- Oct 27 8:20 PM
[The return of the positivist]
I don't think that the analytic-synthetic distinction's too relevant any more. The trouble is that mathematics cannot be captured by neither platonism nor formalism, that many mathematicians like so much. The true answer is through physicalism of course.
I think that computation is the golden standard of mathematics. That is because if mathematics is a science, it is the science of thinking, and thinking is MADE UP OF COMPUTATION. That is to say, the mathematics that lies beyond computer science (i.e. graphs with uncountably many edges) isn't science. It's a pretty harsh statement, given how many academic mathematicians make a living out of, what is essentially the empty set.
Let me say it again, mathematics always involves a kind of reasoning, a form of reasoning that is better and more precise than common sense. And as such that WAY OF THINKING underlies all science.
That is not an UNCANNY COINCIDENCE or anything like that. It happens precisely because the abstract representations in mathematics have proven themselves useful, that they exist at all. Therefore, if one "liberates" mathematics by turning it into an art form, one essentially makes an assault on the entirety of science, of which mathematics is a mostly reliable foundation.
That is to say, mathematical statements gain their meaning only by way of a computational interpretation. When such interpretation is absent, mathematics is nonsense.
Mathematics is just general purpose computations (i.e., an axionatic system of geometry).
Computer science is identical to mathematics.
Universal induction can answer any valid mathematical question.
Halting problem essentially encompasses the entirety of mathematical thought. Of which there is an infinite variety, only limited by computational resources.
Full empiricism explains mathematics: it is just experiments on computer devices. It fully reduces to the physical science of computers.
A set is just an ordered list of bitstrings.
These are the scientific facts we know as they follow from the plain and obvious fact that the brain is a computer. In summary, computational neuroscience proves Godel's silly spiritual philosophy wrong. (I dont even mention how irrelevant quine and putnam are to science of nathematics)
Eray Ozkural, PhD
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