O R G A N O N 7 (1970) M ISC E L L A N E A
A n to ni Korcik (Poland)
EXISTENTIAL PROPOSITIONS IN ARISTOTLE
As regards existential propositions, th e following definition shall serve as the point of departure: existential propositions are propositions of which the predicate (together w ith the copula) is form ed by th e positive o r negative form of verbs such as “to be”, “to exist”. For example, “Men exist”, “Square circles do not exist.” 1
As regards 'both stru ctu re and in terpretation of existential proposi tions, there a re differences betw een authors. Some consider them to be single-m em bered propositions, w ithout predicate, 2 others view th em as subjectless propositions. 3 There are also some w ho regard them as tw o- m em bered propositions, assuming th a t words such as “is”, “th ere is’’, “exists’’, can be viewed as predicates. 4
The term “existential proposition” is n o t found in Aristotle. I t first appears in H erbart as “E xistentialsatz”. Nor did A ristotle work out any theory of existential propositions. In his considerations regarding th e pos sible mode of negating a given proposition he m entions propositions such as “A is,” consisting of b u t two words, or m em bers (later know n as
1 Cf. S. L eśn iew sk i, „P rzyczyn ek do a n a liz y zd a ń eg z y ste n c ja ln y c h ”, P r ze g lą d F ilo zo ficzn y, X IV (191/1), p. 329; L o g ic h e sk iy e ro z su zh d e n iy a , St. P etersb u rg, 1913, p. 57. E x isten tia l p rop osition s in general, w ith p a rticu la r r e fe r e n c e to e x is te n tia l prop osition s in A ristotle, w e r e stu d ied b y H. C orn eliu s, P. T ik h om irov, S. L e ś n ie w sk i and, m o re recen tly, toy G. R ab eau (L e ju g e m e n t d ’e x is te n c e , P aris, 1936), and
S. M ansion (Le ju g e m e n t d ’e x is te n c e ch ez A r is to te , L o u v a in -P a r is, l'946).
2 F. B rentano, P sych o lo g ie v o m e m p irisc h e n S ta n d p u n k te , I. L eip zig, 1874, pp. 276, 283; criticized b y Ch. S ig w a rt, L o g ik , I, T ü b in gen , 1904, p. 93 n.; in terp retation o f ex iste n tia l categoric p ro p o sitio n s is a lso fo u n d in L eib n iz—L., pl., G., V II, 211-217.
3 J. F. H erbart, L eh rb u ch z u r E in leitu n g in d ie P h ilo so p h ie, K önigsberg, 1834, p. 84; se e also M. W. D robisch, N eu e D a rste llu n g d e r L o g ik , H a m b u rg -L eip zig [1836], ,1887, pp. 61f; a lso F. M iklosidh, S u b je k tlo s e S ä tz e , W ien 1883, p. 18.
4 F orem ost am on g th e s e stan d s H. C ornelius, V ersu ch e in e r T h eo rie d e r E x i s t en tia lu r teile, M ünchen, 1894, pp. 3'1, 86; cf. also P. T ik h om irov, “L o g ich esk ii kharak ter eksistenitsdalnykh su z h d e n ii”, V o p ro sy F ilo so fii i P sik h o lo g ii, X L II, 1898, pp. H15f. T his v ie w is also h eld b y S. L eśn iew sk i.
282 A. Korcik
existential propositions), as distinct from propositions of th e p attern
“A is B,” consisting of more th an tw o members, and w here th e copula
"is” comes in as a th ird som ething (De interpr. 19 b, 14-24). He com pares propositions such as “Man w alks” w ith tw o-m em bered proposi tions, pointing out th e analogy w ith respect to negation, w h ere th e p ar ticle “no” has been p u t before th e verb (De interpr. 20 a, 3-5). Else where, he shows them to be reducible to three-m em bered propositions, since th e proposition “M an w alks” is equivalent to the proposition “Man is w alking” (De interpr. 21 b, 5-10). Coming afte r Aristotle, Eudemus, an early Peripathetic, em phasized the difference betw een propositions of the “A is B ” type and those of th e "A is” type. He thought th a t in propositions of the “A is” type the m eaning of the particle “is” differs from th a t which the particle “is” has in propositions of th e “A is B ” ty p e .5 According to Saccheri, th e particle “is” can be used to convey eith er of two senses: 1) th e verbal, and 2) the copulative.
