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Philosophy of mathematics asks questions about mathematical theories and practices. It can include questions about the nature or reality of numbers, the ground and limits of formal systems and the nature of the different mathematical disciplines.

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Cantor's theorem is a prime instance of a diagonalization argument, but far from being the only one. There is nothing particularly mysterious or un-intuitive about diagonalization. I do not know what …
answered Nov 18 '18 by Arno
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This is more a finitist vs non-finitist issue than it is about Platonism or formalism: Admitting that For no integer P(x) holds is sensible statement for a decidable property P is compatible with form …
answered Feb 19 by Arno
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We need to distinguish believing in the actual existence of mathematical objects, and believing that pretending that the mathematical objects exist will only lead us to true conclusions regarding the …
answered Jun 27 '18 by Arno
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An approach to make sense of the necessary vs contingent truth distinction is by considering a theory $T$ and a model $M$ of that theory. Theorems of $T$ are the necessary truths in $T$. Statements th …
answered May 6 '18 by Arno
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Fundamentally, category theory does not seek to model "having a structure". It rather starts from the realization that the way how we use the structure is typically via the structure-preserving or ref …
answered Jun 1 '18 by Arno
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The point raised in the quote is not the same as the question that you are asking. In the quote: It is a difference whether we define what one is, and then we define what two is, and so on, or whethe …
answered Sep 17 '17 by Arno
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There is no agreed upon example of this kind. Let us explore the issues: First, we cannot even come up with a decent example of a problem not solvable by any formal system. If you state the problem …
answered Jan 10 '17 by Arno