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I revisit my earlier arguments for the (trivial) inconsistency of natural languages, and take up the objection that no such argument can be established on the basis of surface usage. I respond with the evidential centrality of surface usage: the ways it can and can't be undercut by linguistic science. Then some important ramifications of having an inconsistent natural language are explored: (1) the temptation to engage in illegitimate reductio reasoning, (2) the breakdown of the knowledge idiom (because its facticity (...) |
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I revisit my earlier arguments for the (trivial) inconsistency of natural languages, and take up the objection that no such argument can be established on the basis of surface usage. I respond with the evidential centrality of surface usage: the ways it can and can't be undercut by linguistic science. Then some important ramifications of having an inconsistent natural language are explored: (1) the temptation to engage in illegitimate reductio reasoning, (2) the breakdown of the knowledge idiom (because its facticity (...) |
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I argue that a recent version of the doctrine of mathematical naturalism faces difficulties arising in connection with Wigner's old puzzle about the applicability of mathematics to natural science. I discuss the strategies to solve the puzzle and I show that they may not be available to the naturalist. |
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I discuss the applicability of mathematics via a detailed case study involving a family of mathematical concepts known as ‘fractional derivatives.’ Certain formulations of the mystery of applied mathematics would lead one to believe that there ought to be a mystery about the applicability of fractional derivatives. I argue, however, that there is no clear mystery about their applicability. Thus, via this case study, I think that one can come to see more clearly why certain formulations of the mystery of (...) |
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It is argued that mathematics is unreasonably effective in fundamental physics, that this is genuinely mysterious, and that it is best explained by a version of Pythagorean metaphysics. It is shown how this can be reconciled with the fact that mathematics is not always effective in real world applications. The thesis is that physical structure approaches isomorphism with a highly symmetric mathematical structure at very high energy levels, such as would have existed in the early universe. As the universe cooled, (...) |
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The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner’s famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of (...) |
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