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Results tagged with mathematical-philosophy
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user 50073
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.
10
votes
Taking a theorem as a definition and proving the original definition as a theorem
Example 1: In some textbooks, the trigonometric functions are defined via geometry. The advantage is that it is simpler to understand, but the disadvantage is that it is difficult to make completely r …
4
votes
Can you do math without knowing how to count?
This question, like many others, is based on a fundamental conceptual error. Any formal system whatsoever that humans can devise and use must be one with unambiguous rules. Therefore its theorems (i.e …
- 2,912
21
votes
Request for examples: verifying vs understanding proofs
From a logic viewpoint, verifying a proof is a syntactic business, also known as symbol pushing, whereas understanding a proof is a semantic matter. I cannot resist giving a layman analogy as an appet …