H. P. Grice's Implication

IMPLICATION

ENGLISH entailment, implicature

FRENCH implication

GERMAN

 nachsichziehen,

zurfolgehaben,

Folge(-rung),

Schluß,

Konsequenz,

Implikation,

Implikatur

GREEK”

sumpeplegmenon [συμπεπλεγμένον]  “sum-peplegmenon”

sumperasma [συμπέϱασμα] “sum-perasma”

sunêmmenon [συνημμένον], “sunemmenon,”

akolouthia [ἀϰολουθία], “akolouthia,”

antakolouthia [ἀνταϰολουθία], “ana-kolouthia.”

LATIN

illatio– from ‘in-fero.’ The Romans adopted two different roots for this, and saw them as having the same ‘sense’ – cf. referro, relatum, proferro, prolatum

inferentia – in-fero.

consequentia, -- con-sequentia. The seq- root is present in ‘sequitur,’ non sequitur. The ‘con-‘ is transliterating Greek ‘syn-’ in the three expressions with ‘syn’: sympleplegmenon, symperasma, and synemmenon. The Germans, avoiding the Latinate, have a ‘follow’ root: in “Folge,” “Folgerung,” and the verb “zur-folge-haben.

And perhaps ‘implicatio,’  which is the root Grice is playing with. In Italian and French it underwent changes, making ‘to imply’ a doublet with Grice’s ‘to implicate’ (the form already present, “She was implicated in the crime.”). The strict opposite is ‘ex-plicatio,’ as in ‘explicate.’ ‘implico’ gives both ‘implicatum’ and ‘implicitum.’ Consequently, ‘explico’ gives both ‘explicatum’ and ‘explicitum.’ In English Grice often uses ‘impicit,’ and ‘explicit,’ as they relate to communication, as his ‘implicatum’ does. His ‘implicatum’ has more to do with the contrast with what is ‘explicit’ than with ‘what follows’ from a premise. Although in his formulation, both readings are valid: “by uttering x, implicitly conveying that q, the emissor CONVERSATIONALY implicates that p’ if he has explicitly conveyed that p, and ‘q’ is what is required to ‘rationalise’ his conversational behavioiur. In terms of the emissor, the distinction is between what the emissor has explicitly conveyed and what he has conversationally implicated. This in turn contrasts what some philosophers refer metabolically as an ‘expression,’ the ‘x’ ‘implying’ that p – Grice does not bother with this because, as Strawson and Wiggins point out, while an emissor cannot be true, it’s only what he has either explicitly or implicitly conveyed that can be true.

Vide:

ANALOGY

PROPOSITION

SENSE

SUPPOSITION

TRUTH

Implication denotes a relation between propositions and statements such that, from the truth-value of the protasis or antecedent (true or false), one can derive the truth of the apodosis or consequent.

More broadly,

“we can say that one idea ‘implies’ another if the first idea cannot be thought without the second one”

(RT: Lalande, “Vocabulaire technique et critique de la philosophie”).

Common usage makes no strict differentiation between “to imply,” “to infer,” and “to lead to.”

Against Dorothy Parker. She noted that those of her friends who used ‘imply’ for ‘infer’ were not invited at the Algonquin.

The verb “to infer,” (from Latin, ‘infero,’ that gives both ‘inferentia,’ inference, and ‘illatio,’ ‘illatum’) meaning “to draw a consequence, to deduce” (a use dating to 1372), and the noun “inference,” meaning “consequence” (from 1606), do not on the face of it seem to be manifestly different from “to imply” and “implication.”

But in Oxonian usage, Dodgson avoided a confusion. “There are two ways of confusing ‘imply’ with ‘infer’: to use ‘imply’ to mean ‘infer,’ and vice versa. Alice usually does the latter; the Dodo the former.”

Indeed, nothing originally distinguishes “implication” as Lalande defines it — “a relation by which one thing ‘implies’ another”— from “inference” as it is defined in Diderot and d’Alembert’s Encyclopédie (1765):

“An operation by which one ACCEPTS (to use a Griceism) a proposition because of its connection to other propositions held to be true.”

The same phenomenon can be seen in the German language, in which the terms corresponding to “implication”

(Nach-sich-ziehen, Zur-folge-haben),

“inference” ([Schluß]-Folgerung, Schluß),

“to infer” (schließen),

“consequence” (Folge[-rung], Schluß, Konsequenz),

“reasoning” ([Schluß-]Folgerung), and

“to reason” (schließen, Schluß-folger-ung-en ziehen) intersect or overlap to a large extent.

In the French language, the expression “impliquer” reveals several characteristics that the expression does not seem to share with “to infer” or “to lead to.”

First of all, “impliquer” is originally (1663) connected to the notion of contradiction, as shown in the use of impliquer in “impliquer contradiction,” in the sense of “to be contradictory.”

This connection between ‘impliquer’ and ‘contradiction’ does not, however, explain how “impliquer” has passed into its most commonly accepted meaning — “implicitly entail” — viz. to lead to a consequence.

