowledge that Tweetie is not a typical bird with respect to flying. Argumentum consensus gentium (argument from the consensus of the nations) is a kind that appeals to the common consent of mankind to support a conclusion. Numerous philosophers and theologians in the past have appealed to this kind of argument to support conclusions like the existence of God and the binding character of moral principles. For example, ‘Belief in God is practically universal among human beings past and present; therefore there is a practical weight of presumption in favor of the truth of the proposition that God exists’. A version of the consensus gentium argument represented by this example has sometimes been put forward in logic textbooks as an instance of the argumentum ad populum (described above) called the argument from popularity: ‘Everybody believes (accepts) P as true; therefore P is true’. If interpreted as applicable in all cases, the argument from popularity is not generally sound, and may be regarded as a fallacy. However, if regarded as a presumptive inference that only applies in some cases, and as subject to withdrawal where evidence to the contrary exists, it can sometimes be regarded as a weak but plausible argument, useful to serve as a provisional guide to prudent action or reasoned commitment. Argumentum ad hominem (literally, argument against the man) is a kind of argument that uses a personal attack against an arguer to refute her argument. In the abusive or personal variant, the character of the arguer (especially character for veracity) is attacked; e.g., ‘You can’t believe what Smith says – he is a liar’. In evaluating testimony (e.g., in legal cross-examination), attacking an arguer’s character can be legitimate in some cases. Also in political debate, character can be a legitimate issue. However, ad hominem arguinformal fallacy informal fallacy 432 4065h-l.qxd 08/02/1999 7:39 AM Page 432 ments are commonly used fallaciously in attacking an opponent unfairly – e.g., where the attack is not merited, or where it is used to distract an audience from more relevant lines of argument. In the circumstantial variant, an arguer’s personal circumstances are claimed to be in conflict with his argument, implying that the arguer is either confused or insincere; e.g., ‘You don’t practice what you preach’. For example, a politician who has once advocated not raising taxes may be accused of “flip-flopping” if he himself subsequently favors legislation to raise taxes. This type of argument is not inherently fallacious, but it can go badly wrong, or be used in a fallacious way, for example if circumstances changed, or if the alleged conflict was less serious than the attacker claimed. Another variant is the “poisoning the well” type of ad hominem argument, where an arguer is said to have shown no regard for the truth, the implication being that nothing he says henceforth can ever be trusted as reliable. Yet another variant of the ad hominem argument often cited in logic textbooks is the tu quoque (you-too reply), where the arguer attacked by an ad hominem argument turns around and says, “What about you? Haven’t you ever lied before? You’re just as bad.” Still another variant is the bias type of ad hominem argument, where one party in an argument charges the other with not being honest or impartial or with having hidden motivations or personal interests at stake. Argumentum ad baculum (argument to the club) is a kind of argument that appeals to a threat or to fear in order to support a conclusion, or to intimidate a respondent into accepting it. Ad baculum arguments often take an indirect form; e.g., ‘If you don’t do this, harmful consequences to you might follow’. In such cases the utterance can often be taken as a threat. Ad baculum arguments are not inherently fallacious, because appeals to threatening or fearsome sanctions – e.g., harsh penalties for drunken driving – are not necessarily failures of critical argumentation. But because ad baculum arguments are powerful in eliciting emotions, they are often used persuasively as sophistical tactics in argumentation to avoid fulfilling the proper requirements of a burden of proof. Argument from authority is a kind of argument that uses expert opinion (de facto authority) or the pronouncement of someone invested with an institutional office or title (de jure authority) to support a conclusion. As a practical but fallible method of steering discussion toward a presumptive conclusion, the argument from authority can be a reasonable way of shifting a burden of proof. However, if pressed too hard in a discussion or portrayed as a better justification for a conclusion than the evidence warrants, it can become a fallacious argumentum ad verecundiam (see below). It should be noted, however, that arguments based on expert opinions are widely accepted both in artificial intelligence and everyday argumentation as legitimate and sound under the right conditions. Although arguments from authority have been strongly