time and necessity: the sea-battle

The passage in Aristotle’s logical works which has received perhaps the most intense discussion in recent decades is On Interpretation 9, where Aristotle discusses the question whether every proposition about the future must be either true or false.

Though something of a side issue in its context, the passage raises a problem of great importance to Aristotle’s near contemporaries (and perhaps contemporaries).

A contradiction (antiphasis) is a pair of propositions one of which asserts what the other denies.

A major goal of On Interpretation is to discuss the thesis that, of every such contradiction, one member must be true and the other false.

In the course of his discussion, Aristotle allows for some exceptions.

One case is what he calls indefinite propositions such as “A man is walking”:

– nothing prevents both this proposition and “A man is not walking” being simultaneously true.

This exception can be explained on relatively simple grounds.

A different exception arises for more complex reasons.

Consider these two propositions:

– There will be a sea-battle tomorrow
– There will not be a sea-battle tomorrow

It seems that exactly one of these must be true and the other false.

But if (1) is now true, then there must be a sea-battle tomorrow, and there cannot fail to be a sea-battle tomorrow.

The result, according to this puzzle, is that nothing is possible except what actually happens: there are no unactualized possibilities.

Such a conclusion is, as Aristotle is quick to note, a problem both for his own metaphysical views about potentialities and for the commonsense notion that some things are up to us.

He therefore proposes another exception to the general thesis concerning contradictory pairs.

This much would probably be accepted by most interpreters.

What the restriction is, however, and just what motivates it are matters of wide disagreement.

It has been proposed, for instance, that Aristotle adopted, or at least flirted with, a three-valued logic for future propositions, or that he countenanced truth-value gaps, or that his solution includes still more abstruse reasoning.

The literature is much too complex to summarize: see Anscombe, Hintikka, D. Frede, Whitaker, Waterlow.

Historically, at least, it is likely that Aristotle is responding to an argument originating in the Megarian School.

He ascribes the view that only that which happens is possible to the Megarians in Metaphysics IX (Θ).

The puzzle with which he is concerned strongly recalls the “Master Argument” of Diodorus Cronus, especially in certain further details.

For instance, Aristotle imagines the statement about tomorrow’s sea battle having been uttered ten thousand years ago.

If it was true, then its truth was a fact about the past; if the past is now unchangeable, then so is the truth value of that past utterance.

This recalls the Master Argument’s premise that “what is past is necessary”.

Diodorus Cronus was active a little after Aristotle, and he was a Megarian (see Dorion 1995 for criticism of David Sedley’s attempt to reject this).

It seems to me reasonable to conclude that Aristotle’s target here is some Megarian argument, perhaps an earlier version of the Master.

via: http://plato.stanford.edu/archives/spr2012/entries/aristotle-logic/

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