Time, Necessity, and Ability

1. The Master Argument I will discuss the so-called “Master Argument” attributed to Diodorus Cronos in the light of some contemporary speculations on indexicals. In one version, this argument goes as follows: Premise 1. The past, relative to any time t, is necessary. Premise 2. The impossible cannot follow from the possible. Therefore, Conclusion. The possible is that which either is or will be (thus, what will not be is impossible). It is widely recognized that something else is required to deduce the conclusion from the two premises. There are a variety of proposals, but the underlying idea seems to be that the past in some way determines the present and future, that is, Premise 3. Whatever is or will be follows from what is past. Accordingly, if what is or will be follows from the past, then, by Premise 1, it follows from what is necessary. Then, by premise 2, it must itself be necessary. Since a proposition, state-of-affairs, or, as I shall speak, a situation, is necessary only if its opposite is impossible, then nothing other than what does happen or will happen can happen. Nothing depends on the use of tense in Premise 3 and the conclusion of this argument. Both can easily be recast tenselessly in terms of a generalization over any time t. That is, Premise 3 is: whatever exists at a time t or comes after t follows from what comes before t. The conclusion is: the possible is that which either obtains (is true) at t or obtains (is true) after t (thus, what does not obtain at t or after t is impossible).