Logic

The Stoics developed a logic different from Aristotle's, and to a large extent independently from him. Their greatest logician, Chrysippus, lived from about 280 to 206 B.C.E. and, as with most of the Stoics, his thought has mostly to be reconstructed from reports and fragments in later writers. Whereas Aristotelian syllogistic is a term-logic, Stoic logic was propositional: it explored the relations between what they called "assertibles"—that is to say, sentences that can be used to make assertions. Assertibles can be simple ("It is day") or complex ("If it is day, it is light"/ "It is day or it is not light"). The argument forms classified by the Stoics involve one complex and one simple assertible: for example, "If it is day, it is light. It is day. So, it is light." This is the first of five "indemonstrables"—basic argument forms—distinguished by Chrysippus. The Stoics had a schematic way of representing the indemonstrables—what they called their "modes"—using ordinal numbers. The four remaining modes of the five indemonstrables are (2) If the first, then the second; not the second; so not the first; (3) Not both the first and the second; the first; so not the second; (4) Either the first or the second; the first; so not the second; (5) Either the first or the second; not the first; so the second. Since the assertibles could be either negative or positive, and the complex assertible could itself include complex assertibles ("If both the first and the second, then the third"), there was quite a wide range of indemonstrable argument schemes. But Stoic logic was not limited to them. Nonindemonstrable forms of argument could be valid, and the Stoics had a theory of "analysis" in which, using certain basic rules (themata) and, if wanted, additional theorems, the nonindemonstrable arguments were shown to be made up of demonstrable ones or of conversions of them.

Stoic logicians also explored modal concepts. One of their main starting points was provided by the fourth-century B.C.E. Megaric logician Diodorus Cronus, who formulated a "Master Argument," the subject of many attempts at reconstruction by modern historians, which attempts to show that, from the premises that true past propositions are necessary, and that an impossibility never follows from what is possible, it follows that nothing is possible except what is or will be true. The Stoic logicians rejected the argument by querying one or other of its premises, and Chrysippus developed his own understanding of possibility and necessity.