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Results tagged with mathematical-philosophy
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user 28128
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.
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Did Euler prove theorems by example?
In his 2014 book, Giovanni Ferraro writes at beginning of chapter 1, section 1 on page 7:
Capitolo I
Esempi e metodi dimostrativi
Introduzione
In The Calculus as Algebraic Analysis, Craig Fraser, r …
3
votes
1
answer
321
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Nancy Cartwright's dichotomy
Nancy Cartwright introduced an interesting distinction with regard to modeling of physical phenomena. According to Cartwright, a mathematical theory is not applied directly to such phenomena. Rather, …
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0
answers
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Gauss, Cantor, and infinite confusion
There is an interesting comment by Gauss on "infinite magnitude as a
complete thing" that has invited varying interpretations. In a
well-known passage, Gauss criticized the use of infinity in
mathema …
- 16.6k
15
votes
1
answer
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Are key theorems finitistically reducible?
Simpson writes on page 378 of his Subsystems of Second Order
Arithmetic:
"For example, all of the following key theorems of infinitistic
mathematics are provable in WKL$_0$ and therefore, by theorem I …
- 16.6k
12
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answers
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Has Dedekind's proof of existence of infinite sets been analyzed by historians?
This pdf by David Joyce notes that in paragraph 66 of his famous essay, Dedekind claims to prove the existence of an infinite set.
The proof exploits the assumption that there exists a set $S$ of all …
- 16.6k
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2
answers
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Euler's mathematics in terms of modern theories?
Some aspects of Euler's work were formalized in terms of modern infinitesimal theories by Laugwitz, McKinzie, Tuckey, and others. Referring to the latter, G. Ferraro claims that "one can see in operat …
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3
votes
1
answer
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What is the modern consensus on the difficulty of infinitesimals?
At a related thread at MSE an expert in reverse mathematics noted that "As the modern consensus is that only nonstandard models have infinitesimals, it will be quite challenging to give a concrete exa …
- 16.6k
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6
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Intuitionistic logic as quantization of classical logic?
A classically trained mathematician is more likely to be familiar (at least anecdotally) with an area of mathematical physics such as deformation quantization than with intuitionistic logic. It is he …
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2
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Is there a source linking Robinson's work in wing theory with his theory of infinitesimals?
Abraham Robinson worked in applied mathematics for several decades. MathSciNet lists 12 articles by Robinson in wing theory. His production included the book
Robinson, A.; Laurmann, J. A. Wing theory …
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Assessing effectiveness of (epsilon, delta) definitions [closed]
There is much discussion both in the education community and the mathematics community concerning the challenge of (epsilon, delta) type definitions in calculus and the student reception of them. The …
- 16.6k