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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 '20 at 9:54
  • But if there are no objects, no stones either, so nobody can count them. May 25 '20 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 '20 at 16:44
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    Certainly. Any universe without living beings would be such a universe.
    – polcott
    May 30 '20 at 16:22
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Logic and mathematics are theories just like contemporary physics is a theory. These theories postulate the existence of objects like sets and numbers and the truth of propositions like the modus ponens and the axiom of extensionality.

To a holistic empiricist, the value of these theories and hence the evidence for the truth of the propositions as well as the ontological status of the objects hinges on the empirical capability of (the web of) these theories.

The better these theories enable us to make predictions into the future that come 
true, the better established are propositinos and objects.

Easy to see that objects we currently believe to exist as well as propositions we currently hold true -- even logical and mathematical ones -- can be swept away by a better theory.

There need not be a different universe, to come back to your question, just better theories in our universe. So to speak.

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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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