The Stoic analysis of tense and of plural propositions in Sextus Empiricus, 'Adversus Mathematicos' X 99.

I. THE CONTEXT

After recording two arguments of Diodorus' in support of the thesis that nothing is moving ([Greek Text Omitted]) but something has moved ([Greek Text Omitted]) (M. x 85-90), Sextus sets down five objections to these arguments (M. x 90-6). According to the first objection, a perfective proposition (such as 'This has moved') cannot be true at some time if the corresponding continuative proposition (such as 'This is moving') is never true (M. x 90-2) ('perfective' and 'continuative' translate [Greek Text Omitted] and [Greek Text Omitted]).

Sextus reports also some answers to these objections (M. x 97-111). The reply to the first objection (M. x 97-102) he attributes to Diodorus himself. It consists of three examples which are supposed to show that a perfective proposition may be true at some time even if the corresponding continuative proposition is never true. In the first example, Diodorus imagines that A married at one time and B married one year later. Then the perfective proposition 'These men have married' (formulated while A and B are being indicated) is now true, but the corresponding continuative proposition 'These men are marrying' (formulated while A and B are being indicated) is never true: when A was marrying, B wasn't marrying yet, and when B was marrying, A wasn't marrying any more, so that at both times 'These men are marrying' (formulated while A and B are being indicated) was false (its falsity at other times is trivial).

M. x 99 contains a criticism of this answer by Diodorus.

II. WHO ARE DIODORUS' CRITICS?

The terminology employed in M. x 99 strongly suggests that Diodorus is being criticised by the Stoics (cf. Frede [1978: 306]). For Stoic logicians often use the noun [Greek Text Omitted] ('object') to denote meanings (see S. E. M. VIII 12; D. L. VII 57; Mates [1953-61: 134]). Also [Greek Text Omitted] ('ambiguity') belongs to the Stoic logical jargon (see D. L. VII 44, 62, 178 and 193, cf. [Greek Text Omitted] in Chrysipp. Quaest. Log., PHerc. 307 col. XI 14-15 and D. L. VII 47 and [Greek Text Omitted] in Gal. Capt. XIV 595, 16 Kuhn, S. E. M. IX 136 and D. H. Comp. IV 21, 76, 14 Aujac-Lebel). Even for [Greek Text Omitted] ('containing'), which has the form [Greek Text Omitted] accusative of an abstract noun and is equivalent to [Greek Text Omitted], there are Stoic parallels: [Greek Text Omitted] ('valid', or 'deductive') is used interchangeably with [Greek Text Omitted] (see S. E. P. II 135; 143; 170; M. VIII 314; 385); [Greek Text Omitted] and [Greek Text Omitted] occur in passages reporting logical theories of the Stoics (see S. E. M. XI 9; 29-30; D. L. vn 60); Chrysippus (Quaest. Log., PHerc. 307 col. x 9-10) uses [Greek Text Omitted] ('contained propositions').

Chrysippus criticised Diodorus on points of modal logic and of theory of meaning (see Cic. Fat. 12-13; 15; Epict. Diss. II 19, 1-9; Gell. XI 12, 1-3, cf. Cic. Ac. n 143). He also wrote works About Singular and Plural Expressions in six books and About Perfective Propositions in two books (see D. L. VII 192; 190). Chrysippus' interest in singulars and plurals shows also in some fragments of his Logical Investigations (see PHerc. 307 fr. 14-7; coll. I 13; 15-26; n 21-6; VI 8-9; 11; 13-35; VII 9-22). The passages preserved in columns VI and VII deal with expressions like [Greek Text Omitted] [Greek Text Omitted] and [Greek Text Omitted], i.e. expressions which from the point of view of grammar are singular but have meanings involving the idea of a multiplicity of objects: Chrysippus discussed the question whether such expressions must be considered singular or plural (cf. Schol. in Dionys. Thr. 230, 3-9; 545, 18-25; Simpl. in Cat. 160, 27-8). Further passages proving that Chrysippus studied the problem of plurals are S. E. M. XI 11-13 (analysed and partly translated below, section VIII), Schol. in Hom. Il. I 129, I 47 Erbse and Var. L. x 59. The Stoic attack of S. E. M. x 99, to which Sextus reports no answer by Diodorus, could have taken place after Diodorus' death - its author might be Chrysippus.

According to Marrone [1984:421-3] Chrysippus applies 'singular' and 'plural' not to predicates and propositions, i.e. meanings, but only to linguistic expressions. This interpretation is supported by a passage of the Logical Investigations (PHerc. 307 col. II 21-6) which contains an argument concluding that there are no plural predicates. This is an unreliable ground, because the previous lines (col. II 10-21) contain two similar arguments concluding, respectively, that there are no past tense predicates nor past tense propositions and that there are no passive predicates: but Chrysippus' work About What Is Said with Tense in two books (D. L. VII 190) is listed among treatises concerning propositions (cf. Plu. Soll. Anim. III 961c), and from Diogenes Laertius (VII 64) we learn that, according to orthodox Stoic logic, some …