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Results tagged with mathematical-philosophy
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user 11260
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.
15
votes
Origin of the noun "mathematician"
TL;DR: no, it does not seem to be the case that the mathematicians of Pythagoras had the narrowly defined meaning of practitioners of mathematics, but were rather more general scholars.
$\bullet$ G …
- 188k
0
votes
Examples of random matrices that are not iid
Q: Are there any physical processes from the real world that are modeled by truly random operators that have their components iid / or not iid (in some basis)?
A widely studied example of a random mat …
- 188k
10
votes
Accepted
Unreasonable application of mathematics to the other areas
One of the earliest contributions along this line is from Goethe, Über Mathematik und deren Mißbrauch (1826). When describing the abuse (Mißbrauch) in the applications of mathematics to the natural wo …
- 188k
0
votes
Accepted
Generalized Fourier integral and steepest descent path, saddle point near the endpoints
Series expansion of the integrand around $\varphi=\pi$ and integration gives
$$H = 2ika\int_{-\pi/2}^{\pi/2}\cos{(\varphi-\phi)}e^{ika[\cos{\varphi}+\cos{(\varphi-\phi)}]}\ d\varphi$$
$$\qquad\qquad=2 …
- 188k
12
votes
Gödel on pure mathematics and medieval theology
I am quite certain a paraphrase of the quote "the only place where medieval theology survives is pure math", attributed to one of Gödel's essays by Chaitin, does not appear in his collected works (see …
- 188k
11
votes
Can mathematics help in defining free-will?
Seth Lloyd published A Turing test for free will.
The theory of computation implies that, even when our decisions arise
from a completely deterministic decision-making process, the outcomes
of that p …
- 188k
6
votes
Modeling in pure math
Perhaps geometric proofs of algebraic relations could be an early example of mathematical modeling. I am thinking of the geometric proof of Pythagoras theorem. We know that Euclidean geometry is equiv …
4
votes
Accepted
Nancy Cartwright's dichotomy
Cartwright's case study, model building for the theory of superconductivity, has been explored further in the Ph.D.thesis The Role of Concrete Models in the Revolution in Superconductivity (A. Chattor …
- 188k
11
votes
Accepted
Has Dedekind's proof of existence of infinite sets been analyzed by historians?
See pages 107 and following and pages 244 and following of Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics by José Ferreirós (2008).
Dedekind and the set-theoretical …
- 188k
6
votes
Accepted
Where can you find Grothendieck's "Récoltes et Semailles"?
http://people.math.jussieu.fr/~leila/grothendieckcircle/RetS.pdf
archived at the Wayback Machine
- 188k
5
votes
Accepted
Literature about formalization of "natural reasoning" in mathematical logic
Quantum logic might be one example of "a non-standard way of doing logic motivated by the nature of reality," as described in Quantum Logic in Historical and Philosophical Perspective.
- 188k
3
votes
Information theory from negative probability
In the context of information theory, negative probabilities explain the quantum mechanical phenomenon of probability backflow, as described in section 5 of Waiting for the Quantum Bus (Bracken and Me …
- 188k
10
votes
Accepted
Searching for an early, highly theoretical, even philosophical, math paper on models or smal...
Stanley Milgram, The Small World Problem, Psychology Today 2, 60 (1967)
seems to fit the bill: +50 years old, "kind of philosophical", and yes, iconic -- cited more than 9,000 times. There are a few r …
- 188k
39
votes
What was Hilbert's view of Gödel's Incompleteness Theorems?
The reaction of Hilbert to Gödel is described in detail by Solomon Feferman in Gödel on finitism, constructivity and Hilbert’s program (2011).
Hilbert was unaffected by any of the reconsiderations of …
- 188k
21
votes
Books on the relationship between the Socratic method and mathematics?
An influential book on the teaching of mathematics via the Socratic method is Imre Lakatos, Proofs and Refutations. The full book can be browsed on Google, and individual chapters can be donwloaded fr …
- 188k