1) The particle “is” is used in the verbal sense, w henever something
is confirm ed or negated unconditionally, th a t is to say, w henever th e ex istence of the subject is affirm ed or negated; as in th e proposition: “Adam is a m an,” or rather, “Adam was a m an,” “A lexander’s horse does not exist” (equivalent to: “A lexander’s horse is n o t in existence”). Relevant to this exam ple of Saccheri’s is A ristotle’s view recorded in De interpr. 21 a, 21-24, w here th e point is m ade th a t it is not law ful to predicate of a dead m an th a t he is man; or of A B th a t it is B, since A entails something no t compatible w ith B.
2) The particle “is” is used in the copulative sense, w hen something
is affirm ed or negated conditionally, th a t is to say, w hen the predicate predicates about th e subject conditionally, on condition th a t th e subject does not exist; as, for instance, in th e proposition: “P ete r is m an.” Here no m ore than a relation between th e predicate (man) and the subject (Peter) is predicated, th a t is, th e existence of P eter-m an is asserted con ditionally, not unconditionally. The proposition is equivalent to th e pro position: “If P eter exists, m an exists.” 6
Both A ristotle and Eudemus th in k th a t th e particle “is” in existential propositions is used in the verbal sense. According to Aristotle, a posi tive proposition, if true, is one th a t either links up or juxtaposes some th ing to something else (Met. 1027 b, 20-22; Met. 1051 b, 2-5), the copula or particle “is”, w hether obvious or implicit, indicating th e ju x ta
5 Cf. C. P rantl, G e sc h ic h te d e r L o g ik im A b e n d la n d e , I, L eipzig, 1927, p. 355. 6 Cf. H. S acch eriu s, L ogica d e m o n s tr a tiv e , A u gu stae U biorum , 1735, pp. 15, 9: “H uic su b iectu m clariu s in tellig es, quid sit cop u la est su m i in v i verb i, quid s it su- m i in v i copula. S u m itu r in v i v erb i quando prop ositio est ab solu ta, siv e quando a liq u id affirm aitur au t n egatu r ab solu te, u t in dictas propositionitous, P etru s fu it hom o. E contra su m itu r in v i copulae, q u an d o a llq u id a ffirm atu r au t n eg a tu r co n - d itio n a te; adeo ut affirm atu r aut n eg a tu r p raed icatam de su b iecto sub conditione, q u od e x is tit su b ieotu m .”
Existential Propositions in Aristotle 283 position; thus, w ithout th e copula th ere w ould be no proposition (De
interpr. 17 a, 11-12, also 19 b, 12-13); w ith reference to th e particle
{prosthesis) see ibid. 21 b. 26-28.
B ut w h at does this copula link up o r juxtapose in propositions like “m an is” ?—Or, rather, w h at is “m an” linked up to, o r juxtaposed to, in th a t proposition? According to Aristotle, to affirm of somebody (for instance, of man) o r something th a t he (or it) “is”, am ounts to saying th a t he (or it) is a substance, or its content, its accidents; or th a t w hich is predicated of th e substance; o r th a t w hich continues in a relation of w hatever kind w ith regard to the substance (Met. 1033 b, 5-10; 1017 a, 7-22). 7
The purport of these basic loci would seem to be that, fo r Aristotle, if som ething is said to be so and so, th e assertion also implies th e exist
ence of the something.
Elsewhere, how ever (De interpr. 21 a, 24-28), A ristotle asserts th a t from th e proposition “Homer is a poet” it does not follow th a t Homer is (exists); from th e proposition th a t som ething is it is not perm itted to in fer th a t something does inform . This is th e reason w hy from the propo sition th a t the object represented is something it does not follow th a t th e ob ject is (i.e., exists). Similarly, if a non-existent something is made object of representation, it is not perm issible to infer th a t it is something,
th a t is, something th at has existence (De interpr. 21 a, 32-33).
