Commentary on Hurford

Abstract: 63 words
Main Text: 1022 words
References: 16 words
Total Text: 1101 words

No problem for Aristotle's subject and predicate

Guy Politzer
Psychologie Cognitive, Université de Paris VIII
Centre National de la Recherche Scientifique
2, rue de la Liberté
93526 Saint-Denis
France

(33) 3 44 55 38 43
politzer@univ-paris8.fr

Abstract

It is argued that, in the traditional subject-predicate sentence, two interpretations of the subject term coexist, one intensional and the other extensional, which explains the superficial difference between the traditional S-P relation and the predication of predicate logic. Data from psychological studies of syllogistic reasoning support the view that the contrast between predicate and argument is carried over to the traditional S-P sentence.

That the predicate-argument structure of modern languages on the one hand and of logical formulae on the other hand have a precursor in the integration by the brain of two pathways, one to locate an individual object and one to identify properties seems plausible. This division of labor between predicate and argument is well respected by first order predicate logic ( FOPL ). But, at first sight, it would seem to be at variance with the Aristotelian sentence (henceforth A-sentence ) which superficially does not require the argument (the subject ) to be an individual variable, nor for the subject and the predicate to belong to different kinds of terms ( i. e. , the same term can be the subject of one sentence and the predicate of another ): This is what the author calls "the Aristotle problem", to which a simple solution will be proposed.

It will be useful to separate two senses of predicate : (i) in its modern, logical sense, a predicate (henceforth predicateL) is a function from a singular term to a sentence expressing a proposition about the object to which the singular term refers; (ii) in its traditional, grammatical sense, the predicate (henceforth predicateG) is that which is affirmed or denied of the other term, the subject. I believe that the solution to the problem at hand lies in a dual interpretation of the subject term. In his conception of terms, Aristotle took the intensional or the extensional point of view, depending on the domain explored ( putting greater emphasis on the former in his theory of the proposition and near exclusive emphasis on the latter in his theory of the syllogism). I suggest that the Aristotelian subject should be treated ( by theorists ) and can be processed (by speakers) from both points of view. With an intensional reading, the subject functions as a predicateL (which trivially licenses the occupation of the subject slot and of the predicateG slot by the same term ). But with an extensional reading, the subject functions as a class providing generic individual terms, which licenses the occupation of the subject place to play the role of an argument in association with the predicateL. In brief, the traditional A-sentence superficially expresses a higher-order predication but its generic subject term is of the same logical type as the other arguments to which the predicateG may apply (qua predicateL ): Predication in the A-sentence is understandable on the same grounds as the basic predication, from which it does not differ in nature.

From the inception of categorization, the A-sentence predication could start to develop, taking generic individual objects as its subject: "x is a predator" (with temporal anteriority ) and "x is yellow" are conflated into "the predator is yellow". Indeed, it would be uneconomical to formulate, e. g., the x is S and P when the first predication is temporally or cognitively already established, hence the shorter formulation the S is P. Now, in remarking that "FOPL is more distanced from the surface of natural languages", the author makes an understatement: FOPL, at least with standard quantification, fails to capture what the A-sentence captures by using the generic term of the subject class, namely the anteriority of the first predication (Sx) with regard to the second (Px). For example, in the rendering of some cat is black, ( $x) (Cx & Bx), C and B are treated on a par, except if one remedies this by using restricted quantification, ($x: Cx)(Bx), which captures well the prior predication.

There is indirect evidence that for Aristotle the deep structure of sentences like some S are P coincides with their expression in FOPL. This is suggested by one of his methods to solve syllogisms, namely ecthesis. Consider his proof for Darapti: all M are P; all M are S; therefore some P are S. First, extract an individual x; now, since both P and S are predicated of this individual, it follows that one of the two is predicated of the other: some S are P. In other words, some S are P is proved by the fact that there is an individual that has both properties P and S. This turns out to be a paraphrase of the FOPL formula ($x)(Sx & Px). But notice that in this syllogism, S and P play parallel roles (except in the conclusion where the end term labelled S is, by convention, allocated to the subject place) so that none of the terms S and P takes precedence over the other; this leads to another psychologically acceptable conclusion some P are S.

If, as I have argued, the nature of the predication in the A-sentence does not differ from the basic predication in which (in agreement with the author's claim) the object attended to (the subject) and the property attributed to it have a different status, it follows that people should be sensitive to this difference in status. Of course, this meets speakers' intuitions of a contrast between subject and predicateG; but also this ought to have testable consequences: People should be reluctant to exchange the role of the subject and of the predicateG. This is precisely one of the most robust and remarkable findings in the psychological study of syllogistic reasoning. There are two related phenomena. One is called the figural effect (Johnson-Laird & Steedman, 1978). Irrespective of the logical status of the syllogisms, people have a tendency to produce a conclusion whose terms (subject and predicateG) reproduce the role which they have in the premises. Take for example the syllogism some M are P; all S are P, from which most people fail to recognize that nothing follows; instead, they provide some conclusions, most of which are some S are P, and only very few some P are S. The other phenomenon concerns valid syllogisms. The four most difficult syllogisms to solve (for which the success rate is typically below 15 percent) coincide with the only ones in which both end terms change grammatical role from premise to conclusion (for example: no P are M; all M are S; therefore some S are not P).


References

Johnson-Laird, P. N. , & Steedman, M. (1978). The psychology of syllogisms. Cognitive Psychology, 10, 64-99.