Abstract
It is widely held that as a nego suppositum, Chrysippus’ response to Diodorus Cronus’ Master Argument is that the impossible “this man has died” follows from the possible “Dio has died”. A principal claim of this article is that Chrysippus was not actually committed, against Diodorus, to the tenet that there are deductions and conditionals whereby from the possible the impossible follows. I argue that this is most likely part of a Chrysippean exemplum fictum of a real dialectical discussion and it merely reflects a Chrysippean dialectical strategy, a merely instrumental agreement (συγχώρησις) with Diodorus on the admissibility of some single-premised arguments. As historical evidence for my conjecture I highlight two key passages by Sextus Empiricus which help to understand that Chrysippus’ real tenet was an ancient implicational counterpart of a deictic version of the Identity-Elimination Rule, whereas most likely, according to Diodorus the identitarian major premiss of this rule is redundant, so that it must be eliminated.
References
Alessandrelli, M. 2013. Il problema del lekton nello Stoicismo antico. Firenze: Olschki.Search in Google Scholar
Ammonius,. 1897. Aristotelis de Interpretatione commentarius. A. Busse (ed). Berlin: (CAG IV.5).10.1515/9783112361023Search in Google Scholar
Arnim, H. V. 1964. Stoicorum Veterum Fragmenta. 4. [including a fourth one of indexes by M. Adler]. Stuttgart: Teubner. cited as ‘SVF’ by volume:fragment: numbers.Search in Google Scholar
Atherton, C. 1993. Stoics on Ambiguity. Cambridge: Cambridge University Press.Search in Google Scholar
Barnes, J. 1980. Proof Destroyed. In M. Schofield, M. Burnyeat & J. Barnes (eds.), Doubt and Dogmatism. Studies in Hellenistic Epistemology, 161–181. Oxford: The Clarendon Press.Search in Google Scholar
Barnes, J. 1997. Logic and the Imperial Stoa. Leiden: Brill.10.1163/9789004321007Search in Google Scholar
Barnes, J. 2007. Truth. Oxford: Oxford University Press.Search in Google Scholar
Bobzien, S. 1993. Chrysippus’ Modal Logic and its Relation to Philo and Diodorus. In K. Döring & Th Ebert (eds.), Dialektiker und Stoiker, 63–84. Stuttgart: Steiner.Search in Google Scholar
Bobzien, S. 1997. The Stoic on Hypotheses and Hypothetical Arguments. Phronesis 42(3). 299–312.10.1163/15685289760518180Search in Google Scholar
Bobzien, S. 1998. Determinism and Freedom in Stoic Philosophy. Oxford: Oxford University Press.Search in Google Scholar
Bohnemeyer, J. 2015. Deixis. In J. Wright (ed), International Encyclopedia of the Social and Behavioral Sciences vol. 6 2nd, 52–57. Amsterdam: Elsevier.10.1016/B978-0-08-097086-8.52031-5Search in Google Scholar
Castagnoli, L. 2010. Ancient Self-Refutation: The Logic and History of the Self-Refutation Argument from Democritus to Augustine. Cambridge: Cambridge University Press.Search in Google Scholar
Diels, H., et al. 1836–1870. Commentaria in Aristotelem Graeca. eds. 26. Academiae Litterarum Regiae Borussicae: Berlin, Reimer. rpt. Stuttgart-Bad Cannstatt: Frommann-Holzboog, 1990; re-issue of volumes published in Venice ca. 1550 (several volumes are multiple); cited as ‘CAG’.Search in Google Scholar
Ebert, TH. 2008. In Defence of the Dialectical School. In F. Alesse (ed.), Anthropine Sophia, 275–293. Napoli: Bibliopolis.Search in Google Scholar
Empiricus, Sextus. 1912. 1954. Opera, 3. H. Mutschmann & J. Mau (eds). indexed by K. Janáček. Leipzig: Teubner. Outlines of Pyrrnonism designated as ‘PH’; Adversus Mathematicos, designated as ‘M’.Search in Google Scholar
Gellius, A. 1968. Noctes Atticae. 2. P.K. Marshall (ed). Oxford: The Clarendon Press. cited as ‘Noct. Att.’ by vol. chapt. paragr. numbers.10.1093/oseo/instance.00134326Search in Google Scholar
Hansen, P.A. 1983–89. Carmina Epigraphica Graeca. 2. Berlin: de Gruyter. designated ‘CEG’, all references are to vol. 1, published 1983.Search in Google Scholar
Hülser, K. 1987–88. Die Fragmente zur Dialektik der Stoiker. 4. Stuttgart: Frommann-Holzboog. (Paginated continuously across the four volumes; line number(s) indicated by ‘l.’ or ‘ll.’.).Search in Google Scholar
Ingenkamp, H.G. 1967. Untersuchungen zu den pseudoplatonischen Definitionen. Wiesbaden: Harrassowitz.Search in Google Scholar
Laertius, Diogenes. 1925. Lives of Eminent Philosophers. 2. Greek and English. R.D. Hicks (ed). tr. London, Heinemann; New York: G.P. Putnam’s Sons. cited as ‘DL’ by book: chapternumbers.Search in Google Scholar
Papazian, M.B. 2001. Chrysippus and the Destruction of Propositions: A Defence of the Standard Interpretation. History and Philosophy of Logic 22. 1–12.10.1080/01445340010022013Search in Google Scholar
Papiae, 1998. Ars Grammatica. R. Cervani (ed). Bologna: Patron.Search in Google Scholar
Rosenberg, S. & C. Manekin. 1988. Themistius on Modal Logic. Jerusalem Studies in Arabic and Islam 2. 83–103.Search in Google Scholar
Sedley, D. 1982. The Stoic Criterion of Identity. Phronesis 27(3). 255–275.10.1163/156852882X00177Search in Google Scholar
Seel, G. 2018. The puzzles of the Master Argument and their solutions. Philosophical Inquiry, International Quarterly 41(2-3). 81–93.10.5840/philinquiry2017412/317Search in Google Scholar
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