ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and DiodorusCronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and modal (...) theorems, and to make clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy. (shrink)
ABSTRACT: Summary presentation of the surviving logic theories of Philo the Dialectician (aka Philo of Megara) and DiodorusCronus, including some general remarks on propositional logical elements in their logic, a presentation of their theories of the conditional and a presentation of their modal theories, including a brief suggestion for a solution of the Master Argument.
ABSTRACT: Part 1 discusses the Stoic notion of propositions (assertibles, axiomata): their definition; their truth-criteria; the relation between sentence and proposition; propositions that perish; propositions that change their truth-value; the temporal dependency of propositions; the temporal dependency of the Stoic notion of truth; pseudo-dates in propositions. Part 2 discusses Stoic modal logic: the Stoic definitions of their modal notions (possibility, impossibility, necessity, non-necessity); the logical relations between the modalities; modalities as properties of propositions; contingent propositions; the relation between the Stoic (...) modal notions and those of DiodorusCronus and Philo of Megara; the role of ‘external hindrances’ for the modalities; the temporal dependency of the modalities; propositions that change their modalities; the principle that something possible can follow from something impossible; the interpretations of the Stoic modal system by B. Mates, M. Kneale, M. Frede, J. Vuillemin and M. Mignucci are evaluated. -/- For a much shorter English version of Part 1 of the book see my ‘Stoic Logic’, in K. Algra et al. (eds), The Cambridge History of Hellenistic Philosophy, Cambridge 1999, 92-157. For a shorter, updated, English version of Part 2 of the book see my 'Chrysippus' Modal Logic and its Relation to Philo and Diodorus', in K. Doering / Th. Ebert (eds) Dialektiker und Stoiker (Stuttgart 1993) 63-84. (shrink)
In this paper we examine Prior’s reconstruction of Master Argument  in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom ( P ): ‘ p Λ G p ⊃ P G p ’. This formula was used by Prior in his original analysis of Master Argument. ( P ) (...) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by ( P ) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. (shrink)
My aim is to figure out whether Aristotle’s response to the argument for fatalism in De Interpretatione 9 is successful. By “response” here I mean not simply the reasons he offers to highlight why fatalism does not accord with how we conduct our lives, but also the solution he devises to block the argument he provides for it. Achieving my aim hence demands that I figure out what exactly is the argument for fatalism he voices, what exactly is his solution, (...) whether his solution is coherent, and whether it does indeed succeed. I find that the argument is essentially bivalence plus that the truth of a proposition stating that an event will happen in the future entails that this event will necessarily happen, that Aristotle’s solution is to restrict bivalence when it comes to propositions about contingent future events, that this solution is coherent, and that while it does not rule out the possibility of fatalism, it does succeed in blocking the argument for fatalism offered within chapter 9. (shrink)
Diodoruscronus was a megaric logician who was reputed to have derived from uncontroversial premises the surprising conclusion that the possible is that which either is or will be the case. Versions of his lost argument have been reconstructed recently by prior, Hintikka, And rescher. I analyze and compare these versions and argue that none of them forms a sound argument.
The ‘Dialectical school’ denotes a group of early Hellenistic philosophers that were loosely connected by philosophizing in the — Socratic — tradition of Eubulides of Megara and by their interest in logical paradoxes, propositional logic and dialectical expertise. . Its two best known members, DiodorusCronus and Philo the Logician, made groundbreaking contributions to the development of theories of conditionals and modal logic. Philo introduced a version of material implication; Diodorus devised a forerunner of strict implication. Each (...) developed a system of modal notions that satisfies the basic logical requirements laid down by modern standard modal theories. In antiquity, DiodorusCronus was famous for his so called Master Argument, which aims to prove that only the actual is possible. (shrink)
Chrysippus claims that some propositions perish. including some true conditionals whose consequent is impossible and antecedent is possible, to which he appeals against Diodorus?s Master Argument. On the standard interpretation. perished propositions lack truth values. and these conditionals are true at the same time as their antecedents arc possible and consequents impossible. But perished propositions are false, and Chrysippus?s conditionals are true when their antecedent and consequent arc possible, and false when their antecedent is possible and consequent impossible. The (...) claim of the Master Argument that Chrysippus rejects, then, is stronger ihan usually supposed. (shrink)
This paper discusses the 'master argument' of diodorus cronos from a semantic perspective. An argument is developed which suggests that proposition (1), 'every proposition true about the past is necessary', May have provided the principal motivation for diodorus denial of proposition (3), I.E., His equation of possibility with present-Or-Future truth. It is noted that (1) and (3) are jointly inconsistent only given the assumption of a linear ordering of time. It is further noted that diodorus' fatalism "could" (...) be employed to justify this additional assumption. However, To then use the conclusion of the 'master' to argue for fatalism would obviously be circular. I suspect, Rather, That diodorus' assumption of temporal linearity was implicit and uncritical. (shrink)
On prior's reconstruction, The master argument of diodorus contains an equivocation and so is invalid for one class of diodorean "propositions." but diodorus knew of such "propositions" and an argument in his treatment of motion can be used to bring them under the master argument's sway. Also, Despite the consensus of antiquity, The master argument does not commit diodorus to determinism, Although it commits him to non-Deterministic theses which can be easily misinterpreted as deterministic.
We develop a modified system of standard logic, Augmented Standard Logic (ASL), and we employ ASL in an effort to show that, contrary to prevailing opinion, both Aristotle and Diodorus presented impressive arguments, having valid structures and highly plausible premisses, in their famous fatalism debate. We argue that ASL, which contains standard logic and a full system of modal and temporal logic emanating from a modicum of primitives, should not only enable one to appreciate the sophisticated philosophizing which characterized (...) this ancient debate, but should prove to be quite useful in application to contemporary issues. (shrink)