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OPINION - On the axiom of choice

I find it distasteful that non-mathematicians think that Gödel's work introduces a level of subjectivity to mathematics. I agree that one can construct an arbitrary number of mathematical universes via selecting an arbitrary set of axioms. But I disagree that they are somehow all equivalent in value or structural consistency. I personally believe that there is one mathematical universe (or category of universes that are structurally equivalent via something like an isomorphism) that has the most structural consistency and can give the human mind the most insight. I personally believe that there are axioms that are representations of structural properties of physical reality. And I believe that there is a set of axioms that aligns perfectly with the physical universe, and subsequently allows the human mind to comprehend its logic to the fullest extent. I believe this because the way that the human mind understands logic is already a consequence of physical reality. Our ability to understand the simplest mathematical mechanisms (such as addition and multiplication) are enabled via physical mechanisms (such as neurons in the brain). And I suppose the real question is whether or not there is something universal to pattern recognition and the dissection and assembly of information. If we could create a brand new universe and watch evolution start over again, would mathematical understanding emerge the same way? Would the types of intelligence that life produces always produce the same axiomatic window to understand mathematics? I am inclined to believe that it would. I cannot prove this, but I feel that it is likely true because nature filters for effectiveness and efficiency. I think pattern recognition abstracts itself via evolution, and each time it abstracts itself, it gains a higher vantage point. And the process of abstraction always generalizes such that the common things are held constant. An organism that can form a linear causal timeline to understand its environment has a massive advantage over an organism that can only form an associative correlative timeline if the organisms can easily manipulate their environment. I suspect that an organism that can form an associative correlative timeline has a massive advantage over an organism that can form a linear causal timeline if the organisms cannot easily manipulate their environment. I also suspect the same arguments could hold for when an environment is ordered (and can be linearly parsed) and when an environment is chaotic (and cannot easily be parsed). I suspect the emergence of capabilities that allow a species to manipulate its environment inevitably leads to the emergence of the capability to understand linear logic. And I suspect the greater the degree of manipulation, the more perfect the logic becomes. 

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