H. P. Grice on Takeuti's conjecture

H. P. Grice on Takeuti's conjecture. 


Grice considers that it would be strong support for his aequi-vocality thesis ("must" is monosemous) if this or that modal expression (involving, say, "must" -- but why is it insensitive to use 'must' in the imperative mode?) is introduced into this or that system or calculus of natural 'deduction,' as it were, designed to handle both the buletic mode and the doxastic mode, independently of any reference to any other constraint in such a system, -- and, in particular, independently of any reference to this or that mode!

Grice hoped to find what Gentzen called an  "introduction rule" and also, surely, an "elimination rule" which would (as it should) be generic for this or that, say, unary or dyadic functor, or any other functor, which may later yield this or that 'satisfactoriness-function' to provide this or that 'satisfactoriness-condition.'

Suggestions are not hard to come by. 

Let us suppose that we are seeking to provide an "introduction rule" and an "elimination rule" for a particular modality: "must." 

********

For an "introduction rule," one might consider the following (I think equivalent) forms --


"IF"-INTRODUCTION RULE FOR GENERIC "MUST" (We will use the square as the modal operator, bearing in mind its generic reading). 

If 'φ' is demonstrable, '□φ' is demonstrable.

UTTERER'S/REASONER'S PROCEDURE:

Derive '□φ' from 'φ ', provided  'φ' depends on no assumption. 

********

For an "elimination rule," we may consider:

UTTERER'S/REASONER'S PROCEDURE:

Derive 'φ' from '□φ' 

***

In either rule, it is to be understood, of course, that this or that substituend of the syntactical the dummy 'φ' would contain either the '!' marker, or the '.' marker. 

Both "!p" (to follow Hofstadter and McKinsey) and ".p" would be proper substituends for 'φ.'


Of course, if we accept this or that suggestion of this or that introduction and elimination rule, we shall also have to accept whatever uncomfortable consequences either the introduction rule or elimination rule may entail, such as 'consequentia mirabilis,' the reason for its name being pretty puzzling to me. 

In particular, we shall have to meet the opposition of this or that philosopher who thinks, at least with respect to "must," that there is a need to distinguish a strictly semantic (or satisfactoriness-evaluable) "must" (qua valid) and a partially merely syntactical notion of "must" (qua provable).

The grounds on which such a contention is based may be a demand for a distinct notion of "must" by reference to which, in this or that proof of soundness (validity, validitas), or of completeness, the adequacy or strength of this or that notion of "provable" (provability-in-a-system -- such as the one Myro created in Grice's name, System G)  might be supported.

Or the grounds may be the intuitively not unattractive idea that the NON-provability and NON-disprovability of some conjectural claim, φ, should the claim be "neither provable nor disprovable," should not prohibit the conjectural claim (or its negation) from being attachable to 
"□," yielding, "□φ."

We just might never know to which of them, "φ" or "~φ," "□" attaches, yielding either "□φ" or "□~φ."

Such questions as these plainly deserve study.

But Grice feels he has no time to pursue them further, and leaves them to Michael Freedman!

Grice's suggested "elimination" rule for "□φ" ("Derive "φ" from "□φ.") treats "□" as generic, holding across the buletic and doxastic board, that *any* "must" utterance *entails* (or as Kleene prefers, *yields*) the result of dropping the "□" operator.

The use made of this or that MODE (now, not modal) operator, buletic (!) and doxastic (.) allows for a REVERSAL of the standard idea that this or that feature of "□" attaches only to some specific mode. 

A substitution of 


'□φ' 

for a buletic mode surely does not entail the DOXASTIC SATISFACTORINESS  of  "φ."

("Close the door!" does not entail that the door 
is closed).


With respect to this suggestion, the salient problem will be one of interpretation, as Peirce will love it, once it is understood that 'φ' should surely NOT be restricted to the doxastic mode marker but may cloak a buletic operator, with proper substituends being either "!φ" (buletic) or ".φ" (doxastic). 

The Grecians knew very well what they meant by 'buletic'!

What is it to mean to say that 

Let it be that the door is closed.

or worse,

Close the door!

is *entailed* (as Moore would put it) by, or is derivable from this expansion below?

It is necessary that let it be that the door is closed.

The door must-b be closed.

On the face of it, two lines of interpretation seem to offer themselves.

To say that this derivability obtains (i.e. that a "must" modally qualified utterance in the buletic mode ENTAILS its co-relative UN-qualified buletic counterpart) 

amounts to saying:

****

Anyone who utters (or wills):

The door must-b be closed.

is COMMITED to seeing (accepting) (cannot consistently refuse to accept) 

Close the door!
'I shall close the door'
The door will-b be closed. 

*****

Alternatively, this 'entailment' talk may commit us to saying:

If this or that species of 'satisfactoriness' attaches to "The door must-b be closed" (in its buletic species), it attaches to "The door will-b be closed."

Grice thinks one should be at liberty to adopt either of these interpretations of Moore's "entailment" with premise and conclusion in the buletic mode. 

Perhaps the first reading is more philosophical in that it does NOT rest on the priority of the doxastic over the buletic, which never holds!

There is, of course, a larger class of modals (not to be confused with my two MODES, buletic and doxastic), including not only "must," or "necessary", but "ceteris paribus", "might", "probable", and so forth, to which the project of characterisation by means of a pair of an introduction rule and an elimination rule has to be extended.

Introduction/Elimination of 'ceteris paribus'
Introduction/Elimination of 'might'
Introduction/Elimination of 'probable'
etc.

CETERIS PARIBUS
+
Derive "cp p" from "p"
-
Derive "p" from "cp"

POSSIBLE
+
Derive <>P from "p"
-
Derive p from <>p

PROBABILITY
+
Derive Pr(p) from p
-
Derive p from Pr(p)

This extension above might not be plain sailing! 

The very centrepiece of the programme itself needs some further elaboration. 

Can one be sure, for instance, that the provision of this or that syntactic rule, an introduction rule and an elimination rule, is sufficient for the unique determination of a concept such as "must"?

Or:

Might it be that, while this or that concept of modality  (as per 'modal logic') requires the availability of an introduction rule and an elimination rule, more than one modal concept (or even more than one concept, not necessarily in every case modal) may be associated with a single pair of rules, so that MORE STUFF THAN THE PROVISION of an introduction rule and an elimination rule is needed for a full discrimination of any one concept? 

How are we to find out and justify any answer to such a question, i.e. as to whether an introduction rule and an elimination rule is ALL we need?

And what should be said, in a generic account of 'modality' as applied to mode-generic utterances, of Takeuti's conjecture, viz. that the character of the *introduction* rule for this or that device determines (and conditions -- Takeuti's implicature being that it shouldn't) the character of the corresponding elimination rule for the device? 

The first question and the question regarding Takeuti's conjecture concerning our freedom to decide the form of an 'elimination rule' regardless of the form of the device's corresponding and prior 'introduction' rule, Grice leaves on one side, proceeding to what he calls "more pressing matters."

In any case, it might be argued that Takeuti's 'conjecture' is a 'conjecture' no more. 

It has been settled, if that helps.

(Takeuti was pleased). 

But Grice's point is that the settlement was NOT officiated for GENERIC modal-relativised mode-marked utterances, and Grice goes on to note one feature of our ordinary use of 'must' where Takeuti may be needed, and his conjecture re-unsettled.

For Grice has so far made no mention of the fairly obvious fact that, if the 'introduction rule' for "must" in effect bids us ascribe necessity to whatever is *demonstrable*, necessity is essentially relative to this or that system or theory, since it is within that or that system, calculus, or theory that this or that demonstration is achieved.

Spinoza dreamed that much of his 'ethica more geometrico'!

And indeed is upon the very *constitution* (never mind 'construction') of this or that system or theory within which demonstration is achieved that the very possibility of demonstration depends. 

So long as the PARENT or SENIOR (rather than the JUNIOR) system is held invariant, reference to the 'system,' 'calculus,' or 'theory,' may perhaps be safely omitted.

But if the reference-system is NOT invariant (and morality is its own realm) and if such a variation carries with it variation in the type or dimension of necessity, anonymity in such reference to this or that theory, system, or calculus, can no longer be safely preserved. 

This, Grice suggests, is the situation which prevails in the world today -- especially after Witters, and Foucault!

There are notorious different varieties of necessity or "must."

Grice freely qualifies them:

There's LOGICAL necessity of the type Quine denied but Grice and Strawson defended.

There's metaphysical necessity, as when Aristotle says that God must be the thinker of thoughts.

Then there's physical necessity, as when Newton said that the apple must freely fall.

Then there's psychological necessity of the type Freud dreamed of and D. F. Pears didn't.

Then there's moral necessity, of the type Judith Baker liked to philosophy on!

Then there's practical necessity, of the type R. M. Hare found it otiose to talk when he titled his essay, "Practical inferences."

Then there's legal necessity, of the type A. M. Honoré ("who attended, like me, Clifton" -- Grice) was obssessed with!

And, then, (why not?) there's even ichthyological (perhaps), that attaches to the pirots.

The OED says that a pirot is an extinct fish.

"Do not multiply necessities beyond necessity."

As Grice see things, each of these adjectives serves to indicate a more or less specific type of system or theory or calculus with references to which necessity obtains, and thus "demonstrability," of the type we use in this or that introduction rule, but particularly in this or that *elimination* rule. 

Some of the consequences or likely developments of a position of this sort should not be ignored, at least by this or that Griceian (Why is it that they all seem to be obsessed with the terminological point about the explicatum?) 

The idea of treating this or that type of "must" or necessity as explicable by a reference to the theory or system or calculus which determines or defines, or constitutes, or stipulates, "demonstrability" will, in certain cases, lead to a reversal of the assumptions about the priority of one mode-marker over another mode-marker, which this or that philosopher might be inclined to make. 

(Grice included: buletic mode DOMINATES!).

A philosopher might regard it as rational to suppose that what a logical theory (or system or calculus) does is to systematize or stipulate or constitute a corpus of antecedently, or pre-theoretically (or 'informal,' as Strawson prefers) given items incorporating this or that logical necessity.

