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Results tagged with mathematical-philosophy
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user 1459
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.
37
votes
What is Realistic Mathematics?
I think you need to be clearer about how directly useful you need your mathematical concepts to be to the study of the real world. For example, suppose you find PDEs useful for modelling physical phen …
- 29k
37
votes
Can a mathematical definition be wrong?
This is not quite an answer to the question you are asking, but the definition of a function is an obvious example of a concept that underwent considerable change, though perhaps one might argue that …
23
votes
Is there any formal foundation to ultrafinitism?
I've been interested in this question for some time. I haven't put any serious thought into it, so all I can offer is a further question rather than an answer. (I'm interested in the answers that have …
- 29k
16
votes
Accepted
Supervenience in mathematics
I want to try another answer, not because I think you will necessarily accept it, but because if you don't then I think your reasons for not doing so will clarify the question.
One definition of supe …
- 29k
13
votes
Believing the Conjectures
I initially wrote this as a comment, but it got too long and it sort of contains an example, so here goes. Reflection seems false in a number of contexts, since there are many properties that can't be …
12
votes
Reasons for the importance of planarity and colorability?
I think that planarity figures more heavily in typical undergraduate courses than its importance at research level would warrant. I'm not saying that it's not important at research level, but I do thi …
9
votes
Supervenience in mathematics
It seems to me that even if the exact philosophical notion doesn't quite apply to mathematics, there are other notions, similar but a bit more precise, that do. For example, mathematical structures ca …
- 29k