Indeed, these two usages (“impliquer” connected with contradiction” and otherwise) constantly interfere with one another, which certainly poses a number of difficult problems.

The same phenomenon can be found in the case of “import,” commonly given used as “MEAN” or “imply,” but often wavering instead, in certain cases, between “ENTAIL” and “imply.”

In French, the noun “import” itself is generally left as it is

(“import existentiel,” v. SENSE, Box 4).

“Importer,” as used by Rabelais, 1536, “to necessitate, to entail,” forms via  It.“importare,” as used by Dante), from the Fr. “emporter,” “to entail, to have as a consequence,” dropped out of usage, and was brought back through Engl. “import.”

The nature of the connection between the two primary usages of Fr. “impliquer” (or It. “implicare”), “to entail IMPLICITitly” and “to lead to a consequence,” nonetheless remains obscure, but not to a Griceian.

Another difficulty is understanding how the transition occurs from Fr. “impliquer,” “to lead to a consequence,” to “implication,” “a logical relation in which one statement necessarily supposes another one,” and how we can determine what in this precise case distinguishes “implication” from “PRAE-suppositio.”

We therefore need to be attentive to what is implicit in Fr. “impliquer” and “implication,” to the dimension of Fr. “pli,” a pleat or fold, of Fr. “re-pli,” folding back, and of the Fr. “pliure,” folding, in order to separate out “imply,” “infer,” “lead to,” or “implication,” “inference,” “consequence”—which requires us to go back to Latin, and especially to medieval Latin.

Once we have clarified the relationship between the usage of “implication” and the medieval usage of “implicatio,” we will be able to examine certain derivations (as in Sidonius’s ‘implicatura,” and H. P. Grice’s “implicature”) or substitutes (“entailment”) of terms related to the generic field (for linguistic botanising) of “implicatio,” assuming that it is difficulties with the concept of implication (e. g., the ‘paradoxes,’ true but misleading, of material versus formal implication – ‘paradox of implication’ first used by Johnson 1921) that have given rise to this or that newly coined expression corresponding to this or that original attempt.

Finally, this whole set of difficulties certainly becomes clearer as we leave Roman and go further upstream to Grecian, using the same vocabulary of implication, through the conflation of several heterogeneous gestures that come from the systematics in Aristotle and the Stoics.

The Roman Vocabulary of Implication and the Implicatio

A number of different expressions in medieval Latin can express in a more or less equivalent manner the relationship between propositions and statements such that, from the truth-value of the antecedent (true or false), one can derive the truth-value of the consequent:

illatio,

inferentia,

consequentia.

Peter Abelard (Petrus Abelardus, v. Abelardus) makes no distinction in using the expression “consequentia” for the ‘propositio conditionalis,’ hypothetical.

Si est homo, est animal.

Dialectica, 473)

and the expression “inferentia” for

Si non est iustus homo, est non iustus homo.

(Dialectica., 414).

It is certainly true that “illation” appears above all in the context of Aristotle’s “Topics,” and denotes more specifically a reasoning, or “argumentum,” in Boethius), allowing for a consequence to be drawn from a given place, e. g.,

“illatio a causa,”

“illatio a simili,”

“illatio a pari,”

“illatio a partibus.”

“Consequentia” sometimes has a very generic usage, as in:

Consequentia est quaedam habitudo inter antecedens et consequens.”

“Logica modernorum,” 2.1:38 –

Cfr. Grice on Whitehead as a ‘modernist’!

“Consequentia” is in any case present in the expression “sequitur” and in the expression “con-sequitur” (to follow, to ensue, to result in).

“Inferentia” frequently appears, by contrast, in the context of the Aristotle’s “De Interpretatione,” on which Grice lectures, whether it is as part of Apuleius’s Square of Oppositions (‘figura quadrata spectare”), in order to explain the “law” of the four sides of the square:

propositio opposita

propositio sub-contraria

propositio contradictoria, and

proposition sub-alterna.

Logica modernorum, 2.1:115.

As explored by P. F. Strawson and brought to H. P. Grice’s attention, who refused to accept Strawson’s changes and restrictions of the ‘classical’ validities because Strawson felt that the ‘implication’ violated some ‘pragmatic rule,’ while still yielding a true statement.

Or “inferentia” is used in order to determine the rules for ‘conversio’  from ‘convertire,’ converting propositions (Logica modernorum 131–39).

Nevertheless, “inferentia” is used for the dyadic (or triadic, alla Peirce) relationship of implication, and not the expressions from the “implication” family.

Surprisingly, a philosopher without a classical Graeco-Roman background could well be mislead into thinking that “implicatio” and “implication” are disparate!

A number of treatises explore the “implicits” (a “tractatus implicitarum”), viz. this or that ‘semantic’ property of the proposition said to be an ‘implicatum’ or an ‘implication,’ or ‘proposition relativa.’ E.g. “Si Plato tutee Socrates est, Socratos tutor Platonis est,” translated by Grice, “If Strawson was my tutee, it didn’t show!”.