And then there's perhaps the  even more natural supposition, "such as I witnessed G. J. Warnock held," that this or that moral theory does (or would if there were such a theory) systematise antecedently (or pre-theoretical, or informal) given items relating to this or that moral obligation or this or that moral incumbency.

"As my tutor Hardie told me, surely you won't wait for the PHILOSOPHER to tell you what you must do, Grice!"

("I then changed my topic to that of personal identity." -- Grice.)

But Grice's proposal would disallow those modes of thinking. 

If this or that incumbency is a moral necessity, and this or that moral necessity is what is syntactically "demonstrable" in an (acceptable) moral theory or system, or calculus (alla Spinoza's ethica more geometrico), the system, calculus, or theory, comes first and cannot be informatively characterised as this system or theory or calculus relating to this or that incumbency or this or that moral necessity!

It is a pre-condition, as Kant would have it.

That is why he thought, unlike Collingwood, that there could not be a philosophy without this or that presupposition. 

Similarly, a logical theory must be independently characterisable (or explained, or constituted, or stipulated) otherwise than by reference to its concern with this or that logical necessity!

This reversal of direction Grice finds appealing in not being "blatantly viciously circular," and particularly as this reversed direction emphasises the central importance of the construction of this or that theory, system, or calculus. 

No system, no necessity. 

No moralist, no "mos."

mos , mōris, m. etym. dub.; perh. root ma-, measure; cf.: maturus, matutinus; prop., a measuring or guiding rule of life; hence,

I.manner, custom, way, usage, practice, fashion, wont, as determined not by the laws, but by men's will and pleasure, humor, self-will, caprice (class.; cf.: consuetudo, usus).

I. Lit.: “opsequens oboediensque'st mori atque imperiis patris,” Plaut. Bacch. 3, 3, 54: “huncine erat aequum ex illius more, an illum ex hujus vivere?” Ter. Heaut. 1, 2, 24: alieno more vivendum est mihi, according to the will or humor of another, id. And. 1, 1, 125: “nonne fuit levius dominae pervincere mores,” Prop. 1, 17, 15: morem alicui gerere, to do the will of a person, to humor, gratify, obey him: “sic decet morem geras,” Plaut. Most. 3, 2, 35; Cic. Tusc. 1, 9, 17: “animo morem gessero,” Ter. And. 4, 1, 17: “adulescenti morem gestum oportuit,” id. Ad. 2, 2, 6; v. gero.—

II. The will as a rule for action, custom, usage, practice, wont, habit: “leges mori serviunt,” usage, custom, Plaut. Trin. 4, 3, 36: “legi morique parendum est,” Cic. Univ. 11: “ibam forte Viā Sacrā, sicut meus est mos,” custom, wont, Hor. S. 1, 9, 1: “contra morem consuetudinemque civilem,” Cic. Off. 1, 41, 148: “quae vero more agentur institutisque civilibus,” according to usage, according to custom, id. ib.: “mos est hominum, ut nolint eundem pluribus rebus excellere,” id. Brut. 21, 84: “ut mos est,” Juv. 6, 392; “moris erat quondam servare, etc.,” id. 11, 83: “more sinistro,” by a perverted custom, id. 2, 87.— So with ut: “morem traditum a patribus, ut, etc.,” Liv. 27, 11, 10: “hunc morem servare, ut, etc.,” id. 32, 34, 5: “virginibus Tyriis mos est gestare pharetram,” it is the custom, they are accustomed, Verg. A. 1, 336: “qui istic mos est?” Ter. Heaut. 3, 3, 1: “mos ita rogandi,” Cic. Fam. 12, 17, 1: “ut mos fuit Bithyniae regibus,” Cic. Verr. 2, 5, 11, § 27: moris est, it is the custom: “negavit, moris esse Graecorum, ut, etc.,” id. ib. 2, 1, 26, § 66; Vell. 2, 37, 5: “quae moris Graecorum non sint,” Liv. 36, 28, 4; cf.: “(aliquid) satis ex more Graecorum factum,” id. 36, 28, 5: “ut Domitiano moris erat,” Tac. Agr. 39.—Plur.: “id quoque morum Tiberii erat,” Tac. A. 1, 80: “praeter civium morem,” contrary to custom, to usage, Ter. And. 5, 3, 9: sine more, unwonted, unparalleled: “facinus sine more,” Stat. Th. 1, 238; so, “nullo more,” id. ib. 7, 135: “supra morem: terra supra morem densa,” unusually, Verg. G. 2, 227 (cf.: “supra modum): perducere aliquid in morem,” to make into a custom, make customary, Cic. Inv. 2, 54, 162: “quod jam in morem venerat, ut, etc.,” had become customary, Liv. 42, 21, 7.—

B. In partic., in a moral point of view, conduct, behavior; in plur., manners, morals, character; in a good or bad sense: “est ita temperatis moderatisque moribus, ut summa severitas summā cum humanitate jungatur,” manners, Cic. Fam. 12, 27, 1: “suavissimi mores,” id. Att. 16, 16, A, 6: boni, id. Fragm. ap. Non. 254, 8.—Prov.: “corrumpunt mores bonos colloquia mala,” Vulg. 1 Cor. 15, 33: “justi,” Cic. de Or. 2, 43, 184: “severi et pudici,” Plin. 28, 8, 27, § 106: “sanctissimi,” Plin. Ep. 10, 20, 3: feri immanisque natura, Cic. Rosc. Am. 13, 38: “totam vitam, naturam moresque alicujus cognoscere,” character, id. ib. 38, 109: “eos esse M'. Curii mores, eamque probitatem, ut, etc.,” id. Fam. 13, 17, 3; id. de Or. 2, 43, 182: “mores disciplinamque alicujus imitari,” id. Deiot. 10, 28: “perditi,” id. Fam. 2, 5, 2: “praefectura morum,” the supervision of the public morals, Suet. Caes. 76: “moribus et caelum patuit,” to good morals, virtue, Prop. 4 (5), 11, 101. “amator meretricis mores sibi emit auro et purpurā,” polite behavior, complaisance, Plaut. Most. 1, 3, 128: “propitiis, si per mores nostros liceret, diis,” i. e. our evil way of life, Tac. H. 3, 72: “morum quoque filius,” like his father in character, Juv. 14, 52: “ne te ignarum fuisse dicas meorum morum, leno ego sum,” i. e. my trade, Ter. Ad. 2, 1, 6: “in publicis moribus,” Suet. Tib. 33; 42.—

III. Transf.

A. Quality, nature, manner; mode, fashion: “haec meretrix fecit, ut mos est meretricius,” Plaut. Men. 5, 4, 8: “mores siderum,” qualities, properties, Plin. 18, 24, 56, § 206: “caeli,” Verg. G. 1, 51: “Carneadeo more et modo disputare,” manner, Cic. Univ. 1: “si humano modo, si usitato more peccāsset,” in the usual manner, Cic. Verr. 2, 2, 3, § 9: “Graeco more bibere,” id. ib. 1, 26, 66: “apis Matinae More modoque,” after the manner of, like, Hor. C. 4, 2, 27: “Dardanius torrentis aquae vel turbinis atri More furens,” Verg. A. 10, 604: “more novalium,” Col. 3, 13, 4: “caeli et anni mores,” Col. 1, Praef. 23: “omnium more,” Cic. Fam. 12, 17, 3; so, “ad morem actionum,” Quint. 4, 1, 43: “elabitur anguis in morem fluminis,” like, Verg. G. 1, 245: “in hunc operis morem,” Hor. S. 2, 1, 63: “pecudum in morem,” Flor. 3, 8, 6: “morem vestis tenere,” mode, fashion, Just. 1, 2, 3.—

B. A precept, law, rule (poet. and postAug.): “moresque viris et moenia ponet,” precepts, laws, Verg. A. 1, 264; cf.: “pacis inponere morem,” id. ib. 6, 852: “quod moribus eorum interdici non poterat,” Nep. Ham. 3: “quid ferri duritiā pugnacius? sed cedit, et patitur mores,” submits to laws, obeys, is tamed, Plin. 36, 16, 25, § 127: “ut leo mores Accepit,” Stat. Ach. 2, 183: “in morem tonsa coma, = ex more ludi,” Verg. A. 5, 556.

There is, Grice notes, no reason to expect that this or that theory or system or calculus by reference to which the general characterizations of a modality, such as necessity, is to be diversified, will be either detached from or independent of each other. 

Unless we stipulate that "metaphysical necessity" comes first -- as part of the Theory-theory that metaphysics is supposed to be.

One might thus expect to find a serial relationship within groups of this or that system, theory, or calculus:

A philosopher (qua metaphysician, now) might hold that a Theory A (say logic) is presupposed by theory B (say metaphysics), which in turn is presupposed by theory C (say physics).

I call him Churchland!


Or which in turn is presupposed by theory D (say physiology)


I call him Hawking, only he ain't no philosopher!

-- In which we may expect to find our "theory-space" being stocked bit by bit with this or that extension of prior occupants thereof. 

But perhaps not every extension of a JUNIOR theory (rather than the PARENT or SENIOR Theory-theory will give the (a new) adverbial or adjective with which to modify such modals as "necessary". 

One, and not just a fisherman, might expect that there is this or that special law or generality which is common and peculiar to fish (or pirot -- say the physiology of the gill -- 



GRICE ON ICHTHYOLOGICAL NECESSITY: THE GILL

But I would doubt whether this fact (if it be a fact) would give one a special type of necessity, viz., ichthyological necessity. 

Then there are pigs, and grices.

Is there a grice-necessity?

Was it necessary for the grice to become exinct?

The grice was voracious in the extreme, and excessively difficult to confine in pasture or to fatten.

The grice was also destructive and mischievous, and therefore OUGHT, that is, must, gradually to be extirpated.

This, combined with the increasing import of other breeds from the Scottish mainland, resulted in a dwindling grice population, and sometime between the middle of the 19th century and the 1930s the grice became extinct.

