He was most notable for logic innovations, including his master argument formulated in response to
Aristotle's discussion of
future contingents.
Diogenes Laërtius says that Diodorus also made use of the
Sorites paradox, and is said to have invented two others of the same kind, viz.
The Masked Man and
The Horns, which are, however, also ascribed to
Eubulides. Aulus Gellius claims that he also rejected the view that words are ambiguous, any uncertainty in understanding was always due to speakers expressing themselves obscurely. According to Sextus Empiricus, he also maintained that space was indivisible, and consequently that motion was impossible. He further denied the coming into existence and all multiplicity both in time and in space; but he considered the things that fill up space as one whole composed of an infinite number of indivisible particles.
Master argument Aristotle, in his work
On Interpretation, had wrestled with the
problem of future contingents. In particular, whether one can meaningfully regard future
contingents as true or false now, if the future is open; and, if so: how?
Alexander of Aphrodisias tells us that Diodorus believed that that alone is possible which either is happening now, or will happen at some future time. When speaking about facts of an unrecorded past, we know that a given fact either occurred, or did not occur—without knowing which of the two is true; therefore, we affirm only that the fact
may have occurred. So too about the future: either the assertion that a given fact will—at some time—occur, or else the assertion that it will
never occur, is positively true; the assertion that it
may or may not occur, at some time or another, represents only our ignorance as to which of the two is true. or
ruling argument ( /
ho kurieuôn logos). The most succinct description of it is provided by
Epictetus: The argument called the master argument appears to have been proposed from such principles as these: there is in fact a common contradiction between one another in these three propositions, each two being in contradiction to the third. The propositions are: (1) every past truth must be necessary; (2) that an impossibility does not follow a possibility; (3) something is possible which neither is nor will be true. Diodorus observing this contradiction employed the probative force of the first two for the demonstration of this proposition: That nothing is possible which is not true and never will be. Epictetus' description of the master argument is not in the form as it would have been presented by Diodorus, which makes it difficult to know the precise nature of his argument. To modern logicians, it is not obvious why these three premises are inconsistent, or why the first two should lead to the rejection of the third. Modern interpretations therefore assume that there must have been extra premises in the argument tacitly assumed by Diodorus and his contemporaries. One possible reconstruction is as follows: For Diodorus, if a future event is not going to happen, then it was true in the past that it would not happen. Since every past truth is necessary (proposition 1), it was necessary that in the past it would not happen. Since the impossible cannot follow from the possible (proposition 2), it must have always been impossible for the event to occur. Therefore if something will not be true, it will never be possible for it to be true, and thus proposition 3 is shown to be false. Epictetus goes on to point out that
Panthoides,
Cleanthes, and
Antipater of Tarsus made use of the second and third proposition to demonstrate that the first proposition was false.
Chrysippus, on the other hand, agreed with Diodorus that everything true as an event in the past is necessary, but attacked Diodorus' view that the possible must be either what is true or what will be true. He thus made use of the first and third proposition to demonstrate that the second proposition was false. ==Nom de plume==