“implicitus,” “implicita,” and “implicitum,” “participium passatum” from “implicare,” in Roman is used for “to be joined, mixed, enveloped.”

“Implicare” adds to these usages the idea of an unforeseen difficulty, “impedire,” and even of deceit, “fallere.” Why imply what you can exply?

The source of the philosophers’s usage of ‘implicatre’ is a passage from Aristotle’s “De interpretation” on the contrariety of propositions (14.23b25–27), in which “implicita” (that sould be complicita, and ‘the utterer complicates that p”) renders Gk. “sum-pepleg-menê,” “συμ-πεπλεγμένη,” f. “sum-plek-ein,” “συμ-πλέϰein,” “to bind together,” as in ‘complicatio,’ complication, and Sidonius’s ‘complicature,’ and Grice’s ‘complicature.’ “One problem with P. F. Strawson’s exegesis of J. L. Austin is the complicature is brings.”

This is from the same family as “sum-plokê,” “συμ-πλοϰή,” which Plato (Pol. 278b; Soph. 262c) uses for the ‘second articularion,’ the “com-bination” of letters that make up a word, and, more philosophically interesting, for ‘praedicatio,’ viz., the interrelation of a noun, or onoma or nomen, as in “the dog,” and a verb, or rhema, or verbum, -- as in ‘shaggisising’ -- that makes up a propositional complex, as “The dog is shaggy,” or “The dog shaggisises.” (H. P. Grice, “Verbing from adjectiving.”)

Aristotle:

“hê de tou hoti kakon to agathon SUM-PEPLEG-MENÊ estin.”

“Kai gar hoti ouk agathon anagkê isôs hupolambanein ton auton.”

“ἡ δὲ τοῦ ὅτι ϰαϰὸν τὸ ἀγαθὸν συμπεπλεγμένη ἐστίν.”

“ϰαὶ γὰϱ ὅτι οὐϰ ἀγαθὸν ἀνάγϰη ἴσως ὑπολαμϐάνειν τὸν αὐτόν.”

De Int. 23b25–27.

Boethius:

Illa vero quae est:

Quoniam malum est quod est bonum.

IMPLICATA est.

Et enim:

“Quoniam non bonum est.”

necesse est idem ipsum opinari.

Aristoteles latinus, 2.1–2, p. 36, 4–6.

J. Tricot:

“Quant au jugement,

“Le bon est mal.”

ce n’est en réalité qu’une COMBINAISON de jugements, cars sans doute est-il nécessaire de sous-entendre en même temps “le bon n’est pas le bon.” (Trans. Tricot, 141)

And cf. Mill on ‘sous-entendu’ of conversation.

This was discussed by H. P. Grice in a tutorial with Reading-born English philosopher J. L. Ackrill at St. John’s.

With the help of H. P. Grice, J. L. Ackrill tries to render Boethius into the vernacular (just to please Austin) as follows:

Hê de tou hoti kakon to agathon SUM-PEPLEG-MENÊ estin, kai gar hoti OUK agathon ANAGKê isôs hupo-lambanein ton auton.

Illa vero quae est, ‘Quoniam malum est quod est bonum,’ IMPLICATA est, et enim, ‘Quoniam non bonum est,’ necesse est idem ipsum OPINARI.

“The belief expressed by the proposition, ‘The good is bad,’ is COM-PLICATED or com-plex, for the same person MUST, perhaps, suppose also the proposition, ‘The good it is not good.’

Aristotle goes on, “For what kind of utterance is “The good is not good,” or as they say in Sparta, “The good is no good”? Surely otiose. “The good” is a Platonic ideal, a universal, separate from this or that good thing. So surely, ‘the good,’ qua idea ain’t good in the sense that playing cricket is good. But playing cricket is NOT “THE” good: philosophising is.”

H. P. Grice found Boethius’s commentary “perfectly elucidatory,” but Ackrill was perplexed, and Grice intended Ackrill’s perplexity to go ‘unnoticed’ (“He is trying to communicate his perplexity, but I keep ignoring it.”

For Ackrill tried to ‘correct’ his tutor.

Aristotle, Acrkill thought, is wishing to define the ‘contrariety’ between two statements or opinions, or not to use a metalanguage second order, that what is expressed by ‘The good is bad’ is a contrarium of what is expressed by ‘The good is no good.’”

Aristotle starts, surely, from a principle.

The principle states that  maximally false proposition, set in opposition to a maximally true proposition, deserves the name “contrary” – and ‘contrarium’ to what is expressed by it.

In a second phase, Aristotle then tries to demonstrate, in a succession of this or that stage, that ‘The good is good,’ (To agathon agathon estin,’ “Bonum est bonum”) is a maximally true proposition.”