The legacy of grice remains, however, for ever.

The wild bulb vernal squill is known locally (in Griceland) as "grice's onions" because it was a favourite food of the, er, grice. 

Grice thinks that any theory (or system or theory) which creates a further adjective to modify 'necessity' -- or adverb, as in "ichthyologically necessary" -- must provide an extension of a certain degree or kind of generality, which the theory or calculus or system of ichthyology seems to fail to reach.

But then Grice claimed, "But then I'm not a fisherman!"

"On top, I have no idea how such this or that type, or this or that level, of generality should be characterized, if at all." 

Grice then wonders whether his reflection on the 'relativity' or specificity of necessity (and maybe other modalities) to a theory or a system or a calculus (alla Carnap) aids him in his defence of the Aequi-vocality Thesis against the threat seemingly presented by one-sided relativization of such modalities to this or that person, this or that agent, this or that utterer, this or that reasoner. 

Grice thinks that his exploration may thus help, provided that he can represent any personal (or agent) relativity sometimes exhibited by this or that practical modal as a special case of relativity to a given system, theory, of calculus (alla Carnap).

Grice goes on to consider what the import of the relativization of a particular modal, say 'necessary' to an individual person or creature, or pirot, or agent, or utterer, might be. 

One interesting possibility is that the relativization indicates a person (or pirot, as Grice prefers) whose judgement or opinion it is that something or other is, doxastically, the case: 

"For Dr. Keate, of Clifton, it is necessary that every boy should or must or ought to be beaten at least once a week."

(Some of us Old Cliftonians will remember doctor Keate!)  

(And some saw him at Eton, too!)

He also thought that schoolboys were reptiles. 

The case of Doctor Keate, as it happens, is an uninteresting one, in that this kind of relativity is not restricted to this or that practical modal, nor indeed to this or that modal, simpliciter.

"For . . ." works as a generic sentence-adverbial:

For Dr. Keate schoolboys are a species of reptile."

Surely he would not be otiose enough to say that a schoolboy OUGHT to be a reptile.

Other more authentic cases (less pseudo) of modality-relativization are also more interesting. 

The admittedly unidiomatic utterance:

"It is necessary with respect to Mrs. Thatcher that Mr. Heath (rather than 'Nico' Henderson) become the Ambassador to the United States -- at once. Utterered May 1979.)

might be interpreted as saying that

-- It is Mrs. Thatcher who ordains this fate for Mr. Heath.

-- It is Mrs. Thatcher to whose advantage it would be thus to dispose of Mr. Heath, 

-- It is Mrs. Thatcher's business to see that the transformation is effected.

Symbolise that by

"Heath MUST-1 go to Washington."
"Heath MUST-2 go to Washington."
"Heath MUST-3 go to Washington."

In fact, Mrs Thatcher did politely ask Edward Heath, whom she knew quite well, to take up the post.

Alas, Heath blatantly refused the "kind offer."

And thus, a surprise extension to 'Nico' Henderson's career came about because of the election of Margaret Thatcher as Prime Minister in May of 1979. 

Heath having rejected Thatcher's 'necessity,' Mrs Thatcher felt the need to invite 'Nico' Henderson to return to service from early retirement as Ambassador to Washington, where he served until 1982. 

"Mrs Thatcher," Henderson told THE TIMES, "had first asked Edward Heath to take up the post, but he had refused the offer, don't know why." 

As it happens, Henderson became enormously popular in Washington (as Heath wouldn't) and he and his wife formed a close personal friendship with Reagan at a crucial time. 

Henderson (as Heath would have not) was particularly successful in maintaining friendly relations between "England" (or UK, as Henderson never called her) and "The New World," when that friendship was under some strain.


But Grice disgresses. 

Leaving on one side for a moment the by no means unimportant first alternative, Grice puts the other modes of interpretation to work. 

It is not too difficult to envisage a body of precepts about how to behave, relating to a single particular person, who is intended to be both agent and beneficiary with respect to the operation of these precepts.

Nor is it a great additional effort to suppose these "junior" precepts to be DERIVABLE (alla Spinoza) from a limited number of parent or senior precepts, still however retaining reference to the particular individual, and generally, with the aid of further factual premises, a system or calculus or theory, or 'immanuel' which constitutes a self-help manual (or 'immanuel') for that individual (Call that individual Immanuel -- "Cant, Immanuel Cant.")

It seems by no means out of the question that, if the references to that individual (Immanuel Kant) are to be irreducible (not eliminable in favour of references to classes of person to which the individual belongs, say Germans, or Germans living in the little village where Cant lived, or Germans of Scots descent, or Scots), the first interpretation might also have to be brought into play.

The manual (the immanuel) is a manual (or immanuel) for a particular individual, Immanuel Kant (and for no other individual, say, his brother, if he had one) just because Immanuel Kant (as we now call him) has 'legislated' (rightly or wrongly) what his ends, i.e. Immanuel Kant's ends, are to be. 

(It's different with Howard).

Grice is inclined to think of this more or less articulated 'egoistic' (if not 'solipsistic') manual (or immanuel) of this sort as underlying morality!

Such a subjectivist relativist I am!


Grice now has, he hopes, reached the idea of a relativised modalities, as connected to 'establishability' in a 'personalized system,' such as Immanuel's system.  

Let us now see if the patterns of either the introduction rule or the elimination rule can be extended to relativised necessity, regarded in this Kantian light. 

There seems to be no particular problem, pace Takeuti, about allowing an "introduction rule" which tells us as per below.

INTRODUCTION RULE 
+
Introduction rule for a modal-relative mode-marked utterance.

IF it is establishED that φ in Immanuel Kant's 'personalized' system, theory, or calculus (Immanuel Kant's 'immanuel'), 

'it is necessary, in relation to: Immanuel Kant, that φ' is establishABLE. 

***

And now we come to Takeuti's problem, or 'conjecture.'

Takeuti's conjecture has been settled in this or that realm, but not in EVERY realm

As Takeuti seems to have subspected, the accompanying "elimination rule" for modality is, however, slightly less promising, or "far less" promising, as Takeuti would put it, and Takeuti would possibly agree with us that Takeuti's conjecture should (or must) be unsettled!

One seems to be in 'conceptual' trouble if one supposes such an "elimination rule" to tell or advice us:

If one is committed to the idea that it is necessary with respect to Immanuel Kant that φ, 

one is also committed to *whatever is expressed* by φ.

Or if alla Kant, we formulate it in the 'shall' idiom:


If thou shalt be commited to the idea that, in relation to Immanuel Kant, □φ,

thou shalt be commmited to *whatever is explicitly conveyed* by φ.


For such an "elimination rule" is just not acceptable!

For why what is necessary for Immanuel Kant (according to his immanuel) should be necessary for me?

Let "φ" be a buletic utterance such as "Let it be that Immanuel Kant doth not lie."

And the UTTERER's commitment to the idea that *Immanuel Kant*'s system requires IMMANUEL KANT not to lie does not ipso facto (if we can speak of 'facto' here) involve THE UTTERER (or reasoner) in accepting (volitively, or buletically) let, say, Grice, not lie. 

However, Takeuti is right. "Elimination rule" is a trick. And the philosopher should NOT be forced to let the formulation of this or that elimination rule be CONDITIONED upon the way he has formulated the corresponding INTRODUCTION rule for the same device. 

VERSION B OF THE ELIMINATION RULE FOR "MUST" -- according to Takeuti, or following Takeuti's suggestion.

If we take, following Takeuti, the "elimination rule" for "must," rather, as telling or advising us:

If it is necessary in relation to Immanuel Kant that let Immanuel Kant not lie, "let Immanuel Kant not lie" is

SATISFACTORY-qua-relativised-TO-Immanuel-Kant.

the situation is easier.

This Version B of the elimination rule -- a version  that would have pleased Takeuti, since its formulation is not conditioned by the corresponding introduction rule -- seems inoffensive (or harmless) enough, even for Takeuti, we hope.

We shall call it the AGENT-RELATIVE-MODAL-marked mode-marked utterance.

It involves what Grice elsewhere calls a 'subjective condition' -- re: intending, and re: reasoning. 

Grice's second interpretation or reading of the "elimination rule" for "must parallels the SECOND option, with respect to the form of the "elimination rule" for UNrelativized (or absolute) necessity, or "must" simpliciter, or NOT-AGENT-RELATIVE. 

So perhaps the deferred selection should be made, in favour of that SECOND option.

But let us, without relying on the encouraging aspect of this Takeuti-type procedure regarding the formulation of an "elimination" rule NOT mirror the corresponding prior "introduction" rule for this or that device, turn our attention to an assessment of the prospects of yet a different procedure, viz. an attempt to exhibit the seeming or alleged (by Hume) one-sidedness of the appearance of relativity in this or that modality in the buletic zone as an illusion, a 'surface' phenomenon (as Chomsky might put it and as as Hofstadter and McKinsey WOULD NOT want -- they distinguish between 'satisfactory,' satisfied,' and 'correct,' anyway) explicable in terms of this or that absolute (or unrelativised) modality.

Considered in relation to necessity, the idea would be that, e.g., to say:

"It is necessary for Nixon to apply for the Regius Chair of Moral and Pastoral Theology" 

or 

It is necessary, relative to Nixon, that let Nixon apply for the Regius Chair of Moral and Pastoral Theology.

Or more generally

It is necessary, relative to Agent A1, that let A1 do action alpha.

is merely to produce a specimen of conditional (hypothetical) necessity -- a kind of necessity which is by no means confined to the practical (buletic, or volitive) area. 

What is expressed by such an utterance can be represented as a consequence of two premises, to wit:

It is necessary that let ANY AGENT A who satisfies condition C apply for The Regius Chair of Moral and Pastoral Theology.

where 'C' represents some possibly quite complex condition -- and 

The agent Nixon does fulfill condition C.

