Philo disputed with Diodorus respecting the idea of the
possible and the criteria of the truth of
conditional statements. In regards to things possible, Diodorus maintained that possible was identical with necessary, i.e. that possible is "that which either is or will be true". Philo instead defined possible as "that which is capable of being true by the proposition's own nature", Both Philo and Diodorus sought for criteria for the correct form of conditional propositions, and each of them did so in a manner corresponding to what he maintained respecting the idea of the possible. Philo regarded a conditional as true unless it has both a true
antecedent and a false
consequent. Precisely, let
T0 and
T1 be true statements, and let
F0 and
F1 be false statements; then, according to Philo, each of the following conditionals is a true statement, because it is not the case that the consequent is false while the antecedent is true (it is not the case that a false statement is asserted to follow from a true statement): • If
T0, then
T1 • If
F0, then
T0 • If
F0, then
F1 The following conditional does not meet this requirement, and is therefore a false statement according to Philo: • If
T0, then
F0 Indeed,
Sextus says "According to [Philo], there are three ways in which a conditional may be true, and one in which it may be false." Philo's criterion of truth is what would now be called a
truth-functional definition of "if ... then"; it is the definition used in
modern logic. In contrast, Diodorus allowed the validity of conditionals only when the antecedent clause could never lead to an untrue conclusion. A century later, the
Stoic philosopher
Chrysippus attacked the assumptions of both Philo and Diodorus. ==References==