And the reason for this is that “To agathon agathon estin,” or “Bonum bonum est,” applies to the essence (essentia) of “good,” and ‘predicates’ “the same of the same,” tautologically.

Now consider Aristotle’s other proposition “The good is the not-bad.”

This does not do. This is not a maximally true proposition.

Unlike “The good is good,” The good is not bad” does not apply to the essence of ‘the good,’ and it does not predicate ‘the same of the same’ tautologically. Rather, ‘The good is not bad,’ unless you bring one of those ‘meaning postulates’ that Grice rightly defends against Quine in “In defense of a dogma,” – in this case, (x)(Bx iff ~Gx) – we stipulate something ‘bad’ if it ain’t good -- is only true not by virtue of a necessary logical implication, but, to echo my tutor, by implicature, viz. by accident, and not by essence involved in the ‘sense’ of either ‘good’ or ‘bad,’ or ‘not’ for that matter.

Aristotle equivocates when he convinced Grice that an allegedly maximally false proposition (‘the good is bad’) entails or yields the negation of the same attribute, viz., ‘The good is not good,’ or more correctly, ‘It is not the case that the good is good,’ for this is axiomatically contradictory, or tautologically and necessarily false without appeal to any meaning postulate. For any predicate, Fx and ~Fx.

The question then is one of knowing whether ‘The good is bad’ deserves to be called the contrary proposition.

Aristotle replies that the proposition, ‘The good is bad,’ “To agathon kakon estin,” “Bonum malum est,” is NOT the maximally false proposition opposed to the maximally true, tautological, and empty, proposition, “The good is good,” ‘To agathon agathon estin,’ “Bonum bonum est.”

“Indeed, “the good is bad” is sumpeplegmenê.

This term condenses all of the moments of the transition from the simple idea of a container, to the “modern” idea of implication or of presupposition.

For Boethius, the proposition is duplex, or equivocal.

The proposition  has a double meaning, “because it contains within itself [“continet in se, intra se”]: bonum non est”; and Boethius concludes that only two “simple” propositions can be said to be contrary.

Commentarii in librum Aristotelis Peri hermêneais, 1st ed., 219.

This latter thesis is consistent with Aristotle’s, for whom only “the good is not good” (simple proposition) is the opposite of “the good is good” (simple proposition).

However, the respective analyses of “the good is bad,” a proposition that Boethius calls implicita, are manifestly NOT the same.

Indeed, for Aristotle, the “doxa hoti kakon to agathon [δόξα ὅτι ϰαϰὸν τὸ ἀγαθόν],” the opinion according to which the good is bad, is only contrary to “the good is good” to the extent that it “contains” (in Boethius’s terms) “the good is not good”; whereas for Boethius, it is to the extent that it contains bonum non est —a remarkably ambiguous expression in Latin (it can mean “the good is not,” “there is nothing good,” and even, in the appropriate context, “the good is not good”).

Abelard goes in the same direction as Aristotle: “the good is bad” is “implicit” with respect to “the good is not good.”

He explains clearly the meaning of “implicita.”

“That is to say, implying ‘the good is not good’ within itself, and in a certain sense containing it.”

[“implicans eam in se, et quodammodo continens]”

Glossa super Periermeneias, 99–100.

But he adds, as Aristotle did not:

“Because whoever thinks that ‘the good is bad’ also thinks that ‘the good is not good,’ whereas the reverse does not hold true.”

“sed non convertitur.”

This explanation is decisive for the history of implication, since one can certainly express in terms of “implication” in some usage what Abelard expresses when he notes the nonreciprocity of the two propositions.

One can say that “the good is bad” implies or presupposes “the good is not good,” whereas “the good is not good” does not imply “the good is bad.”

Modern translations of Aristotle inherit these difficulties.

Boethius and Abelard bequeath to posterity an interpretation of the passage in Aristotle according to which “the good is bad” can only be considered the opposite of “the good is good” insofar as, an “implicit” proposition, it contains the contradictory meaning of “the good is good,” viz., “the good is not good.”

It is the meaning of “to contain a contradiction” that, in a still rather obscure way, takes up this analysis by specifying the meaning of impliquer.

In any case, the first attested use in French of the verb is in 1377 in Oresme, in the syntagm “impliquer contradiction.”

 (RT: DHLF, 1793).

These same texts give rise to another analysis.

A propositio implicita is a proposition that “implies,” that is, that contains two propositions called explicitae, and that are its equivalent when paraphrased.

Thus, “homo qui est albus est animal quod currit.”

A man who is white is an animal who runs” contains the two explicits: “homo est albus” and “animal currit.”

Only by “exposing” or “resolving” (expositio, resolutio) such an implicita proposition can one assign it a truth-value.

“Omnis implicito habet duas explicitas.”

Verbi gratia: Socrates est id quod est homo, haec implicita aequivalet

huic copulativae constanti ex explicitis.

Socrates est aliquid est illud est homo, haec est vera, quare et implicita vera.

Every “implicit” has two “explicits.”