Indeed, as Grice notes, if one allows oneself to QUANTIFY over this or that condition (whatever the condition may be, for surely what condition is Nixon fulfilling?), we can represent its meaning by the following:
(EC). There is this or that condition C such that it is necessary that let this or that agent A, who fulfils the condition C apply for The Regius Chair in Moral and Pastoral Theology. AND. Nixon fulfills condition C.

The paraphrase, as Grice notes, uses no relativized modal -- relativised to Nixon, that is -- and, furthermore, is not importantly different in character from a proper expansion of the doxastic: 

This bit of metal, being gold (i. e., fulfilling the condition of having the chemical composition of Gold) MUST dissolve in aqua regia.

Grice doubts whether this attempt to 'conjure away' agent-relativization (and this or that 'subjective condition') from the concept of practical necessity can succeed. 

In the scenario Grice explores, Nixon is spoken of as being both the personal agent who is or should be CONCERNED about what is being explicitly conveyed to be a matter of necessity.

But Nixon is ALSO being spoken as the agent (or patient) whose doings (to apply to the chair) (or sufferings) are of concern. 

Often the same personal agent does operates (as here) in both roles (the role of '... is concerned' and the role of '... doing' or '... being done,' if that's not too rude.

And where this is so, it is cosy to fall into the idea that a SINGLE reference to the agent (or patient) is all that is needed, and so that relativization can be eliminated. 

But things are not always thus.

Grice invites us to consider:

It is necessary for, to, or in relation to Joe Garagiola, that THE AMERICAN PUBLIC (Garagiola included) retains an interest in baseball.

The Joe-Garagiola utterance seems different in this respect. 



JOE GARAGIOLA

FOR it is of Joe Garagiola's concern that an agent OTHER than himself keeps an interest in baseball.

As Prichard taught us regarding "willing that...' we  need to distinguish between the personal agent (or patient) for whom something is a "reason" or "ground" (or is necessary), and the personal agent or patient about whom the utterer is REFERRING when he explicitly conveys what is necessary, or what there is a reason for. 

Grice finds it, morever, plausible to suggest that, when not one personal agent or patient is either explicitly (via explicatum) or implicitly (via implicatum) referred to as a personal agent or patient for whom something is necessary (or as called for by reason, or a ground), the reason or the necessity is generic, absolute, public and objective, rather specific, relative, private and subjective.

This treatment would represent it as of generic, absolute, public and objective concern that NIXON apply for The Regius Chair of Moral and Pastoral Theology.

But this sounds harsh.

It is surely a matter of specfic, Nixon-relative, private, and subjective necessity that Nixon apply for The Regius Chair of Moral and Pastoral Theology.

This necessity does not yield that it is a matter of proper concern to any other personal agent or patient that Nixon so apply.

While it is not clear exactly what kind or degree of intervention is sanctioned by a generally applicable un-relativized or absolute necessity, it is difficult to avoid the idea that some measure of intervention is justified, ex vi termini, in cases of such necessity. 

As when we say that the claim of a privilege seems rather, ex vi termini, to imply a superior power.


The situation, already complex, is further complicated by a number of additional considerations. 

It might turn out to be the case that a relativized necessiy, though distinct from an absolute necessity, may be backed or supported by an absolute necessity.

What Immanuel Kant must do is ENTAILED by what a rational personal agent must do. 

The PRIVATE, subjective, relative, specific necessity in the case of Nixon, to apply for The Regius Chair of Moral and Pastoral Theology, may be backed, in the first instance, by the ends which Nixon has set for himself.

But the adoption of this or that end might not be arbitrary, or nilly willy, or capricious. 

There might be an acceptable GENERIC status affirming that, for any personal agent of a certain sort (which Nixon is) it should be a matter of private necessity to have this or that end E.

And this generality might itself be a matter of some kind of necessity, buletic or doxastic. 

A private, subjective, relative, specific necessity is distinct from, but possibly supported by, a public, objective, absolute, generic necessity that in certain circumstances such a private necessity may obtain. 

Again, the backing of a private necessity by a public necessity might be not just a feature which is sometimes present, but one which was in one way or another demanded, as Kant would put it, buletically or doxastically.

What Kant calls, in German, "a demand of reason." 

An actual demand (Nachfrage) leads to the valuations of goods. 


It might be possible to argue for the acceptability of this or that "Universalisability Principle," as R. M. Hare calls it, relating to private (relativized) necessity: 

It is doxastically necessary that:

if it is necessary to some agent, Immanuel Kant, that p should be case [that let it be that p]

there is some condition C such that this or that agent Immanuel Kant fulfils and [necessarily] for ANY agent A who fulfils X, it is [practically] necessary for A that let it be that p (that p should be the case).

It is buletically necessary that, if it is necessary to Immanuel Kant that p should be the case, 

let there be some condition C, such that Kant fulfills C, and [necessarily] for ANY AGENT A who fulfills C, it is [practically] necessary for A that let it be that p (that p should be the case). 

Of these two principles, Grice confesses that he is attracted by the second, which makes it NOT a logical (doxastic) requirement, but so to speak a rational (buletic) desideratum that any agent should accept something as a matter of practical necessity 

IFF

the agent can back its acceptance on a general principle about relativized necessity.

Grice develops this in his third Carus lecture.

This will allow this or that personal agent to be subject to this or that private necessity which is nevertheless not rationally well founded (that I shall have a nice cup of tea or that Grice will smoke a cigarette). 

But at this point we are, Grice thinks, just scratching the surface of a very difficult and very important philosophical area.

Much more attention to it is needed. 

Grice gives "a moderately strong green light" to the idea that the emergence of one-sided personal relativization in this or that practical modality SHOULD NOT damage or tarnish his Aequi-vocality Thesis ("must" has only one sense).

Grice similarly gives "a moderately strong RED light" to the idea that such one-sided relativization is an Humeian illusion, to be dissolved into some underlying absolute modality. 


For surely at Clifton and Oxford we are taught to live and let live.

But there, Grice notes, yet a third possibility, viz. that relativization is authentic, but is not one-sided but two-sided, Janus-like, being found on both the buletic side and the doxastic side.

The two sides of the coin of reason.

Along these lines Grice seeks to treat the possession of an essential property (e.g, the possession by a particular table of the property of being made of wood) as analogous to a relativized practical necessity.

It is perhaps essential to the existence of THIS table that it may be made of wood (a table not made of wood would not be THIS table), analogous to the way in which it might be (in a practical case) essential to the existence of a particular specific personal human being or agent/patient, Nixon, that he breathe and perform other vital human functions. 

Further discussion of this idea of an 'essential property' belong to a broader exploration of the notion of 'life' (bios) purpose ('telos'), or metier, and 'final cause.'

Given the verbal (though I hope not conceptual) complexity involved, particularly in the account of Grice gives of what he calls 'modals' ("must"), mode ("!" and ".") with their operators, and in order to make the programme clearer, Grice feels the need to clarify the programme. 

Grice perceives that the 'faculty' of reason (unlike the sub-faculty of philosophy) is most closely connected with "reasoning from p to c" and with this or that reason.

A justificatory reason is the stuff of which reasoning is made.

Reasoning may be required to arrive (in some cases) even at the simplest of reasons.

So it seems proper to proceed from a consideration of the psychological processs of "reasoning" to a consideration of this or that "reason."

Grice distinguishes three types of case (if you like, three ways of using 'reason') with respect to the word 'reason' ('reasons'), which Grice calls the explanatory use or case, the justificatory use or case, and the justificatory-cum-explanatory use or case, which Grice later renames the justificatory-cum-explanatory as the 'personal agent/patient' use or case. 

The three cases (justificatory, explanatory, and mixed) are interconnected, and a prominent way in which they are interconnected is the following.

If someone thinks that a certain set of considerations is a justificatory reason for doing, intending, or believing that p, and if the agent in fact does, intends, or believes that p because he so thinks, A's personal reason for actually doing (intending, believing) that thing is that the afore-mentioned set of considerations obtains.

And to state that an agent does (intends, believes, desires) that p for a specified personal reason is a special case of giving an "explanatory" reason for A's doing (intending, desiring, or believing) that p.

Since a justificatory reasons lie at the heart of this or other reasons of other varieties, it seems proper to consider further the character of a justificatory reason.

A justificatory reason is widely thought to be divisible buletic and doxastic.

It is plain that this or that modal expression, such as 'must', 'ought', 'should', 'necessary', etc. (which I shall label 'common or neutral modals') not only are widely used in the specification of justificatory reasons in a way which is intimately connected with their justificatory character, but also are used on both sides of the buletic/doxastic barrier, on either side of the coin of reason. 

It seems relevant, then, to ask whether this or that common or neutral modal is univocal across this barrier (viz. whether the barrier enforces a change of sense -- as we hope NOT! -- , or whether whatever alleged multiplicities of sense this or that common modal may have appear equally on both sides of the barrier); or whether, on the other hand, there is merely an analogy (as Conte would put it) between the buletic and doxastic employment of this or that common or neutral modal. 

This problem seems highly germane to Kant's claim that there is a single faculty of reason, even though he wrote a treatise for each.

(And on top, a third treatise to allow practical reason to do what doxastic reason Kant, to wit: endow a human being with dignity).

This question (or group of questions) about the possible indifference, or neutrality, or commonality, with respect to their Fregeian 'sense,' of this or that common modal to crossing the barrier is in more ways than one a far from clear question. 

With the idea of making it somewhat clearer, while at the same time gaining some illumination about the relation between a buleetic and a doxastic reason, Grice proposes to use as a springboard a suggestion of Davidson, of  explaining the possibility of giving a structural representation or logical form to this or that utterance involving two modals, which seemingly inhabit opposite sides of the barrier

Davidson uses "desirable" (or desirability) and "probable" (or probability) and Grice applies them in terms of a single maybe to some degree artificial, modal 

"it is acceptable that" 

in combination with one or other of two mode-markers, 

!

and 

⊢

or 

.


followed by a phrastic (radical). 

Grice proposes, however, not to restrict himself indefinitely to this case, and to bring other common modals into the account.

