Questions tagged [philosophy]
Questions involving philosophy of mathematics. Please consider if Philosophy Stack Exchange is a better site to post your question.
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How do we know we get the right answer?
The problem of ontology is one much discussed in mathematical philosophy with much categorization into different schools of thought, but the problem of epistemology seems to be less discussed; ...
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Reference request: which theorems are "interesting" to mathematicians?
Disclaimer: this question is more about philosophy of mathematics than technical mathematics.
Mathematicians always need to choose what to focus their work on. Many pure mathematicians like to say ...
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Codifying ways to think and write about imprecise ideas?
This question will not be about affine spaces; rather those are mentioned here as one of many examples.
A vector space has an underlying set and a field of scalars and an operation of linear ...
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Why is it that most mathematical statements that mathematicians tend to study are decidable?
This is a bit of a philosophical question. Due to Godel, we know that there are undecidable statements in ZFC set theory. But why is it that most statements that mathematicians tend to study in ...
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Apparent Arbitrariness in Mathematics
Something about definitions in mathematics has always interested – confused? - me, I call it “arbitrariness in Mathematics” - it's a bad name, but I don't know a better one. Let me explain:
1st - ...
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How much are mathematics driven by applications?
At some point this provocative question came to my mind:
Are mathematics mostly driven by applications?
I am taking into account some of the comments made to my original question so I want to make ...
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The philosophical significance of Chaitin's Theorem
In a book review of Torkel Franzén's "Gödel’s Theorem:
An Incomplete Guide to Its Use and Abuse" in the Notices the reviewer (Raatikainen) writes:
Franzén also devotes a brief chapter to ...
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What exactly is a set?
It's been proven that the Continuum Hypothesis is independent of ZFC, yet some people still talk about it being "true" or "false", or that we need to search for a non-mathematical ...
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looking for good book on the history of formalism
In 1868 Beltrami published a paper ""Saggio di interpretazione della geometria non-euclidea" that seems to have led to the formalist philosophy of mathematics.
But what was written exactly what were ...
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Can one define informational content of a mathematical expression?
At least in physicist's thinking, information, vaguely, is something that allows one to select a subset from a set.
Say, a system can be in states A and B, we have done a measurement on it (...
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(When) are recursive "definitions" definitions?
This is a "soft" question, but I'm greatly interested in canvassing opinions on it. I don't know whether there is anything like a consensus on the answer. Under what conditions (if any) are ...
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Non-associativeness of composition in deductive systems?
WARNING: The first three and last two paragraphs of this question concern historical/philosophical matters related to a secondary aim of the question. If you are more interested in the properly ...
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Can the tehniques of higher level mathematics solve most of Olympiad level math problems through straighforward applications?
Working through many Olympiad math problems(pre-undergrad) I've found that simple applications of undergrad math will solve many of them. Does this trend go on? Can it be that Putnam problems are ...
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Sheaves in Philosophy
I once found a book on google.books. It was about the applications of sheave theory to philosophy or more general to social studies. I don't remember for sure. i just know it was not the book Sheaves ...
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Strange Consequences of Large Cardinals in Probability
Large cardinal axioms are very strong hypothesizes and as any other strong hypothesis they have many strange consequences in mathematics.
On the other hand we know that if we bring even the least ...
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