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Results tagged with mathematical-philosophy
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user 6153
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.
12
votes
Is Algebraic Geometry really natural?
Algebraic geometry has been an important part of mathematics since Descartes, who pretty much invented it. In other words it is part of 17th century mathematics, like calculus. It happens that there i …
- 12.6k
1
vote
Defining variable, symbol, indeterminate and parameter
Of the various types of "placeholder", certainly a couple have definite mathematical meanings. In logic, the meaning of free and bound variables is set out in detail. And I take "indeterminate" to be …
- 12.6k
16
votes
To what extent is it true that "number theory = mathematics"?
I just don't think it's true, despite my own tastes in topics. Such formulations are substantially a matter of fashion.
There is one basic axis, running from very detailed information at one end (wh …
8
votes
In what ways did Leibniz's philosophy foresee modern mathematics?
My version, quickly, would be that he envisaged "points" that were abstractions. Whence "logical space" as came in first around 1900 (long discussion) as implied by Boolean algebra, which he also anti …
- 12.6k
17
votes
When have we lost a body of mathematics because errors were found?
I feel the answer is obviously "yes", and indeed that much of 19th century mathematics was lost, in a serious sense, for much of the 20th century. I was struck recently by discovering that Henry Fox T …
4
votes
Can a mathematical definition be wrong?
If a definition can be tentative, it can also be wrong. Lakatos has been mentioned already. This is actually a fairly basic issue in understanding how "formal" mathematics advances. Something as funda …
0
votes
What is the "reason" for modularity results?
You'll find logicians who'll explain to you that "number theory" is some collection of theorems to do with Peano arithmetic. Almost exactly wrong, if designed to bring on an existential crisis in numb …