Grice talks about a 'mode' rather than a 'mood' to make it clear that he is not trying to characterize what this or that philosopher would be likely to call a 'mood', Grice certainly expects there to be this or that important link between this or that philosophical use of  'mood' and Grice's 'mode.' 

Grice would justify (or explain) his use of the term 'mode' by reference to his Peirceian views on meaning. 

According to the Peirceian view on "... means ...', what an utterer U means (viz. that p) is to be explained in terms of this or that effect or response -- always a psychological state, stance, or attitude) which the utterer U intends to produce in an actual or possible addressee A, or intends A to adopt. 

Derivatively, or even figuratively (metaphorically) what an utterance, sentence, utterance-part, sentence-part, word, expression in this or that language 'means' is to be explained in terms of directives or procedures (basic or resultant) with respect to the employment of a TOKEN of the TYPE of this or that sentence, in a primitive (basic) way, with a view to inducing in this addressee A a certain kind of effect or response.

Quite a metaphor, eh!?

What the utterer U means very often differs from what his utterance 'means.' (Grice wishes Austin would have given more attention to this -- "a distinction all too frequently ignored by Austin, and apparently denied by Witters!") 

What an utterer U means is in a way generally discernible on the basis of 'knowing' the directive for the specific expression together with facts about the circumstances and intentions of the utterer.

E.g. My aunt Matilda won't use 'runt,' for 'under-sized person.' She may at most IMPLICATE it.

The intended effect or response on the addressee is (in Grice's view) one or other of a set of this or that psychological state, stance or  attitude with respect to some 'propositional complexus', or 'propositional content' (to borrow momentarily a phrase which Grice does not normally use, since Searle overuses it), and Grice's mode-marker each corresponds with one element in this set of this or that attitude (or set of 'modes of thinking'). 

With respect to a particular sentence of the form 

Op + R

mode-marker + radix

Grice imagines the appropriate directive (or procedure, basic or resultant) as arrived at in the following way. 

We have, in the first instance, a 'signification system' S, which will enable us to reach, for Radix, a statement to the effect that Radix signifies that such-and-such.

This may be taken as giving a specification of a 'factivity'- or 'doxastic satisfactoriness-'condition (more loosely, truth-condition, or doxastic-satisfactoriness-condition) for the radix R. 

To be handled by S 1 , the radix R may be of any degree of logical complexity, but is to be pure (free from embedded mode-markers). 

The meaning specification for the particular sentence 

Op + R

is then (in effect) be a directive:

To utter this sentence if you want to induce in the addressee the attitude corresponding to 'Op' (the mode-marker) with respect to that which R signifies (according to system S 1 ). 

Sentences thus provided for will have, in their structures, a single mode-marker with maximal scope (no embedding of such markers). 

However, it may be possible, in the second instance, to extend S1 by setting up S2 (containing S1) which does allow for at least limited embedding of mode-markers. 

The idea which Grice is exploring relates to just such an extension. 

Grice notes that, though he using a fairly standard idea of a 'radical' he is by no means free from qualms about it. 

To return to the most directly relevant issues, Grice's idea is that an examination of this or that justificatory reason leads naturally to an examination of this or that modal (expressing specific kinds of justification) AND mode-markers, which are intimately connected with this or that psychological state, stance or attitude (notably buletic and doxastic) needing justification. 

The stages through which, on this occasion, Grice conducts his exploration of the idea is as follows: 

A partial characterization of mode-markers as used in (or underlying) speech.

This stage Grice  virtually completed.

A brief consideration of this or that modification as might be required or convenient for the employment of this or that mode-marker in the representation of the content of thought (of acceptance)

The application of the idea to be explored to a certain class of a doxastic-acceptability statement (including this or that probability statement) and to a certain class of this or that buletic acceptability statement, viz., a class roughly corresponding to Kant's technical imperative, or rule of skill (as opposed to what he calls a 'counsel of prudence,' aiming at the agent's eudaemonia). 

Then, some reflections on the capability of the initial idea to accommodate the extension of our consideration of a practical acceptability to: 

a "prudential" acceptabilitiy (alla Aristotle, phronesis), and 

a moral or otherwise categorical acceptability.

The connections with Kant are obvious.

Finally, if we survive to that point:

some attempt to assess the progress with respect to the "Univocality Question," or aequi-vocality thesis (regarding Kant's alleged unity of reason, or the two sides of the same coin of reason). 

Grice nearly finishes his discussion of topic C, leaving the remaining topics for a longer day.

So Grice, almost as a Grecian, first lurches uncertainly in the general direction of "Logika" to then meander gently in the suburbs of "Ethika."


In discussing the Univocality Question, or Aequi-vocality thesis, we should be careful, so far as is possible, to distinguish between differences in the semantic features of buletic and doxastic contexts of conversation 

-- which are attributable simply to differences between the two kinds of mode-marker (buletic and doxastic), and 

buletic and doxastic contexts of conversation which are not so attributable, or though so attributable do nevertheless indicate a failure of Univocality (or of equal Multivocality) on the part of this or that common modal. 

We know, of course, in advance, that the mode-marker is going to be importantly different, because of the difference of "direction of fit" (to use Austin's happy jargon, borrowed by Anscombe, but never returned) obtaining between a buletic context of conversation and a doxastic context of conversation.

A primitive (perceptual) belief may be roughly thought of as generated by states of the world, and so serve as checks on the acceptability of more sophisticated beliefs

"Boule," on the other hand, or will (goodwill or evil-ill) primarily affects the world (rather than vice versa), and there is no factual check on the acceptability of volitions parallel to that on the acceptability of beliefs. 

Austin and Anscombe knew this well, and Searle uses the two arrows to represent them.

This difference in the direction of fit is one which enormously impressed Kant, but he failed to find the words to express it!

Grice's second main question with regard to modes is whether it is legitimate to apply devices, which are initially presented as structural elements underlying mode-differences expressed in this or that conversational move, to the representation of the content of thought, and in particular of the content of acceptance-in-thought. 

Since Grice's concern is now with thought (and reasoning) and not with surface conversational utterance, and since we are concerned to provide directives not about how to think, but rather about how to specify what we think, it will plainly be appropriate to substitute a thought-verb for the phrase "to utter to addressee" in the main clause of the schema. 

The verb "accept" would obviously be a proper substituend.

But we may note with interest that the verb "think" itself (if regarded as a maximally general content-governing thought-verb) would also be appropriate since the specific mode of thinking involved (whether a species of acceptance or not) would be identified by the particular mode-operator.

"Think" or 'to cotch', or Chomsky's 'cognise' would also have the advantage of generality, I think (but sometimes I think not).

Rupert Brooke used to say: "FEEL! DON'T THINK!" His implicature is that 'think' applies to the doxastic mode, only!

(But I'm starting to feel Byzantine). 

 So the main clause will now read 

"x accepts (thinks) Op + p". 

Since thinking, unlike conversation, is, in the crudest sense, at least, a one-party game, to retain as the preamble of the antecedent clause "x wills x judges x . . ." would be perverse, if not animistic, otiose, and ultra-Cartesian. 

To consider the simplest of relevant cases, it is difficult indeed for me to think of occasions on which 

"I wanted myself to think that I thought that p" 

would be a happy description of my state. 

("I intend myself to adopt a psychological state to the effect that I hold the psychological state to the effect that p.")

In other words, I want to believe that I believe that it is raining -- even though I know that I don't BELIEVE that it is raining.

So let the revised preamble simply consist of "x". 

Our whole enterprise might seem to be fruitless if we did not allow the following specifiers: 

x accepts (thinks) ⊢ + p 

iff 

x judges p A

x accepts (thinks) ! A + p 

iff x wills that p. 

But what about the two protreptic cases? 

Quite apart from cases in which it is my will now that I should judge that (or will that) p on some future occasion (cases which may exist, but which are not particularly relevant to Grice's present purposes), there are important cases in which I will now that I judge or will now (or next to now) that p.

These are cases in which one's lower nature (within the power structure of one's soul) interferes.

MORALITY CASHES IN DESIRE

An inclination, or some other disturbing factors, stop me from judging or willing that p, but do not stop me from willing that I will or judge that p, a higher-order end state which may or may not in the end win out. 

OBJECT-LANGUAGE, ITERATION

Such cases of incipient incontinence (or akrasia) of will or judgement are endemic to the constitution of a rational being. 

Grice thinks that these cases should be allowed. 

Since, however, Grice's prime concern is with acceptabILITY rather than with realised acceptANCE, and since it seems that what would justify accepting ⊢A p (or !Ap) would also justify accepting ⊢B p (or ! B p), and, again, vice versa, Grice thinks he can, within the scope of "it is acceptable that", safely omit this or that subscript.

A curious phenomenon comes to light. 

Grice begins by assuming (or stipulating) that the verbs 'judge' and 'will' (acceptance-verbs) are to be 'completed' by radicals (phrastics). 

Yet when the machinery developed above has been applied, Grice finds that the verb 'accept' (or 'think') is to be completed by something of the form 'Op + p', that is, by a sentence. 

Perhaps we might tolerate this syntactical ambivalence.

But if we cannot, the remedy is not clear. 

It would, for example, not be satisfactory to suppose that 'that', when placed before a sentence, acts as a 'radicalizer' (is a functor expressing a function which takes that sentence on to its radical).

For that way we should lose the differentiations effected by varying mode-markers, and this would be fatal to the scheme. 

This phenomenon certainly suggests that the attempt to distinguish radicals from sentences may be misguided; that if radicals are to be admitted at all, they should be identified with indicative sentences. 

The operator '⊢' would then be a 'semantically vanishing' operator. 

But this does not wholly satisfy Grice.

For, if '⊢' is semantically vacuous, what happens to the subordinate distinction made by 'A' and 'B' markers, which seems genuine enough? 

We might find these markers 'hanging in the air', like two smiles left behind by the Cheshire Cat. 

Whatever the outcome of this debate, however, I feel fairly confident that I could accommodate the formulation of my discussion to it. 

Fuller Exposition of the 'Initial Idea' 

First, some preliminary points. 

