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In my previous question, here: Can truths about the natural numbers vary across possible worlds?, I started off by saying that "The truths of logic are the same in all possible worlds". But is that really the case? Can there be possible worlds where there are different laws of logic? So, for instance, in the world we live in, classical logic is true, but in some other world, intuitionistic logic is true, and in yet another world, quantum logic is true. Also, have any philosophers written about this issue?

user107952
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    If logic is about inferences, then wouldn't this be like saying that reasoners in a different world could be given "the same" premises as our world, and yet infer different things therefrom, and this according to some higher standard of "evidence"? I'm not saying that that's impossible, but it's possible in our own world already, so... – Kristian Berry Sep 22 '22 at 03:17
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    What do you mean by "logic"? It must be clear to you that the laws of different logics vary in just our world alone, so do you accept that these different logics constitute "logic"? Otherwise, what is your question? – emesupap Sep 22 '22 at 03:43
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    There are different types of logic. There is no LOGIC by itself. There is Aristotelian logic, Fuzzy logic, Mathematical logic and etc. You are directly speaking o. Mathematical logic. There are issues with it. For example how do emptysets apply to the real world? Can one place the empty set of unicorns on the table? How would that be applied to reality? So the question is to vague. – Logikal Sep 22 '22 at 03:44
  • Your question is similar to other questions posed by scientists and philosophers: Are the laws of physics, chemistry, etc the same in every part of the universe for the life of the universe?

    The answer is usually "Yes, until evidence shows otherwise"

     –  Sep 22 '22 at 16:22
  • Not on the standard conception. Moreover, it is not merely that they are true "in" all possible worlds like other necessary truths, they are presupposed to make sense of possible worlds to begin with, see Forster, Modal Aether:"It could be characterised as that part of our theory of nature that remains when all information internal to possible worlds is ignored altogether, rather in the way in which the geometry of space-time is what remains once we expunge events. Let us call it the machinery." – Conifold Sep 23 '22 at 05:02
  • However, one can set up systems of possible worlds based on different logics, and even allow worlds with logic violations, see SEP, Impossible Worlds – Conifold Sep 23 '22 at 05:10
  • Logic might just be a thing we came up with with our laws of logic, so even if it was different logic might not have a meaning – 4117 Sep 23 '22 at 20:32

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No. They absolutely can't. But they may or may not apply.

The reason I feel confident saying this is because any given logic is a set of axioms and some inference rules around how to apply them. If you change either the axioms or the inference rules, you have a new logic.

I think the question you are really asking might be: can there be a possible universe in which classical logic is not useful as a thinking tool? For example, is there a universe in which the law of identity is never a useful abstraction, because nothing is itself? I find that difficult to imagine, but my imagination is limited and I learned to think in a universe where identity is a useful abstraction.

philosodad
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  • What of the set of all worlds, It contains every logical derivation, akin to the principle of explosion? – J Kusin Sep 22 '22 at 17:27
  • @JKusin I do not understand your comment. – philosodad Sep 22 '22 at 19:56
  • The law of identity does not apply to any object in our world. “A man never steps in the same river twice”. – Dcleve Sep 23 '22 at 02:42
  • You can have logic without the law of identity, though it is pretty weird. But I think you are right to say that this is really a question of whether logics have useful application, not whether the logics themselves vary from one place to another. – Bumble Sep 23 '22 at 04:12
  • @Dcleve sure... but something changing doesn't change identity. It is what it is, even if it isn't what it was. – philosodad Sep 23 '22 at 13:56
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Classical logic is not “true” in our world. We know this because classical logic is two state (true/false), but for for most questions we need at least 3 state logic (t/f/unknown) and for empiricism we need four state (t/f/u/nonsense).

So, logic in our world is pluralistic. There are an infinity of logics. And some approximate some aspects of our physical world fairly well, while others are needed for different aspects of it. So, we already are a Universe with the features you asked about.

Dcleve
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