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Could there be a universe where the concept of order and logic and numbers and objects and space and time don't exist ? This would preclude math as we know it. Maybe there is something better than math in other universes where the concept of an object does not exist but other things exist that we cannot fathom in our universe because it is impossible to even imagine.

referring to simple math , like arithmetic. A universe where counting does not exist. You can't count objects. Numbers have no meaning. Space and time have no meaning and there is something else in its place. A place where logic does not exist. I don't have the answer, I am just trying to clarify. Why would some kind of mathematics be inevitable? There could be ways a universe could exist without math.

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    "A universe where counting does not exist. " What does it mean ? Counting is a human activity: no humans, no counting. We count stones: stones do not count themselves. May 25, 2020 at 9:54
  • But if there are no objects, no stones either, so nobody can count them. May 25, 2020 at 9:55
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    There's a mereological argument to be made that objects don't exist objectively, but how we construct meaning. See possible objects.
    – J D
    May 26, 2020 at 16:44
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    Certainly. Any universe without living beings would be such a universe.
    – polcott
    May 30, 2020 at 16:22
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    What does 'exist' mean? You have to question, who could experience such a domain. The Anthropic Principle points to how places with subjectivities could meaningfully constrain what we can be called real, from what is possible.
    – CriglCragl
    Aug 8, 2022 at 20:57

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Short Answer

It depends on the nature of 'could'. How do we know anything could be? This is a central preoccupation in the epistemology of modality. Modality is the study of necessity and contingency in the truth of propositions, and is related to metaphysical presuppositions related to possible world semantics.

Long Answer

Ever since the linguistic turn, it is customary in philosophy to heartily appraise the use of language in a proposition or interrogative for possible insight into the question. In this case, before answering truthfully the question:

Could there be a universe where the concept of order and logic and numbers and objects and space and time don't exist?

one must simply understand ideas like possibility, concept, universe, and existence. This task requires committing to value-laden propositions of both epistemological and ontological sorts. Congratulations, and welcome to metaphysics!

Let's start with the obvious one. When you say possible world, do you mean an actual physical plane of existence? Or are you more like me who views a possible world as a data structure laden with variables, a mere potential representation of a thing-in-itself? The first position which was championed by David Lewis in his On the Plurality of Worlds, and the latter is more inline with Kripke's views. There are many people who accept the many-worlds interpretation, that there is no collapse of a waveform, but rather there are infinitely many physical worlds. What about the basis for determining possibility? How does one decide what is possible and what is not? Do you prefer modal realism to modal rationalism? And then there are questions of existence (the astute reader will see the existential declaration!). What are your views on ontology and meta-ontology? Quine? Carnap? Meinong?

Until you examine your own ontological commitment and other metaphysical presuppositions, it will be mighty difficult for you to embrace a position on this question.

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It depends on ontology of reality. According to physicist Max Tegmark, all universes (all that "exists") are mathematical objects. This can be simplified to claim, I think, that only integer set of numbers exists "by itself", for reason we cannot fathom, and it is impossible to "remove" it from existence or conceive reality without it (reality where integer numbers don't exist).

Every universe is some projection (function) on the integer set. Our universe (or quantum-mutliverse) is therefore mathematical function, which projects integer set to multidimensional object, that we experience as 3+1 dimensional space and time.

We can understand it in a way, that number set have no "preferred" way of looking at it. Every projection of it (any function on it) is equally existent, all of those are just different ways of looking at one thing that really exists: set of integer numbers. So, universes are like optical lenses we use, to see reality. And such a lens can be so special, that it can create emergent space* and time.

  • Well, space is not a problem, any mathematical function creates some sort of space. What is special about "our" function and our universe is, that it creates one dimension of time, arrow of time, which means that information in such function can travel only in one direction of this dimension (past -> future). For all we know, intelligent life is only conceivable at 3 dimensions of space and 1 dimension of time.
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Despite their poetic qualities, such uses of words as, "What if there was a universe with no logic?" seem to betray themselves by failing to reflect on what "if there was" is itself supposed to mean. Since normal logic includes an implicit theory of quantifiers and it is quantification that is assimilated to/over the concept of existence, asking if there was a universe without any logic could be to ask if there was a (as in at least one) universe without quantification at least in terms of the number 1.

So note also that prefix uni-: if this "other universe" cannot quantify over its contents, much less itself, as if it were "one universe," what sense would it make to talk about this universe being fully separate from or causally contiguous with ours? How can a universe be individuated without the concept of individuation?

Now Kant straddled the fence a lot, on this point. He accepted that the logical forms of judgment were not entirely localized in applicability, and would in some vague sense hold for objects of intellectual intuition. However, he does also float the abstract question of other forms of sensible (i.e. passive) intuition than space or time, and understanding/cognition without discursive conceptions. On top of all that, at one point he just claims that overly transcendent questions are basically meaningless, as if asking them is not to ask anything real at all. (A word of caution: those are paraphrases of an unsatisfactory (or not completely satsifactory) translation of Kant's. I say what I say and link to what I link to in good faith, but with an admission of tangential weakness in the presentation.)

Or consider Descartes' vexing/seeming claim that God could have created different eternal truths than He did. Maybe it's less that the law of non-contradiction could have been violated, and more that a world could have been created without enough propositional structure to maintain the purpose or significance of such a law; or no less that it could have been created with some other structure of greater significance. I think there's inescapable pushback, here, from the side of logical quantifiers, but it might not be the same problem (a logic without quantities of existence seems as if it would not itself exist (if, "Logic exists," is even much of a worthwhile statement), but a logic without non-contradiction is not as obviously pointless to imagine).

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Mathematics is about neccessary truths at a very basic level. Whilst another universe could be very different, it will undoubtably have truths that are neccessary, just not the necessary truths of our universe. And hence it will have mathematics but which would not be recognised as mathematics from this universe.

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I totally believe there are universes out there with totally alien concepts we cant imagine in our universe. They may contain something entirely different than what we have like for example in our universe we have stars, galaxys, black holes, spacetime, etc it could be other universes have none of those features but something completely different and inconceivable to us. I ll even go as far as saying that there could be universes where lifeforms arent based on any physic, chemistry, particles but something unknown and wholly alien, things we dont have in our universe

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  • Welcome! Some friendly feedback on your answer to help you understand why it was downvoted. Here, you state a belief, but it would be more helpful and more in keeping with the goals of this site if you provided philosophical arguments that support the answer you give. Ideally, give some references to the philosophical literature so that people who are interested can pursue the inquiry further on their own by reading those sources.
    – Avi C
    Aug 10, 2022 at 18:25

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