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Results tagged with mathematical-philosophy
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user 3154
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.
4
votes
Where are we working when we prove metamathematical theorems?
Real Logicians(*) use primitive recursive arithmetic as their metatheory. As a purely equational, and so unquantified, theory, it is agnostic about the distinction between classical and intuitionisti …
- 2,283
2
votes
Are all mathematical theorems necessarily true?
John Goodrick writes, very much to the point: The last I heard, there was no consensus in the philosophical community as to what exactly a "possible world" is, or whether this is even a coherent notio …
- 2,283
3
votes
The Importance of ZF
This answer is essentially a Joel's version by another route.
ZF(C), possibly with appropriate large cardinal axioms, is one of the three most important formal axiomatisations in the foundations of m …
- 2,283
4
votes
How do they verify a verifier of formalized proofs?
The key point is the idea of the kernel of a theorem prover, as Adam mentioned. To put it another way the kernel is the smallest subset of the theorem prover's code base (and operating system and mac …
- 2,283
9
votes
Alternative axiom to induction
The literature on this question is large!
First recommendation: take a look at George Boolos (1984/1998)'s "The Justification of Mathematical Induction", in Logic, Logic, And Logic, pp. 370—375, Har …
- 2,283
2
votes
Models of ZFC Set Theory - Getting Started
From comment: how do we get from "the abstract" to "the concrete"?
In my partly informed opinion, not by formal model theory! The ability of set theory to describe its own models is one of the pilla …
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