condemned during some historical periods as inherently fallacious, the current climate of opinion is to think of them as acceptable in some cases, even if they are fallible arguments that can easily go wrong or be misused by sophistical persuaders. Argumentum ad judicium represents a kind of knowledge-based argumentation that is empirical, as opposed to being based on an arguer’s personal opinion or viewpoint. In modern terminology, it apparently refers to an argument based on objective evidence, as opposed to somebody’s subjective opinion. The term appears to have been invented by Locke to contrast three commonly used kinds of arguments and a fourth special type of argument. The first three types of argument are based on premises that the respondent of the argument is taken to have already accepted. Thus these can all be called “personal” in nature. The fourth kind of argument – argumentum ad judicium – does not have to be based on what some person accepts, and so could perhaps be called “impersonal.” Locke writes that the first three kinds of arguments can dispose a person for the reception of truth, but cannot help that person to the truth. Only the argumentum ad judicium can do that. The first three types of arguments come from “my shamefacedness, ignorance or error,” whereas the argumentum ad judicium “comes from proofs and arguments and light arising from the nature of things themselves.” The first three types of arguments have only a preparatory function in finding the truth of a matter, whereas the argumentum ad judicium is more directly instrumental in helping us to find the truth. Argumentum ad verecundiam (argument to reverence or respect) is the fallacious use of expert opinion in argumentation to try to persuade someone to accept a conclusion. In the Essay concerning Human Understanding (1690) Locke describes such arguments as tactics of trying to prevail on the assent of someone by portraying him as irreverent or immodest if he does not readily yield to the authority of some learned informal fallacy informal fallacy 433 4065h-l.qxd 08/02/1999 7:39 AM Page 433 opinion cited. Locke does not claim, however, that all appeals to expert authority in argument are fallacious. They can be reasonable if used judiciously. Argumentum ad ignorantiam (argument to ignorance) takes the following form: a proposition a is not known or proved to be true (false); therefore A is false (true). It is a negative type of knowledge-based or presumptive reasoning, generally not conclusive, but it is nevertheless often non-fallacious in balance-of-consideration cases where the evidence is inconclusive to resolve a disputed question. In such cases it is a kind of presumption-based argumentation used to advocate adopting a conclusion provisionally, in the absence of hard knowledge that would determine whether the conclusion is true or false. An example would be: Smith has not been heard from for over seven years, and there is no evidence that he is alive; therefore it may be presumed (for the purpose of settling Smith’s estate) that he is dead. Arguments from ignorance ought not to be pressed too hard or used with too strong a degree of confidence. An example comes from the U.S. Senate hearings in 1950, in which Senator Joseph McCarthy used case histories to argue that certain persons in the State Department should be considered Communists. Of one case he said, “I do not have much information on this except the general statement of the agency that there is nothing in the files to disprove his Communist connections.” The strength of any argument from ignorance depends on the thoroughness of the search made. The argument from ignorance can be used to shift a burden of proof merely on the basis of rumor, innuendo, or false accusations, instead of real evidence. Ignoratio elenchi (ignorance of refutation) is the traditional name, following Aristotle, for the fault of failing to keep to the point in an argument. The fallacy is also called irrelevant conclusion or missing the point. Such a failure of relevance is essentially a failure to keep closely enough to the issue under discussion. Suppose that during a criminal trial, the prosecutor displays the victim’s bloody shirt and argues at length that murder is a horrible crime. The digression may be ruled irrelevant to the question at issue of whether the defendant is guilty of murder. Alleged failures of this type in argumentation are sometimes quite difficult to judge fairly, and a ruling should depend on the type of discussion the participants are supposed to be engaged in. In some cases, conventions or institutional rules of procedure – e.g. in a criminal trial – are aids to determining whether a line of argumentation should be judged relevant or not. Petitio principii (asking to be granted the “principle” or issue of the discussion to be proved), also called begging the question, is the fallacy of improperly arguing in a circle. Circular reasoning should not be presumed to be inherently fallacious, but