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Results tagged with mathematical-philosophy
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user 10384
Philosophical aspects of logic and set theory; truth status of mathematical axioms; Philosophy of Mathematics; philosophical aspects of mathematics in general; relation of mathematics to philosophy; etc. Consider also posting at http://philosophy.stackexchange.com/, where philosophy-of-mathematics is one of the most popular tags.
14
votes
Are key theorems finitistically reducible?
There are various problems with finitistic reducibility as Simpson develops it; for a survey, see §5.3 of my Stanford Encyclopedia of Philosophy entry on reverse mathematics. I tend to agree that the …
- 1,094
10
votes
Comparative analysis of history of mathematics
Jeremy Gray has written a few things that might fit into this category, including the following.
Plato's Ghost: The Modernist Transformation of Mathematics. The book's thesis is that "1890 to 1930 sa …
- 1,094
10
votes
Ultrainfinitism, or a step beyond the transfinite
Perhaps you could take a look at William Reinhardt's paper 'Remarks on reflection principles, large cardinals, and elementary embeddings' (1974). Reinhardt suggests extending the set-theoretic univers …
- 1,094
5
votes
Equivalences between statements of (seemingly) different order
When we say "with set parameters" I take it that what we really mean is something of the form: the axioms of (e.g.) the $\Sigma^0_1$ induction scheme are the universal closures of all formulas of the …
- 1,094