To provide at least a modicum of intelligibility for my discourse, I shall pronounce the judicative operator '⊢' as 'it is the case that', and the volitive operator '!' as 'let it be that'; and I shall pronounce the sequence 'φ, ψ' as 'given that φ, ψ'. 

These vocal mannerisms will result in the production of some pretty barbarous 'English sentences'; but we must remember that what I shall be trying to do, in uttering such sentences, will be to represent supposedly underlying structure.

If that is one's aim, one can hardly expect that one's speech-forms will be such as to excite the approval of, let us say, Jane Austen or Lord Macaulay. 

In any case, less horrendous, though (for my purposes) less perspicuous, alternatives will, I think, be available. 

Further, Grice almost exclusively concerned with alethic and practical arguments, the proximate conclusions of which will be, respectively, of the forms 'Acc (⊢ p)' and 'Acc (! p)'; for example, 'acceptable (it is the case that it snows)' and 'acceptable (let it be that I go home)'. 

There will be two possible ways of reading the latter sentence. 

We might regard 'acceptable' as a sentential adverb (modifier) like 'demonstrably.'

In that case to say or think 'acceptable (let it be that I go home)' will be to say or think 'let it be that I go home', together with the qualification that what I say or think is acceptable; as one might say, 'acceptably, let it be that I go home'. 

To adopt this reading would seem to commit us to the impossibility of incontinence; for since 'accept that let it be that I go home' is to be my rewrite for 'V-accept (will) that I go home', anyone x who concluded, by practical argument, that 'acceptable let it be that x go home' would ipso facto will to go home. Similarly (though less paradoxically) any one who concluded, by alethic argument, 'acceptable it is the case that it snows', would ipso facto judge that it snows. 

So an alternative reading 'it is acceptable that let it be that I go home', which does not commit the speaker or thinker to 'let it be that I go home', seems preferable. 

We can, of course, retain the distinct form 'acceptably, let it be that (it is the case that) p' for renderings of 'desirably' and 'probably'. Let us now tackle the judicative cases. 

Grice starts with the assumption that arguments of the form 'A, so probably B' are sometimes (informally) valid; 'he has an exceptionally red face, so probably he has high blood pressure' might be informally valid, whereas 'he has an exceptionally red face, so probably he has musical talent' is unlikely to be allowed informal validity. 

We might re-express this assumption by saying that it is sometimes the case that A informally yields-with-probability that B (where 'yields' is the converse of 'is inferable from'). 

If we wish to construct a form of argument the acceptability of which does not depend on choice of substituends for 'A' and 'B', we may, so to speak, allow into the object-language forms of sentence which correspond to meta-statements of the form: 

'A yields-with-probability that B'

We may allow ourselves, for example, such a sentence as "it is probable, given that he has a very red face, that he has high blood pressure". 

This will provide us with the argument-patterns: “Probable, given A, that B A So, probably, B” or “Probable, given A, that B A So probably that B”

To take the second pattern, the legitimacy of such an inferential transition will not depend on the identity of 'A' or of 'B', though it will depend (as was stated in the previous chapter) on a licence from a suitably formulated 'Principle of Total Evidence'. 

The proposal which I am considering (in pursuit of the 'initial idea') would (roughly) involve rewriting the second pattern of argument so that it reads: It is acceptable, given that it is the case that A, that it is the case that B. It is the case that A. To apply this schema to a particular case, we generated the particular argument: 

It is acceptable, given that it is the case that Snodgrass has a red face, that it is the case that Snodgrass has high blood pressure. It is the case that Snodgrass has a red face. So, it is acceptable that it is the case that Snodgrass has high blood pressure. 

If we make the further assumption that the singular 'conditional' acceptability statement which is the first premise of the above argument may be (and perhaps has to be) reached by an analogue of the rule of universal instantiation from a general acceptability statement, we make room for such general acceptability sentences as: It is acceptable, given that it is the case that x has a red face, that it is the case that x has high blood pressure. which are of the form "It is acceptable, given that it is the case that Fx, that it is the case that Gx'; 'x' here is, you will note, an unbound variable; and the form might also (loosely) be read (pronounced) as: "It is acceptable, given that it is the case that one (something) is F, that it is the case that one (it) is G." 

All of this is (I think) pretty platitudinous; which is just as well, since it is to serve as a model for the treatment of practical argument. 

To turn from the alethic to the practical dimension. Here (the proposal goes) we may proceed, in a fashion almost exactly parallel to that adopted on the alethic side, through the following sequence of stages: 

Arguments (in thought or speech) of the form: 

Let it be that A It is the case that B so, with some degree of desirability, let it be that C are sometimes (and sometimes not) informally valid (or acceptable). 

Arguments of the form: It is desirable, given that let it be that A and that it is the case that B, that let it be that C Let it be that A It is the case that B so, it is desirable that let it be that C should, therefore, be allowed to be formally acceptable, subject to licence from a Principle of Total Evidence. 

In accordance with our proposal such arguments will be rewritten: 

It is acceptable, given that let it be A and that it is the case that B, that let it be that C Let it be that A It is the case that B so, it is desirable that let it be that C 

The first premises of such arguments may be (and perhaps have to be) reached by instantiation from general acceptability statements of the form: "It is acceptable, given that let one be E and that it is the case that one is F, that let it be that one is G." 

We may note that sentences like "it is snowing" can be trivially recast so as (in effect) to appear as third premisses in such arguments (with 'open' counterparts inside the acceptability sentence; they can be rewritten as, for example, "Snodgrass is such that it is snowing"). 

We are now in possession of such exciting general acceptability sentences as: "It is acceptable, given that let it be that one keeps dry and that it is the case that one is such that it is raining, that let one take with one one's umbrella."

A special subclass of general acceptability sentences (and of practical arguments) can be generated by 'trivializing' the predicate in the judicative premiss (making it a 'universal predicate'). If, for example, I take 'x is F' to represent 'x is identical with x' the judicative subclause may be omitted from the general acceptability sentence, with a corresponding 'reduction' in the shape of the related practical argument. 

We have therefore such argument sequences as the following: (P i ) It is acceptable, given that let it be that one survives, that let it be that one eats So (by U i ) It is acceptable, given that let it be that Snodgrass survives, that let it be that Snodgrass eats (P 2 ) Let it be that Snodgrass survives 
So (by Det) It is acceptable that let it be that Snodgrass eats. We should also, at some point, consider further transitions to: (a) Acceptably, let it be that Snodgrass eats, and to: (b) Let it be that Snodgrass eats. 

And we may also note that, as a more colloquial substitute for "Let it be that one (Snodgrass) survives (eats)" the form "one (Snodgrass) is to survive (eat)" is available; we thus obtain prettier inhabitants of antecedent clauses, for example, "given that Snodgrass is to survive". We must now pay some attention to the varieties of acceptability statement to be found within each of the alethic and practical dimensions; it will, of course, be essential to the large-scale success of the proposal which I am exploring that one should be able to show that for every such variant within one dimension there is a corresponding variant within the other. Within the area of defeasible generalizations, there is another variant which, in my view, extends across the board in the way just indicated, namely, the unweighted acceptability generalization (with associated singular conditionals), or, as I shall also call it, the ceteris paribus generalization. 

Such generalization I take to be of the form "It is acceptable (ceteris paribus), given that φX, that ψX" and I think we find both practical and alethic examples of the form; for example, "It is ceteris paribus acceptable, given that it is the case that one likes a person, that it is the case that one wants his company", which is not incompatible with "It is ceteris paribus acceptable, given that it is the case that one likes a person and that one is feeling ill, that one does not want his company". We also find "It is ceteris paribus acceptable, given that let it be that one leaves the country and given that it is the case that one is an alien, that let it be that one obtains a sailing permit from Internal Revenue", which is compatible with "It is ceteris paribus acceptable, given that let it be that one leaves the country and given that it is the case that one is an alien and that one is a close friend of the President, that let it be that one does not obtain a sailing permit, and that one arranges to travel in Air Force I". 

Grice discusses this kind of generalization, or 'law', briefly in "Method in Philosophical Psychology"

He dilates on its features in the Kant lectures.

I will just remark that it can be adapted to handle 'functionalist laws' (in the way suggested in that address), and that it is different from the closely related use of universal generalizations in 'artificially closed systems', where some relevant parameter is deliberately ignored, to be taken care of by an extension to the system; for in that case, when the extension is made, the original law has to be modified or corrected, whereas my ceteris paribus generalization can survive in an extended system; and I regard this as a particular advantage to philosophical psychology. 

In addition to these two defeasible types of acceptability generalization (each with alethic and practical sub-types), we have non-defeasible acceptability generalizations, with associated singular conditionals, exemplifying what I might call 'unqualified', 'unreserved', or 'full' acceptability claims. 

To express these I shall employ the (constructed) modal 'it is fully acceptable that . . .'; and again there will be occasion for its use in the representation both of alethic and of practical discourse. We have, in all, then, three varieties of acceptability statement (each with alethic and practical sub-types), associated with the modals "It is fully acceptable that . . . " (non-defeasible), 'it is ceteris paribus acceptable that . . . ', and 'it is to such-and-such a degree acceptable that . . . ', both of the latter pair being subject to defeasibility. 

I should re-emphasize that, on the practical side, I am so far concerned to represent only statements which are analogous with Kant's Technical Imperatives (or this or that 'rule of skill' versus his this or that 'counsel of prudence,' that aim at the agent's eudaemonia).

I am now visited by a temptation, to which of course I shall yield, to link these varieties of acceptability statement with common modals; however, to preserve a façade of dignity I shall mark the modals I thus define with a star, to indicate that the modals so defined are only candidates for identification with the common modals spelled in the same way. 

I am tempted to introduce 'it must* be that' as a modal whose sense is that of 'It is fully acceptable that' and 'it ought* to be that' as a modal whose sense is that of 'It is ceteris paribus (other things being equal) acceptable that'; for degree-variant acceptability I can think of no appealing vernacular counterpart other than 'acceptable' itself. 

