All Questions
Tagged with philosophy reference-request
52
questions
5
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1
answer
154
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Is there a mathematical notion of "why"?
Is there a mathematical notion of "why"? That is, are there reasons behind the truth of certain mathematical statements? Personally, my belief is that true mathematical statements just are ...
- 21.4k
2
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0
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375
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Why were evil numbers named "evil"?
According to the entry for Sloane sequence A001969:
Evil numbers: nonnegative integers with an even number of 1's in their binary expansion.
And deeper inside that entry it states that
The terms &...
- 2,250
7
votes
0
answers
175
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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 ...
- 143
0
votes
1
answer
119
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Analytic works versus synthetic works in mathematical research
With the purpose to clarify my ideas about terminology I would like to ask in Mathematics Stack Exchange what is the difference of two verbal expressions: when a professional mathematician understands ...
3
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123
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Ultra-finite math [closed]
Assume our universe is finite in any sense (the information amount was some $10^{120}$ bits, if I remember correct) and deal with the following, slightly (and intendedly) preposterous, scenario:
The ...
- 745
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Reference of language aspects of Mathematics.
I occasionally wonder about the language aspects of Mathematics. Like when I read Vilém Flusser, Tractatus Logico-Philosophicus by Wittgenstein and Godel's Proof by Ernest Nagel and James Newman.
Some ...
- 161
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85
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Reference books for Foundation of Mathematics (Logic and Philosophy)
I am an undergraduate student. And I want to build solid foundation for Mathematics.
I tried google search but could not get proper recommendation.
Please suggest books which covers the subject nicely....
- 143
15
votes
6
answers
2k
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Books on Philosophy of Math by Mathematicians
I'm interested in books on Philosophy of Math written by Mathematicians. Preferably more recent writings. I consider that philosophy in a field should only be done by people that work on the field.
I ...
- 3,309
4
votes
1
answer
252
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Reference request for subjective/objective logic for mathematicians
I am self-learning William Lawvere's Conceptual Mathematics and Sets For Mathematics. He mentioned subjective and objective logic. I really don't understand it. Do I have to read Hegel's to fully ...
- 602
1
vote
1
answer
241
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Is there a top-down approach to set theory?
[Edit: After digesting the comments, doing more research & more thinking, I have reformulated my question]
On the iterative conception of sets, as it is usually expressed, there is no "...
- 347
2
votes
1
answer
110
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Are new mathematics required to solve problems on the frontier of contemporary physics? [closed]
I would like to ask about the following question, and I hope that is suitable. We know that there are relationships between mathematics and mathematical physics, let's say that in physics are used ...
1
vote
0
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25
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Soft question: References for Dedekind's work on quaternions and hypercomplex numbers?
I've been told that quaternions and hypercomplex numbers in general were very important to Dedekind's early as well as late work. Besides Ferreiros' Labyrinth of Thought, ch. 7 and the references ...
2
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0
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101
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Other mathematical theories that are "tiered" like the iterative conception of sets?
In the usual way of constructing the cumulative hierarchy under the iterative conception of sets, sets are constructed in levels. George Boolos, in his "The Iterative Conception of Set", devises a "...
- 2,567
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0
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21
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Has the knowledge of applicability of an idea helped you learn/appreciate a concept? If yes, how?
Can you please elaborate your answer with specific examples?
PS: Sorry, i couldn't find the exact tags. Please excuse me if this question is not suited for the site.
- 519
0
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Do you know a good book or study on the philosophical background of the ZFC axioms?
I'm especially interested in how the Axiom of Choice might be derived from nature through philosophy. After studying basic set theory at university, I could convince myself of the ZF axioms being true,...
- 126