Time and Necessity: Aristotle’s “Sea-Battle”



Time and Necessity: Aristotle’s “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 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 (this is called the “law of the excluded middle”). In the course of his discussion, Aristotle allows for some exceptions. Consider these two propositions:

1.    There will be a sea-battle tomorrow

2.    There will not be a sea-battle tomorrow

According to the Law of the Excluded Middle, it seems that exactly one of these must be true and the other false.

Law of Excluded Middle:

P or ~P is always true, where P is a meaningful statement (which means that one or the other is true, but not both).

So -- 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. If it was true 10,000 years ago that there would be a sea-battle tomorrow, 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. Thus it is necessarily true that there will be a sea-battle tomorrow.

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. Aristotle’s ethical views, for one, rely on the claim that we can deliberate about what is possible, and certain agents are good or bad (if they do X, for example) because they had the power to deliberate (between choices X and Y), and thus freely chose what they actually did do (X). If, however, "what is past is necessary" and the statement “there will be a sea-battle tomorrow” was true 10,000 years ago, then it is a fact about the past and thus necessary. Obviously this conclusion Aristotle finds threatening because he believes that we do not deliberate about what is necessary. For instance, we do not deliberate about mathematical truths or the celestial motions. This is the case because what is "necessary" is inevitable or beyond our power to affect: mathematical truths, celestial motions and the past all cannot be changed by our efforts, and thus are all necessary. This explains both the plausibility of the premises-the past certainly seems beyond our power to affect-and the unacceptability of the conclusion-if all future events are necessary, then they are all beyond our power to effect, rendering deliberation pointless. )

Thus, if statements about the future are governed by the law of the excluded middle, the possibility of free will and ethics are annihilated.

So Aristotle rejects that the truth value of a future statement is governed by the general thesis concerning the Law of the Excluded Middle. Statements about the future are neither true nor false.  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.

Here is the argument Aristotle is worried about:

(i) The Determinist Argument Let 'p' stand for some future-tensed statement, such as 'There will be a sea-battle tomorrow.'

1.    All past truths are necessary truths. (assumption)

2.    An impossibility does not follow from a possibility (assumption)

3.    If something is now, or will be, true, then in the past it was already true that it was going to be true, and likewise for false statements. (assumption)

In order to show that, if something is not going to be the case, then it is not a possibility, first, assume not-p, and show that not-possible p follows.

4.    Not-p. (Assumption for conditional proof)

5.    In the past, "It will be the case that not-p" was true. (From 3 and 4)

6.    In the past, "It will be the case that not-p" was necessarily true. (From 1 and 5)

7.    Therefore, in the past, "It will be the case that p" was impossible. (From 6)

8.    If p, then in the past, "It will be the case that p" was true. (From 3)

9.    Therefore, not-possible p. (From 2, 7, 8)

10.    Therefore, if not-p, then not-possible p. (From 4, 9, conditional proof)

Even more informal version: If something will not be the case-for instance, there will not be a sea-battle tomorrow-then the supposition that it will be the case is not merely false, it is impossible. For if the battle will not be fought (step 4), then it was also true in the past that it would not be fought (5), because true statements about what will be the case were also true in the past (3). And since all past truths are necessary truths (1), in the past that the battle will not be fought was necessarily true (6), and thus that it will be fought necessarily false (7). From the supposition that it would be fought, it follows that in the past it would also be true that it would be fought (8). But since this is impossible (7), and since an impossibility does not follow from a possibility (2), that the battle will be fought is not possible (9). Thus, if something will not be the case, it is not possible for it to be the case. (10)

(handout borrowed from a few sources including the Stanford Encyclopedia and Prof. Keefe at University of Minnesota)

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