theory of inference, by which we may attain knowledge of what is unclear.
The Stoic theory of inference - Stoic logic in the narrow sense of the term-rests upon a detailed theory of
language. It begins with the conception of an axioma or proposition, 'something which in itself denies or
asserts something - e.g. "It is day", "Dion is walking" '. Propositions are either simple or non-simple, the
non-simple being 'those consisting of a repeated proposition or of several propositions' joined by a
connecting particle. (Stoic theory concentrated on three connectives: 'if, 'and', 'or'.) An argument is 'a
system of premises and a conclusion', where premises and conclusion are all propositions, simple or
complex.
Like Aristotle, the Stoics recognized that a logician's business is with forms of argument rather than with
particular inferences; and like Aristotle they achieved the generality which the business requires by the
use of schemata. Again like Aristotle, the Stoics were systematic: 'there are certain arguments which are
non-demonstrable (for they do not need to be demonstrated)' - Chrysippus lists five such arguments,
others list others; and every argument is constructed by way of those. The five 'indemonstrables' play in
the Stoic system the part played in Aristotle's syllogistic by 'perfect' syllogisms: they are basic, and other
argument forms are derivable from them.
In content, Stoic logic is very different from Peripatetic. It corresponds roughly to what modern logicians
call propositional or sentential logic. The foundation of Chrysippus' system consists of the following
argument-schemata, the five indemonstrables: (1) If 1, then 2; but 1: therefore, 2. (ii) If 1, then 2; but not
2: therefore, not 1. (iii) Not both 1 and 2; but 1: therefore, not 2. (iv) Either 1 or 2; but 1: therefore, not 2.
(v) Either 1 or 2; but not 1: therefore, 2. The logic which Chrysippus erected on that modest base was
powerful and sophisticated.
Logic is the servant of knowledge, and its service consists in the provision and ratification of proofs. Not
all arguments are proofs. Rather, 'a proof is an argument which, by way of agreed premises, reveals by
deduction an unclear conclusion'. The notion of 'revelation' - of uncovering or explaining - is crucial to the
closely connected concept of a 'sign'. The world is full of signs - clouds signify future rain, scars are signs
of past wounds - and signs are appropriately expressed by way of conditional propositions; indeed, a sign
was loosely described as 'an antecedent proposition in a sound conditional which reveals the consequent'.
Consider, then, a standard example of a proof: 'If sweat permeates the skin, the skin has imperceptible
pores; but sweat permeates the skin: therefore the skin has imperceptible pores.' The argument has the
form of the first indemonstrable; both its premises are true or 'agreed'; its conditional premiss expresses
the fact that perspiration is a sign of perforation; its conclusion is 'unclear' (the pores are not available to
direct inspection). Thus by virtue of inference we advance from evident facts to a knowledge of what is
unclear.
'Many people believe that if the gods studied logic it would be the logic of Chrysippus.' The Epicureans
dissented - indeed, 'they reject dialectic as redundant' and they preferred to call the third part of
philosophy 'canonics' or the theory of judgement. But they still required some account of how we might
come to know 'unclear' facts. The later Epicureans, whose arguments are preserved in Philodemus' treatise
On Signs, disputed the Stoic theory of signs and substituted an account of their own. Epicurus himself