E. g.“Socrates is that which is a man.”

This “implicit” is equivalent to the following conjunctive proposition made up of two “explicits”:

“Socrates is something and that is a man.”

This latter proposition is true, so the “implicit” is also true.

Tractatus implicitarum, in Giusberti -- Materials for a Study,” 43.

The “contained” propositions are usually relative propositions, which are called implicationes, and this term remains, even though the name “propositio implicita” becomes increasingly rare, perhaps because they are subsequently classified within the larger category of “exponible” propositions, which need precisely to be “exposed” or paraphrased for their logical structure to be highlighted.

In the treatises of Terminist logic, one chapter is devoted to the phenomenon of restrictio, a restriction in the denotation or the suppositio of the noun (v. SUPPOSITION).

Relative expressions (implicationes), along with others, have a restrictive function (vis, officium implicandi), just like adjectives and participles.

In “a man who argues runs,”  “man,” because of the relative expression “who runs,” is restricted to denoting the present — moreover, according to grammarians, there is an equivalence between the relative expression “qui currit” and the participle currens.

Summe metenses, ed. De Rijk, in Logica modernorum, 2.1:464.

In the case in which a relative expression is restrictive, its function is to “leave something that is constant [aliquid pro constanti relinquere],” viz., to produce, in modern terms, a preassertion that conditions the truth of the main assertion without being its primary object.

This is expressed very clearly in the following passage:

Implicare est pro constanti et involute aliquid significare. Ut cum dicitur homo qui est albus currit.

“Pro constanti” dico, quia praeter hoc quod assertitur ibi cursus de homine, aliquid datur intelligi, scilicet hominem album; “involute” dico quia praeter hoc quod ibi proprie et principaliter significatur hominem currere, aliquid intus intelligitur, scilicet hominem esse album.

Per hoc patet quod implicare est intus plicare. Id enim quod intus plicamus sive ponimus, pro constanti relinquimus.

Unde implicare nil aliud est quam subiectum sub aliqua dispositione pro constanti relinquere et de illo sic disposito aliquid affirmare.

“To imply” is to signify something by stating it as constant, and in a hidden manner.

E. g., when we say “the man who is white runs.” I say “stating it as constant” because, beyond the assertion that predicates the running of the man, we are given to understand something else, namely that the man is white; I say “in a hidden manner” because, beyond what is signified primarily and literally, viz. that the man is running, we are given to understand something else within (intus), namely that the man is white.

It follows from this that implicare is nothing other than intus plicare (“folded within”).

What we fold or state within, we leave as a constant.

It follows from this that “to imply” is nothing other than leaving something as a constant in the subject, such that the subject is under a certain disposition, and that it is under this disposition that something about it is affirmed.

De implicationibus, ed. De Rijk, in “Some Notes,” 100)

N.B. Giusberti (“Materials for a Study,” 31) always reads “pro constanti,” whereas the manuscript edited by De Rijk sometimes has “pro contenti,” and sometimes “precontenti,” this latter term attested nowhere else.

This is truly an example of what the 1662 Logic of Port-Royal will describe as an “incidental assertion.”

The situation is even more complex, however, insofar as this operation only relates to one usage of a relative proposition, when it is restrictive. A restriction can sometimes be blocked, and the logical reinscriptions are then different for restrictive and nonrestrictive relative propositions.

One such case of a blockage is that of “false implications,” as in “a [or the] man who is a donkey runs,” where there is a conflict (repugnantia) between what the determinate term itself denotes (man) and the determination (donkey). The truth-values of the propositions containing relatives thus differ according to whether they are restrictive, and of composite meaning—(a) “homo qui est albus currit” (A man who is white runs)—or nonrestrictive, and of divided meaning—(b) “homo currit qui est albus” (A man, who is white, is running).

When the relative is restrictive, as in (a), the implicit only produces one single assertion, as we saw (since the relative corresponds to a preassertion), and is thus the equivalent of a hypothetical. Only in the second case can there be a “resolution” of the implicit into two explicits—(c) “homo currit,” (d) “homo est albus”—and a logical equivalence between the implicit and the conjunction of the two explicits—(e) “homo currit et ille est albus”; so it is only in this instance that one can say, in the modern sense, that (b) implies (c) and (d), and therefore (e).

INTERLUDE:

The Greek vocabulary of implication:

Disparity and systematicity

L. implicature covers and translates an extremely varied Grecian vocabulary that bears the mark of heterogeneous logical and systematic operations, depending on whether one is dealing with Aristotle or the Stoics.

The passage through medieval Latin allows us to understand retrospectively the connection in Aristotelian logic between the implicatio of the implicits (sumpeplegmenê, as an interweaving or interlacing) and conclusive or consequential implication, sumperasma [συμπέϱασμα] in Greek (or sumpeperasmenon [συμπεπεϱασμένον], sumpeperasmenê [συμπεπεϱασμένη], from perainô [πεϱαίνω], “to limit”), which is the terminology used in the Organon to denote the conclusion of a syllogism (Prior Analytics 1.15.34a21–24: if one designates as A the premise [tas protaseis (τὰς πϱοτάσεις)] and as B the conclusion [to sumperasma (συμπέϱασμα)]).

