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I have just read about Aristotle's Three Laws of Logic. I was wondering if statements such as "There is a chance of it raining in the next hour" can be evaluated using the three laws. Can you apply the three laws to statements about the future?

The problem I see is if you say "There is a chance of it raining in the next hour". You can say that is true because no matter how unlikely, there can still be a chance.

If we wait an hour and it hasn't rained, how do we know that "not raining" wasn't actually a pre-defined state of the universe we were yet to experience?

If that is the case, as we cannot predict the future perfectly, would it mean that it is meaningless to apply these laws to statements about the future?

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  • According to the traditional interpretation, the law of excluded middle (or the bivalence, more precisely) does not apply, see the problem of future contingents. He made this exception exactly to avoid the logical fatalism (predestined future). There is no issue with identity and non-contradiction. And there are ways to use more complex (modal, temporal) logics to resolve this issue while keeping even the law of excluded middle. – Conifold Sep 30 '19 at 17:49
  • As Conifold notes future events cause complications.for the LEM. But if we examine predictions for the future they do not usually obey the rules for contradictory pairs, and where they do not no complications arise. Can you find a statement about the future that requires a modification to A's laws? If you can it would be helpful to post it since your example is straightforward and raises no problems. . – user20253 Oct 1 '19 at 11:36
  • cf. temporal logic and the works of A. N. Prior – Geremia Oct 2 '19 at 19:10
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According to Andrea Iacona Aristotle in Chapter 9 of On Interpretations believed that the disjunction of a proposition about the future or its negation was true, but the individual disjuncts were neither true nor false. Consider these two statements:

(1) There will be a sea battle tomorrow.

(2) There will not be a sea battle tomorrow.

Neither of these are necessarily true nor impossible.

For Aristotle, the claim that (1) and (2) are neither true nor false is consistent with the plausible assumption that the disjunction formed by (1) and (2) is true:

(3) Either there will be a sea battle tomorrow or there will not.

Aristotle seems to think that (3) expresses a necessary truth, although the same does not hold for (1) and (2) taken separately...

This maintains the law of the excluded middle for the disjunction (3), but rejects the principle of bivalence for the individual disjuncts, (1) and (2). Neither of them are either true or false.

However, as Iacona points out this leads to further problems with three options:

  1. Neither bivalence nor excluded middle.
  2. Excluded middle without bivalence. This is the position Aristotle appears to favor.
  3. Both bivalence and excluded middle (but apparently without fatalism).

Andrea Iacona. Future Congingents. Retrieved from the Internet Encyclopedia of Philosophy at https://www.iep.utm.edu/fut-cont/

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  • Thank you very much for this extremely well-formed answer. I will do further research into the resources you have mentioned! :) – Hiren Sep 30 '19 at 21:55
  • I'd just note that the principle of bivalence is not necessary for A's logic. Where two statements do not exhaust the possibilities none of the laws apply. The PB is rendered redundant by the Rule for Contradictory Pairs (RCP). Thus there is never a need to abandon the LEM. I am not aware that Aristotle endorsed the PB. He states only that for his laws to apply to two statements they must obey it. I ay this because it deals with almost all the complication that arises on this issue. . – user20253 Oct 1 '19 at 11:44
  • @PeterJ What you are saying is similar to what Iacona presents in her article. One can have the LEM (P v ~P) be true without either P or ~P having a truth value. I agree that PB is not necessary for Aristotle's logic, however, Iacona then proceeds to try to show one can derive it from LEM by considering both disjuncts even though Aristotle is not considering them as either true or false. I don't think that works because it basically accepts PB to show PB. – Frank Hubeny Oct 1 '19 at 12:12
  • What you say seems very relevant and maybe it's a similar point. But unless one of A/not A is true and one false then the LEM will not apply. For pairs of future conditionals it seems clear that neither is true or false, I've always wondered why Aristotle called these cases 'exceptions' rather than just situations in which the rules should not be applied. – user20253 Oct 1 '19 at 12:50
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There isn't any difficulty with the truth or falsehood of statements about future events.

Consider the two following statements:

(1) There will be a sea battle tomorrow.

(2) There will not be a sea battle tomorrow.

Each of these statements is either true or false. If one is true, then the other is false.

Obviously, we don't know the future, but this is absolutely irrelevant. Most of the time, we also don't know the past. A statement claiming that an event took place is either true of false, and this irrespective of whether we happen to know whether it is true or whether it is false.

Consider the two following statements:

(1) There was a sea battle in 527 BC.

(2) There was not a sea battle in 527 BC.

Again, if our notion of truth is to mean anything, either there was or there was not a sea battle in 527 BC.

If there was, then the first statement is true and the second one is false. If there was not, then the first statement is false and the second one is true.

We don't seem to know of any sea battle taking place in 527 BC, but this is effectively irrelevant because there is a clear distinction between the idea that statements are either true or false, and the idea that we may know and not know whether a statement is true or false. The two notions are semantically independent.

However, there is a logical relation: The fact that anyone knows a statement to be true implies that it is true. The fact that anyone knows a statement to be false implies that it is false.

However, and crucially here, the fact that we don't know whether a statement is true or false doesn't imply anything as to whether it is in fact true or false.

We may even do good logic with statements about the future. For example:

The statement "I know that there will be a sea battle tomorrow" logically implies the statement "There will be a sea battle tomorrow".

This implication is crucial to the meaningfulness of the notion of omniscience.

Using transposition, we can also infer the following:

The falsity of statement "There will be a sea battle tomorrow" logically implies the falsity of the statement "I know that there will be a sea battle tomorrow".

The fact, usually recognised as true, that we cannot know the future, is enough of itself to explain that we don't know today whether the statement "There will be a sea battle tomorrow" is true or not.

There is nothing special in this respect about the future. What applies in this respect to the future, also applies to the whole of reality. That is, we may conceive of statements, and we often do, without knowing whether they are true or false. This applies to the future, to the past, or indeed to the present. My next door neighbour is talking to his daughter on the phone. It may well be true, and it may equally be false. I don't know. But the statement is either true or false. Exactly as it would if it was about a future event instead of being about the present.

And if the above is somehow erroneous, then it should be easy to exhibit a counterexample.

As to Aristotle, we shouldn't believe what people claim as to what his views were unless they provide a quote and a link so that we can make sure the claim is at least plausible.

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  • How do we know that each statement like P it must be either true XOR false? Law of excluded middle and law of non-contradiction relate the truth value of a statement and its negation but don't explicitly state that P has exactly one truth value. – ado sar Sep 17 '20 at 15:50
  • @adosar Sorry, not in the scope of this question or of my answer. It would require a long discussion. The short answer is that deductive logique does not work with statements with several truth values. I also don't know what that would mean. It is for people who want to explore the metaphysics of logic to propose understandable concepts. Logic is a fact of life, not a mathematician's dream. You can only describe how logic works. If you don't, then it is not logic and talking as if it was is just equivocation, of which there is plenty about. – Speakpigeon Sep 17 '20 at 17:01

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