After such introduction, we could allow the starred modals to become idiomatically embedded in the sentences in which they occur; as in "A bishop must* get fed up with politicians", and in "To keep his job, a bishop ought* not to show his irritation with politicians". 

But I now confess that I am tempted to plunge even further into conceptual debauchery than I have already; having just, at considerable pains, got what might turn out to be common modals into my structures, I am at once inclined to get them out again. 

For it seems to me that one might be able, without change of sense, to employ forms of sentence which eliminate reference to acceptability, and so do not need the starred modals. 

One might be able, to this end, to exploit "if-then" conditionals (NB 'if . . . then', not just 'if') together with suitable modifiers. 

One might, for example, be able to re-express "A bishop must* get fed up with politicians" as "If one is a bishop, then (unreservedly) one will get fed up with the politicians"; and "To keep his job, a bishop ought* not to show his irritation with politicians" as "If one is to keep one's job and if one is a bishop, then, other things being equal, one is not to show one's irritation with politicians". 

Of course, when it comes to applying detachment to corresponding singular conditionals, we may need to have some way of indicating the character of the generalization from which the detached singular non-conditional sentence has been derived; the devising of such indices should not be beyond the wit of man. 

So far as generalizations of these kinds are concerned, it seems to me that one needs to be able to mark five features: 

(1) conditionality
(2) generality
(3) type of generality (absolute, ceteris paribus, etc., thereby, ipso facto, discriminating with respect to defeasibility or indefeasibility)
(4) mode
(5) (not so far mentioned) whether or not the generalization in question has or has not been derived from a simple enumeration of instances.

Because of their differences with respect to direction of fit, any such index will do real work in the case of alethic generalities, not in the case of practical generalities. 

So long as these features are marked, we have all we need for our purposes. Furthermore, they are all (in some legitimate and intelligible sense) formal features, and indeed features which might be regarded as, in some sense, 'contained in' or 'required by' the concept of a rational being, since it would hardly be possible to engage in any kind of reasoning without being familiar with them. 

So, on the assumption that the starred modals are identifiable with their unstarred counterparts, we would seem to have reached the following positions. 

We have represented practical and alethic generalizations, and their associated conditionals, and with them certain common modals such as 'must' and 'ought', under a single notion of acceptability (with specific variants). 

We have decomposed acceptability itself into formal features. 

We have removed mystery from the alleged logical fact that acceptable practical 'ought' statements have to be derivable from an underlying generalization. 

Though these achievements (if such they be) might indeed not settle the 'univocality' questions, they can hardly be irrelevant to them. 

I suspect that, if we were to telephone the illustrious Kant at his Elysian country club in order to impart to him this latest titbit of philosophical gossip, we might get the reply, "Big deal! Isn't that what I've been telling you all along?"

Grice gives some attention to the matter of formulating an appropriate version of a "Principle of Total Evidence," designed to govern detachment. 

I cannot expect to reach anything better than an approximation to an adequate formulation; but perhaps even that would be a help. I shall start with weight-bearing alethic acceptability-conditionals (singular probability conditionals) and at once two remarks are called for: first, that I am no kind of expert in the theory of probability, so I shall say little and say it fast. 

Second, that the example Grice selects will not be fully representative of reasoning in this area; but perhaps it will be good enough for present purposes. S (subject) owns a firm which makes and sells ornaments constructed from seashells, and S is concerned, at t, to estimate end p.80 whether the firm's business will improve during the coming year. S reflects that, these days, every beachcomber is collecting seashells like mad so as to sell them to firms such as his, so he can get seashells more cheaply; so it is likely, given that he will get seashells more cheaply, that the business will improve. 

He also reflects that his not easily replaceable craftsmen are getting restive for higher pay, and that he may have to give in; so he accepts that, given that the craftsmen are restive, that the business will not improve. He further reflects that ornaments from seashells are all the rage at the moment, so he may be able to put his prices up and make more money. He now consolidates these reflections and judges that it is 'pretty likely, given that he will get seashells more cheaply, that his employees are restive, and that everyone is eager to buy seashell ornaments, that his business will improve'. He now searches further to see if he can find any considerations which, when added to the antecedent of his last judgement, would result in an acceptable conditional favouring the supposition that his business will not improve. After due search, he fails to find any such disturbing consideration; so he 'detaches' and judges that it is pretty likely that his business will improve. 

The salient points here are (1) that, by consolidation (compounding antecedents) of prior acceptability-conditionals, S has reached, by time t, an alethic acceptability-conditional which he accepts, and the antecedent of which he accepts. (2) That after due (proper) search for an 'upsetting' ('disturbing') conditional he has, by time t, failed to come up with one. Let me introduce two simple bits of terminology. Let us say that ψ is an extension of an antecedent φ if ψ is either identical with φ or is a further specification of φ; and let us say that the antecedent of a weighted acceptability-conditional C favours the consequent of C just in case the weight specified in C is above an indifference point (for example, assigns probability rather than improbability). 

Grice attempts to formulate a version of a PTE (applicable to alethic acceptability conditionals): If (a) S accepts at t an alethic acceptability-conditional C 1 , the antecedent of which favours, to degree d, the consequent of C 1 , (b) S accepts at t the antecedent of C 1 , end p.81 (c) after due search by S for such a (further) conditional, there is no conditional C 2 such that (1) S accepts at t C 2 and its antecedent, (2) and the antecedent of C 2 is an extension of the antecedent of C 1 , (3) and the consequent of C 2 is a rival (incompatible with) of the consequent of C 1 , (4) and the antecedent of C 2 favours the consequent of C 2 more than it favours the consequent of C 1 : then S may judge (accept) at t that the consequent of C 1 is acceptable to degree d. For convenience, we might abbreviate the complex clause (C) in the antecedent of the above rule as 'C 1 is optimal for S at t'; with that abbreviation, the rule will run: "If S accepts at t an alethic acceptability-conditional C 1 , the antecedent of which favours its consequent to degree d, and S accepts at t the antecedent of C 1 , and C 1 is optimal for S at C 1 , then S may accept (judge) at t that the consequent of C 1 is acceptable to degree d." Before moving to the practical dimension, I have some observations to make.

(1) I have said here nothing about the initial establishment of weighted acceptability generalizations (from which singular acceptability-conditionals may be derived by instantiation) nor about how to compound them. These are important and difficult questions, but lie outside my immediate purpose. (2) I have been treating an instantiation step from such generalizations to related singular conditionals as 'automatic', reserving the application of detachment to those conditionals as what is subject to a version of PTE. 

But I can imagine someone taking the position that detachment is to be automatic, and that what is to be licensed by some version of PTE is the instantiation step. Obviously, for such a person, a differently formulated version of PTE would be needed. (3) (Importantly) As I have set things up, an inferential licence to detach is relative to a subject (reasoner) S and to a particular time t. I am inclined to regard this feature of such rules as characteristic of defeasible inference. 

 (Importantly) The application of Grice's rule involves a value-judgement: it has to be determined or supposed by S that detachment does follow upon due or proper search for a 'disturbing' conditional. 

While Grice does not have to seek to characterize such a search more precisely, I do not regard this feature of my rule with distaste. I now introduce an example from the practical dimension; it has, I must allow, at certain points a quaintness which might suggest that the whole philosophical story is not yet being told. S is invited by his mother to visit her in Milwaukee next week. 

At this point he accepts the practical acceptability-conditional, which for simplicity I will formulate without (insertible) references to degree of acceptability. The conditional is: "It is acceptable, given that let S give his mother pleasure, and that S is her favourite son, that let S visit her in Milwaukee next week." He reflects, and comes up with the following conditional (based on the fact that his firm is about to do its accounts, and he is head accountant): "It is acceptable, given that let S get ready the firm's accounts and that S is head accountant and it is accounting time, that let S spend next week in his office in Redwood City." He compounds, and comes up with: "It is acceptable, given that let S give his mother pleasure and let S get ready the firm's accounts, and that S is her favourite son and S is head accountant and now is accounting time, that S visit his mother in Milwaukee for a long weekend and return to his office in Redwood City on Tuesday." S is then suddenly reminded that his wife, Matilda, has just had a bad car accident and is lying in hospital in Boise, Idaho, with two broken legs and internal injuries. This prompts him to form the further judgement: "It is acceptable, given that let S sustain Matilda and that S is her husband and she is lying in Boise, Idaho, with two broken legs, internal injuries and much pain, that let S spend next week in Boise, Idaho." S then compounds again and comes up with: "It is acceptable, given that let S give his mother pleasure and get ready the firm's accounts and sustain Matilda, and that S is his mother's favourite son and head accountant at accounting time and Matilda's husband with Matilda lying in Boise, Idaho (etc.), that let S spend next week in Boise, Idaho, and telephone his mother and his office daily." end p.83 (S, we may add, has rejected, or rated lower, a conditional with the same complex antecedent and a variant consequent, namely, "Let S remove Matilda from hospital and take her around with him to Milwaukee and to Redwood City.") Being conscientious about practical inference, S searches (duly) for a further disturbing conditional, finds none, and applies detachment to the last conditional, arriving at: "It is acceptable that let S spend next week in Boise, telephoning his mother and his office daily." 

Now if (as surely we must) we take this example as a paradigm of a certain kind of practical reasoning, it looks to me as if the proposed formulation of a PTE could be applied to it without change, apart from the deletion of the word 'alethic' and the substitution of the word 'practical'. There is the same search for a disturbing feature to upset an acceptability-conditional which thus far holds the day, the same failure to find it, and the same readiness, at that point, to apply detachment.

There are, however, two comments which need to be made which might point to features of practical acceptabilities which would threaten an attempt to represent the common modals in which I am interested as being univocal, or equally multivocal, across the board. (1) I have taken an example in which the 'subject' S (the reasoner) and the particular object to which the acceptability-conditionals refer are one and the same; and one would certainly need to enquire what pertains when they are different; and (2) there may well be, in practical acceptabilities, a concealed relativity to a particular individual in the idea of a set of competing consequents, which my formulation of PTE makes use of. 