When Tricot translates Aristotle’s famous definition of the syllogism at Prior Analytics 1.1.24b18–21, he chooses to render as the French noun consequence Aristotle’s verbal form sumbainei [συμϐαίνει], that which “goes with” the premise and results from it. A syllogism is a discourse [logos (λόγος)] in which, certain things being stated, something other than what is stated necessarily results simply from the fact of what is stated. Simply from the fact of what is stated, I mean that it is because of this that the consequence is obtained [legô de tôi tauta einai to dia tauta sumbainei (λέγω δὲ τῷ ταῦτα εἶναι τὸ διὰ ταῦτα συμϐαίνει)]. (Ibid., 1.1, 24b18–21; italics J. Tricot, bold B. Cassin)

To make the connection with the modern sense of implication, though, we also have to take into account, as is most often the case, the Stoics’ use of the same terms. What the Stoics call sumpeplegmenon [συμπεπλεγμένον] is a “conjunctive” proposition; for example: “And it is daytime, and it is light” (it is true both that A and that B). The conjunctive is the third type of nonsimple proposition, after the “conditional” (sunêmmenon [συνημμένον]; for example: “If it is daytime, then it is light”) and the “subconditional” (parasunêmmenon [παϱασυνημμένον]; for example: “Since it is daytime, it is light”), and before the “disjunctive” (diezeugmenon [διεζευγμένον]; for example: “Either it is daytime, or it is night”) (Diogenes Laertius 7.71–72; cf. RT: Long and Sedley, The Hellenistic Philosophers, A35, 2:209 and 1:208).

One can see that there is no implication in the conjunctive, whereas there is one in the sunêmmenon in “if . . . then . . . ,” which constitutes the Stoic expression par excellence (and as distinct from the Aristotelian syllogism). Indeed, it is around the conditional that the question and the vocabulary of implication opens out again. The Aristotelian sumbainein [συμϐαίνειν], which denotes the accidental nature of a result, however clearly it has been demonstrated (and we should not forget that sumbebêkos [συμϐεϐηϰός] denotes accident; see SUBJECT, I), is replaced by akolouthein [ἀϰολουθεῖν] (from the copulative a- and keleuthos [ϰέλευθος], “path” [RT: Chantraine, Dictionnaire étymologique de la langue grecque, s.v. ἀϰόλουθος]), which denotes instead being accompanied by a consequent conformity: This connector (that is, the “if”) indicates that the second proposition (“it is light”) follows (akolouthei [ἀϰολουθεῖ]) from the first (“it is daytime”) (Diogenes Laertius, 7.71). Attempts, beginning with Philo or Diodorus Cronus and continuing to the present day, to determine the criteria of a “valid” conditional (to hugies sunêmmenon [τὸ ὑγιὲς συνημμένον] offer, among other possibilities, the notion of emphasis [ἔμφασις], which Long and Sedley translate as “entailment” and Brunschwig and Pellegrin as “implication” (Sextus Empiricus, The Skeptic Way, in RT: Long and Sedley, The Hellenistic Philosophers, 35B, 2:211 and 1:209), a term that is normally used to refer to a reflected image and to the force, including rhetorical force, of an impression. Elsewhere, “emphasis” is explained in terms of dunamis [δύναμις], of “virtual” content (“When we have the premise which results in a certain conclusion, we also have this conclusion virtually [dunamei (δυνάμει)] in the premise, even if it is not explicitly indicated [kan kat’ ekphoran mê legetai (ϰἂν ϰατ̕ ἐϰφοϱὰν μὴ λέγεται)], Sextus Empiricus, Against the Grammarians 8.229ff., trans. D. L. Blank, 49 = RT: Long and Sedley, The Hellenistic Philosophers, G36 (4), 2:219 and 1:209)—where connecting the different meanings of “implication” creates new problems.

One has to understand that the type of logical implication represented by the conditional implies, in the double sense of “contains implicitly” and “has as its consequence,” the entire logical, physical, and moral Stoic system. It is a matter of to akolouthon en zôêi [τὸ ἀϰόλουθον ἐν ζωῇ], “consequentiality in life,” as Long and Sedley translate it (Stobeus 2.85.13 = RT: Long and Sedley, The Hellenistic Philosophers, 59B, 2:356; Cicero prefers congruere, De finibus 3.17 = RT: Long and Sedley, The Hellenistic Philosophers, 59D, 2:356).

