The Significance of Current Criticisms of the Syllogism

THE SIGNIFICANCE OF CURRENT CRITICISMS OF THE SYLLOGISM I. Is THE SYLLOGISM FuNDAMENTAL To ALI~ DEDUCTIVE INFERENCE. ITH respect to the syllogism, Prof. Lewis has spoken with both assurance and finality: "To regard the syllogism as indispensable, or as reasoning par excellence , is the apotheosis of stupidity." 1 The applicability of this apparent judgment from on high would seem to be unmistakable. For so far as these present essays are concerned,2 one corollary of the conclusions reached thus far would certainly be that there is no form of deductive argument or ·demonstration but what is ultimately dependent on the syllogism. Thus in our first paper we tried to show that of the two possible varieties of propositional composition, the conjunctive and the implicative, it is simply impossible to describe or account for implicative compounds on a truth-functional basis. And the reason such a thing is impossible is because the connection between the component propositions in any such compound is in no wise dependent upon the mere truth or falsity of the propositions thus combined. Instead, the connection in most cases 3 depends upon the mediation between two extreme terms by a third or middle term. Nevertheless, the grounds for this last point will doubtless bear recapitulation. Thus it will be. remembered how in de1 Lewis, C. 1, "A Survey of Symbolic Logic," (Berkeley: University of California Press, 1918), pp. l-2. 2 Previous articles in this series are "Aristotelian and Mathematical Logic," The Thomist, XIII (Jan. 1950), pp. 50-96, and "Basic Confusions in Current Notions of Propositional Calculi," XIV (April 1951), pp. 238-258. 3 i.e. in all cases in which it is not a question of either an inductive or an immediate inference. 624 CURRENT CRITICISMS OF THE SYLLOGISM 625 scribing so-called implicative compounds, we pointed out that there were really two kinds of them, hypothetical compounds and categorical compounds. Of the latter, those that were most properly implicative were the so-called causal propositions . On the other hand, the hypotheticals were represented by conditionals and disjunctives. Now all of these compounds being implicative in character, there must necessarily be in each of them an implicative relationship between one proposition functioning as antecedent and another functioning as consequent (i. e. between premise and conclusion) .4 But in virtue of what may the antecedent in such instances be said to t'mply the conclusion? There are three possible alternatives. It may be that the antecedent provides inductive evidence of the consequent or conclusion. Or it may be that the consequent is not a conclusion from the antecedent at all, but only a different way of stating the same thing, an " immediate inference," in other words. Or :finally, it may be that the antecedent contains, either implicitly or explicitly, a middle term that mediates between the subject and predicate term of consequent-in which case the whole conditional or causal proposition would really be in the nature of an enthymeme.5 Now of these three alternatives, the first is obviously not relevant to our present concerns. As for the second, it does not so much invalidate our thesis as confirm it-the thesis, namely, that all deductive inference is syllogistic. In fact, as we were at such pains to try to show in our second paper, an immediate inference does not :represent an inference from a proposition but rather a property of a proposition.6 And if we • This summary statement would, of course, have to be amplified somewhat in order to fit the case of disjunctive propositions. Cf. " Aristotelian and Mathematical Logic," loc. cit., pp. 67-68. 5 Cf. the fuller discussion of this in our first paper, loc. cit., pp. 74-79. • Indeed, the point would seem to be that when the same notions or concepts come into play in the two cases, then immediate inferences may be seen to involve a difference of " intention " as compared with mediate inferences. Thus, for example, when one asserts that if virtue is knowl.,dge, it can be taught, what one is talking about or intending are real natures or essences of things, viz. virtue, knowledge, and teachability. On the other hand, let one assert that if...