can be fallacious where the circular argument has been used to disguise or cover up a failure to fulfill a burden of proof. The problem arises where the conclusion that was supposed to be proved is presumed within the premises to be granted by the respondent of the argument. Suppose I ask you to prove that this bicycle (the ownership of which is subject to dispute) belongs to Hector, and you reply, “All the bicycles around here belong to Hector.” The problem is that without independent evidence that shows otherwise, the premise that all the bicycles belong to Hector takes for granted that this bicycle belongs to Hector, instead of proving it by properly fulfilling the burden of proof. The fallacy of many questions (also called the fallacy of complex question) is the tactic of packing unwarranted presuppositions into a question so that any direct answer given by the respondent will trap her into conceding these presuppositions. The classical case is the question, “Have you stopped beating your spouse?” No matter how the respondent answers, yes or no, she concedes the presuppositions that (a) she has a spouse, and (b) she has beaten that spouse at some time. Where one or both of these presumptions are unwarranted in the given case, the use of this question is an instance of the fallacy of many questions. The fallacy of equivocation occurs where an ambiguous word has been used more than once in an argument in such a way that it is plausible to interpret it in one way in one instance of its use and in another way in another instance. Such an argument may seem persuasive if the shift in the context of use of the word makes these differing interpretations plausible. Equivocation, however, is generally seriously deceptive only in longer sequences of argument where the meaning of a word or phrase shifts subtly but significantly. A simplistic example will illustrate the gist of the fallacy: ‘The news media should present all the facts on anything that is in the public interest; the public interest in lives of movie stars is intense; therefore the news media should present all the facts on the private lives of movie stars’. This argument goes from plausible premises to an implausible conclusion by trading on the ambiguity of ‘public interest’. In one sense informal fallacy informal fallacy 434 4065h-l.qxd 08/02/1999 7:40 AM Page 434 it means ‘public benefit’ while in another sense it refers to something more akin to curiosity. Amphiboly (double arrangement) is a type of traditional fallacy (derived from Aristotle’s list of fallacies) that refers to the use of syntactically ambiguous sentences like ‘Save soap and waste paper’. Although the logic textbooks often cite examples of such sentences as fallacies, they have never made clear how they could be used to deceive in a serious discussion. Indeed, the example cited is not even an argument, but simply an ambiguous sentence. In cases of some advertisements like ‘Two pizzas for one special price’, however, one can see how the amphiboly seriously misleads readers into thinking they are being offered two pizzas for the regular price of one. Accent is the use of shifting stress or emphasis in speech as a means of deception. For example, if a speaker puts stress on the word ‘created’ in ‘All men were created equal’ it suggests (by implicaturum) the opposite proposition to ‘All men are equal’, namely ‘Not all men are (now) equal’. The oral stress allows the speaker to covertly suggest an inference the hearer is likely to draw, and to escape commitment to the conclusion suggested by later denying he said it. The slippery slope argument, in one form, counsels against some contemplated action (or inaction) on the ground that, once taken, it will be a first step in a sequence of events that will be difficult to resist and will (or may or must) lead to some dangerous (or undesirable or disastrous) outcome in the end. It is often argued, e.g., that once you allow euthanasia in any form, such as the withdrawal of heroic treatments of dying patients in hospitals, then (through erosion of respect for human life), you will eventually wind up with a totalitarian state where old, feeble, or politically troublesome individuals are routinely eliminated. Some slippery slope arguments can be reasonable, but they should not be put forward in an exaggerated way, supported with insufficient evidence, or used as a scare tactic.

informal logic: Grice preferred ‘material’ logic – “What Strawson means by ‘informal logic’ is best expressed by ‘ordinary-language logic,’ drawing on Bergmann’s distinction between the ordinary and the ideal.” Also called practical logic, the use of logic to identify, analyze, and evaluate arguments as they occur in contexts of discourse in everyday conversations. In informal logic, arguments are assessed on a case-by-case basis, relative to how the argument was used in a given context to persuade someone to accept the conclusion, or at least to give some reason relevant to accepting the conclusion.