It is the same word, akolouthia [ἀϰολουθία], that refers to the conduct consequent upon itself that is the conduct of the wise man, the chain of causes defining will or fate, and finally the relationship that joins the antecedent to the consequent in a true proposition. Victor Goldschmidt, having cited Émile Bréhier (in Le système stoïcien, 53 n. 6), puts the emphasis on antakolouthia [ἀνταϰολουθία], the neologism coined by the Stoics that one could translate as “reciprocal implication,” and that refers specifically to the solidarity of virtues (antakolouthia tôn aretôn [ἀνταϰολουθία τῶν ἀϱετῶν], Diogenes Laertius 7.125; Goldschmidt, Le système stoïcien, 65–66) as a group that would be encompassed by dialectical virtue, immobilizing akolouthia in the absolute present of the wise man. “Implication” is, in the final analysis, from then on, the most literal name of the system as such.

References:

Aristotle.  Anal. Pr.. ed. H. Tredennick,  in Organon, Harvard.

Goldschmidt, Victor. Le système stoïcien et l’idée de temps. Paris: Vrin.

Sextus Empiricus. Against the Grammarians, ed. D. L. Blank. Oxford: Oxford

END OF INTERLUDE

Now for “Implication”/“Implicature”

The term “implicature” was introduced in 1967 by H. P. Grice in the William James Lectures (Harvard), which he delivered under the title “Logic and Conversation.”

These lectures set out the basis of a systematic approach to communication, viz, concerning the relation between a proposition p and a proposition q in a conversational context.

The need is felt for a term that is distinct from “implication,” insofar as “implication” is used for a relation between propositions, whereas an “implicature” is a relation between this or that statement, within a given context.

An “implication” is a relation bearing on the truth or falsity of this or that proposition, whereas “implicature” brings an extra meaning to this or that statement it governs.

Whenever “implicature” is determined according to its context, it enters the field of pragmatics, and therefore has to be distinguished from presupposition.

Logical implication is a relation between two propositions, one of which is the logical consequence of the other.

An equivalent of “logical implication” is “entailment,” as used by Moore.

‘Entail’ is derived from “tail” (Fr. taille; ME entaill or entailen = en + tail), and prior to its logical use, the meaning of “entailment” is “restriction,” “tail” having the sense of “limitation.”

An entailment is a limitation on the transfer or handing down of a property or an inheritance.

The two usages of entailment have two elements in common:

a) the handing down of a property; and

b) the limitation on one of the poles of this transfer.

In Moore’s logical “entailment,” a PROPERTY is transferred from the antecedent to the consequent, and normally in semantics, the LIMITATION on the antecedent is stressed.

One might thus advance the hypothesis that the mutation from the juridical use to the philosophical use occurred by analogy on the basis of these common elements.

Whitehead makes a distinction between material implication and formal implication.

A material implication (“if,” symbolized by the horseshoe “⊃,” because it resembles an arrow) is a Philonian implication (because it was formalized by Philo of Megara), is only false when the antecedent is true and the consequent false.

In terms of a formalization of communication, this has the flaw of bringing with it a counter-intuitive semantics, since a false proposition implies materially any proposition:

If the moon is made of green cheese, 2 + 2 = 4.

The “ex falso quodlibet sequitur,” which is how this fact is expressed, has a long history going back to antiquity (for the Stoics and the Megarian philosophers, it is the difference between Philonian implication and Diodorean implication.

It traverses the theory of consequence and is ONE of the paradoxes of material implication that is perfectly summed up in these two rules of Jean Buridan:

First, if P is false, Q follows from P; Second, if P is true, P follows from Q.

(Bochenski, History of Formal Logic, 208).

A formal implication (see Russell, Principles of Mathematics, 36–41) is a universal conditional implication:

{Ɐx (Ax ⊃ Bx)} (for any x, if Ax, then Bx).

Different means of resolving the paradoxes of implication have been used.

C. I. Lewis’s “strict” implication (Lewis and Langford, Symbolic Logic) is defined as an implication that is reinforced such that it is impossible for the antecedent to be true and the consequent false, yet it has the same alleged flaw as a ‘material’ implication (an impossible—viz., necessarily false—proposition strictly implies any proposition).

The relation of entailment introduced by Moore in 1923 is a relation that avoids this or that paradox by requiring a logical derivation of the antecedent from the consequent (in this case,

If 2 + 2 = 5, 2 + 3 = 5

is false, since the consequent cannot be logically derived from the antecedent.

Occasionally, one has to call upon the pair “entailment”/“implication” in order to distinguish between an implication in the sense of material implication and an implication in Moore’s usage, which is also sometimes called “relevant” implication (Anderson and Belnap, Entailment), to ensure that the entire network of expressions is covered.

Along with this first series of expressions in which “entailment” and “implication” alternate with one another, there is a second series of expressions that contrasts two kinds of “implicature,” or ‘implicata.’

“Implicature” (Fr. implicature, G. Implikatur) is formed from “implication” and the suffix –ture, which expresses a ‘resultant aspect,’ ‘aspectum resultativus’ (as in “signature”; cf. L. temperatura, from temperare).