For 'rival' possible consequents might have to be described as specifying members of a set of actions or states of affairs which are possible, open, or achievable; and then the questions "possible for whom?", "achievable by whom?" might be embarrassing, as compelling a relativization of practical modals to particular persons. Would we be talking about achievability or possibility for the reasoner, for the subject of the acceptability-conditional, or for some third party? I shall not expand on these matters at this point, since they are closely related to enquiries which I shall address in the next chapter. Bating these anxieties, when we advert to non-weighted ceteris paribus acceptabilities, I also see no reason why the propounded end p.84 Fig. 3. Formulation of a Principle of Total Evidence Note: Omit phrases in brackets for unweighted kind of acceptability. formulation of PTE should not be applied both in the alethic and the practical dimensions, provided of course that references to weights or degrees are eliminated by deletion of the phrases which on Fig. 3 are enclosed in brackets. 

There is, however, sometimes detectable in this region a situation in which, when we come to apply detachment, we are in a stronger position than that which I have so far been envisaging. The phenomenon in question might perhaps arise not only with regard to weighted acceptabilities; but of this I am uncertain. It is, as I shall indicate, of some philosophical interest. Consider a not wholly realistic example. A doctor is considering how to treat a patient whom I shall call "Pidduck". I shall phrase his reflections in terms of the expressions 'ought*', 'must*', and the colloquial 'is to' (vice "let it be that"). 

The doctor has, or has available to him, the following acceptabilityconditionals, each of them derived by instantiation from a ceteris paribus generalization which is (we pretend) well established. (1) "Given that Pidduck is to be relieved of cephalalgia (an ailment, a common symptom of which is headache), and that Pidduck is of blood group O, then Pidduck ought* to take aspirin." (2) "Given that Pidduck is to be relieved of cephalalgia and also of gasteroplexis (an ailment, a common symptom of which is stomach cramp), and that Pidduck is of blood group O, then Pidduck ought* to be treated by electromixosis (the very latest thing in this region of therapy)." end p.85 (3) "Given that Pidduck is to be relieved of cephalalgia and also of gasteroplexis, and that Pidduck is of blood group O and that his blood has an abnormally high alcohol content, then Pidduck ought* to be given gentle massage until his condition changes." 

The doctor accepts the antecedents of the first two conditionals, but rejects the antecedent of the third; he does not find an abnormally high alcohol content in Pidduck's blood. Not only, however, does he reject the antecedent of conditional (3), but he considers that he has ample grounds for rejecting the antecedent of any conditional which extends the antecedent of (2); he regards Pidduck's condition as a perfectly normal case of cephalalgia combined with gasteroplexis; though there are (perhaps indefinitely many) good ceteris paribus generalizations with antecedents extending the antecedent of the generalization from which conditional (2) is derived, he is confident that none of them applies to Pidduck. In such a situation, I suggest, the doctor is entitled to treat (in a non-medical sense) Pidduck's case as if it fell under a full-acceptability generalization (one which is not defeasible), which would be expressed by changing, in the generalization of (2), the word 'ought*' to the word 'must*'. 

He can then at once apply detachment, and decide (think) that Pidduck must* be given electromixosis. The licence, in circumstances comparable with these, to shift from 'ought*' to 'must*' is relevant to a celebrated complaint about Kant's ethical theory. 

KANT'S VIEW ON COOPERATION

Expressed in Grice's terms, I think that Kant believed that an impure, imperfect or 'meritorious' obligation, such as the obligation to develop one's talents, or, more relevant in terms of Grice's "principle of conversational helfpulness," to help others or co-operate with others, could be allowed to fall under this or that generalization ascribing one or other form of defeasible practical acceptability.

We could, in Kant's terms, allow, in the case of the principle of conversational helpfulness, conflicting grounds of obligation, though not conflicting obligations. 

But with respect to a pure, perfect or strict obligation, like obligations to tell the truth or to keep promises, this treatment is not available.

(Grice does not make the distinction, since under his principle of conversational helpfulness falls a desideratum of conversational candour!)

Such a pure obligation has to be thought of as matters of practical law, as falling (that is) under generalizations which invoke full (unqualified) practical acceptability. I suspect that he took this position partly from certain theoretical considerations and partly because he felt that, if he allowed the possibility of exceptions in such cases, allowed the 'must' to become an 'ought' (in the vernacular sense), he would be failing to capture the stringency which he felt to attach to particular cases of perfect obligation. 

His 'hard line' in this matter has brought down on his head a modicum of ridicule, in respect of his well-known contention that one should tell the truth even to a would-be murderer searching for his intended victim. 

It seems to me that one could honour Kant's non-theoretical motivation, and at the same time save him from ridicule, by an application of the licence which I have sketched. 

I have not yet attempted to characterize the form of 'moral' acceptabilities, but let us suppose that, in the first instance, they differ from the practical acceptabilities which I have distinguished in that the generalizations associated with them omit, from their antecedents, any 'volitive' sub-clause; they are of the form Acc (⊢ Fx; ! Gx). Now it would be quite open to us to maintain that even the generalizations connected with 'perfect obligation' are of the ceteris paribus variety, and so to be expressed in terms of 'ought*'; but that, at the same time, it very often happens that, with respect to a particular case, we know that none of the sometimes defeating features applies; and so that, with respect to such cases, one is authorized to shift from 'ought*' to 'must*'. 

This seems to me to be not only a position which would both preserve Kant's intuition and save him from ridicule, but to be also a position of considerable plausibility. 

Embedding of Mode-Markers and (again, Satisfactoriness (alla Hofstadter and McKinsey)

Grice brings reminder of, and a slight enlargement upon a previous reflection

Speaking from a 'genitorial' point of view,2 I would regard reasoning as a faculty for enlarging our acceptances by the application of forms of transition, from a set of acceptances to a further acceptance, which are such as to ensure the transmission of value from premisses to conclusion, should such value attach to the premisses. 

By 'value' I mean some property which is of value (of a certain kind of value, no doubt). 

Truth is one such property, but it may not be the only one.

And we have now reached a point at which we can identify another, namely, practical value (goodness). 

In this Grice is following Hofstadter and McKinsey.

So each of these should be thought of as special cases of a more general notion of "satisfactoriness."

Let us work out a little more fully, though abstractly, how such a treatment might be constructed.  

We have sentence-radicals which qualify for 'radical truth' or 'radical falsity'; some of those which so qualify, also qualify for 'radical goodness' or 'radical badness'. 


We have judicative sentences ('⊢'-sentences) which are assigned truth (or falsity) just in case their radicals qualify for radical truth (or radical falsity); and we have volitive sentences ('!' sentences) which are assigned practical value (or disvalue) just in case their radicals qualify for radical goodness (or badness). 

Since the sentential forms will indicate which kind of value is involved, we can use the generic term 'satisfactory'. 

We import into the object language the phrases 'It is true that' and 'It is good that'; 'It is true that ⊢p' is to be satisfactory qua true just in case '⊢ p' is satisfactory qua true; and 'it is good that ! p' is to be satisfactory qua true just in case '! p' is satisfactory qua having practical value. 

And we introduce 'it is acceptable that' (with the syntactical provisions which I have been using); on the practical side, 'It is acceptable that ! p' will be true just in case 'it is good that ! p' is true.

We could now, if we wished, introduce generalized versions of some standard binary connectives; using 'φ' and 'ψ' to represent sentences (in either mode), we could stipulate that ⌈φ & ψ⌉ is satisfactory just in case ⌈φ⌉ is satisfactory and ⌈ψ⌉ is satisfactory, ⌈φ or ψ⌉ is satisfactory just in case one of the pair, ⌈φ and ψ⌉, is satisfactory, and ⌈φ → ψ⌉ is satisfactory just in case either ⌈φ⌉ is unsatisfactory or ⌈ψ⌉ is satisfactory. There are, however, a number of points to be made. (1) It is not fully clear to me just how strong the motivation would be for introducing such connectives, nor whether, if they are introduced, restrictions should not be imposed. The problematic examples will be, of course, the mixed ones (those in which one clause is judicative and the other volitive). It seems natural to look end p.88 for guidance from ordinary speech. "The beast is filthy and don't (I shan't) touch it" seems all right, but "Don't touch the beast and it is filthy" seems dubious, and "Touch the beast and it will bite you", while idiomatic, is not a conjunction, nor a genuine invitation to touch the beast. And "Either he is taking a bath or leave the bathroom door open" is perhaps intelligible, but "Leave the bathroom door open or he is taking a bath" seems considerably less so. (2) It is perhaps worth noting that, in unmixed cases, satisfactoriness would be specifiable either as satisfactoriness qua truth or as satisfactoriness qua practical value; but for mixed cases no such specification would be available unless we make a special stipulation (for example, that the volitive mode is to be dominant). 

The real crunch comes, however, with negation (which I have been carefully ignoring). 'Not ⊢p' might perhaps be treated as equivalent to '⊢ not-p', but what about 'Not ! p'? What do we say in cases like, perhaps, "Let it be that I now put my hand on my head" or "Let it be that my bicycle faces north", in which (at least on occasion) it seems to be that neither '! A' nor '! ~A' is either satisfactory or unsatisfactory? What value do we assign to '~ ! A' and to '~ ! ~A'? Do we proscribe the forms altogether (for all cases)? But that would seem to be a pity, since '~ ! ~A' seems to be quite promising as a representation for 'you may (permissive) do A'; that is, I signify my refusal to prohibit your doing A. 

Do we disallow embedding of these forms? But that (again if we use them to represent 'may') seems too restrictive. Again, if '! A' is neither satisfactory nor unsatisfactory, do we assign a third 'value' to '! A' ('practically neuter'), or do we say that we have a 'practical value gap'? These and other such problems would require careful consideration; but I cannot see that they would prove insoluble, any more than analogous problems connected with presupposition are insoluble; in the latter case the difficulty is not so much to find a solution as to select the best solution from those which present themselves.