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Results tagged with mathematical-philosophy
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user 2733
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.
4
votes
Is rigour just a ritual that most mathematicians wish to get rid of if they could?
Please would somebody better qualified than me to do so write accounts here of Reallisability and Proof Mining.
0
votes
Extensionality in HoTT versus extensionality in internal language of a category
No, sorry, but you haven't got the point of HoTT.
$x \equiv y$ means "$x$ is the same as $y$", so they are terms such that one can be transformed into the other by "rewrite rules" such as expanding o …
- 8,481
24
votes
Categorical foundations without set theory
Since Tom Leinster queries my reference to actual/completed versus
potential/incomplete infinities, maybe we should ask a philosopher
whether I am using these terms in the standard way.
In any case, …
- 8,481
46
votes
Accepted
Categorical foundations without set theory
On the subject of categorical versus set-theoretic foundations there
is too much complicated discussion about structure that misses the
essential point about whether "collections" are necessary.
It d …
- 8,481
17
votes
Intuitionistic logic as quantization of classical logic?
MathOverflow is a valuable resource because it is interdisciplinary. Some of the people who have written about this question come from a traditional pure mathematical background where classical logic …
- 8,481
17
votes
(Fictive) story of a time where people reasoned only up to isomorphism
As Todd has already written an answer for me, maybe I can claim it as an Answer:
Exercise 1.1 in my book Practical Foundations of Mathematics
(CUP 1999) reads,
When Bo Peep got too many sheep to see …
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