“Implication” may be thought as derived from “to imply” and “implicature” may be thought as deriving from “imply”’s doulet, “to implicate” (from L. “in-“ + “plicare,” from plex; cf. the IE. plek), which has the same meaning.

Some mistakenly see Grice’s “implicature” as an extension and modification of the concept of presupposition, which differs from ‘material’ implication in that the negation of the antecedent implies the consequent (the question “Have you stopped beating your wife?” presupposes the existence of a wife in both cases).

In this sense, implicature escapes the paradoxes of material implication from the outset.

Grice distinguishes two kinds of implicature, conventional and non-conventional, the latter sub-divided into non-conventional non-converastional, and non-conventional conversational.

Conventional implicature and a conventional implicatum is practically equivalent to presupposition prae-suppositum, since it refers to the presuppositions attached by linguistic convention to a lexical item or expression.

E. g. “Mary even loves Peter” has a relation of conventional implicature to “Mary loves other entities than Peter.”

This is equivalent to:

“ ‘Mary even loves Peter’ presupposes ‘Mary loves other entities than Peter.’

 With this kind of implicature, we remain within the lexical, and thus the semantic, field.

Conventional implicature, however, is different from material implication, since it is relative to a language (in the example, the English for the word “even”).

With conversational implicature, we are no longer dependent on a linguistic expression, but move into pragmatics (the theory of the relation between statements and contexts).

Grice gives the following example: If, in answer to someone’s question about how X is getting on in his new job, I reply, “Well, he likes his colleagues, and he’s not in prison yet,” what is implied pragmatically by this assertion depends on the context (and not on a linguistic expression). It is, for example, compatible with two very different contexts: one in which X has been trapped by unscrupulous colleagues in some shady deal, and one in which X is dishonest and well known for his irascible nature.

BIBLIOGRAPHY

Abelard, Peter. Dialectica. Edited by L. M. De Rijk. Assen, Neth.: Van Gorcum, 1956. 2nd rev. ed., 1970.

———. Glossae super Periermeneias. Edited by Lorenzo Minio-Paluello. In TwelfthCentury Logic: Texts and Studies, vol. 2, Abelaerdiana inedita. Rome: Edizioni di Storia e Letteratura, 1958.

Anderson, Allan Ross, and Nuel Belnap. Entailment: The Logic of Relevance and Necessity. Vol. 1. Princeton, NJ: Princeton University Press, 1975.

Aristotle. De interpretatione. English translation by J. L. Ackrill: Aristotle’s Categories and De interpretatione. Notes by J. L. Ackrill. Oxford: Clarendon, 1963. French translation by J. Tricot: Organon. Paris: Vrin, 1966.

Auroux, Sylvain, and Irène Rosier. “Les sources historiques de la conception des deux types de relatives.” Langages 88 (1987): 9–29.

Bochenski, Joseph M. A History of Formal Logic. Translated by Ivo Thomas. New York: Chelsea, 1961. Boethius. Aristoteles latinus. Edited by Lorenzo Minio-Paluello. Paris: Descleé de Brouwer, 1965. Translation by Lorenzo Minio-Paluello: The Latin Aristotle. Toronto: Hakkert, 1972. ———. Commentarii in librum Aristotelis Peri hermêneias. Edited by K. Meiser. Leipzig: Teubner, 1877. 2nd ed., 1880. De Rijk, Lambertus Marie. Logica modernorum: A Contribution to the History of Early Terminist Logic. 2 vols. Assen, Neth.: Van Gorcum, 1962–67. ———. “Some Notes on the Mediaeval Tract De insolubilibus, with the Edition of a Tract Dating from the End of the Twelfth-Century.” Vivarium 4 (1966): 100–103.

Giusberti, Franco. Materials for a Study on Twelfth-Century Scholasticism. Naples, It.: Bibliopolis, 1982.

Grice, H. P. “Logic and Conversation.” In Syntax and Semantics 3: Speech Acts, edited by P. Cole and J. Morgan, 41–58. New York: Academic Press, 1975. (Also in The Logic of Grammar, edited by D. Davidson and G. Harman, 64–74. Encino, CA: Dickenson, 1975.)

Lewis, Clarence Irving, and Cooper Harold Langford. Symbolic Logic. New York: New York Century, 1932.

Meggle, Georg. Grundbegriffe der Kommunikation. 2nd ed. Berlin: De Gruyter, 1997.

Meggle, Georg, and Christian Plunze, eds. Saying, Meaning, Implicating. Leipzig: Leipziger Universitätsverlag, 2003.

Moore, G. E.. Philosophical Studies. London: Kegan Paul, 1923.

Rosier, I. “Relatifs et relatives dans les traits terministes des XIIe et XIIIe siècles: (2) Propositions relatives (implicationes), distinction entre restrictives et non restrictives.” Vivarium 24: 1 (1986): 1–21.

Russell, Bertrand. The Principles of Mathematics. Cambridge: Cambridge University Press, 1903.

Strawson, P. F.. “On Referring.” Mind 59 (1950): 320–44.