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Results tagged with lo.logic
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user 10819
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
14
votes
When are two proofs of the same theorem really different proofs
Some additional recent references on "equivalence" or "homotopy" between proofs include
S. Awodey, Type theory and homotopy, also on the arXiv
Various notes by V. Voevodsky
Not that I understand m …
- 5,575
12
votes
Is PA consistent? do we know it?
To be specific, I'll focus on the second question of the title, "Is PA consistent? do we know it?"
As noted by Noah Snyder on the meta thread, this question itself already uses "philosophical" langua …
11
votes
What is Realistic Mathematics?
Is there any other canonical candidate which arises? My question here is mainly about opinions or some sort of vision which explains why this or that model or object of study arises naturally.
I' …
- 5,575
7
votes
1
answer
1k
views
categorifying induction in homotopy type theory
In trying to understand homotopy type theory, I stumbled upon the following silly question, which is likely to be trivial for the experts.
Let $B=\sqcup_{n\in\Bbb N} BS_n$, which I'd like to think of …
- 5,575
7
votes
The sets in mathematical logic
That is to say, mathematical logic is using intuitive set theory. So, is there any paradox in mathematical logic?
Yes, in set theory whose logic is based upon naive set theory there is Berry's pa …
- 5,575
6
votes
What if Current Foundations of Mathematics are Inconsistent?
What if the current foundations of Mathematics are inconsistent?
Had this kind of opinion been expressed before?
The opinion that the Peano Arithmetic is likely to be inconsistent is not uncommon, a …
2
votes
Accepted
What is known about links with a countably-infinite number of tame components?
I don't think that knot theorists are going to be very interested in such infinite links, but they do occur sometimes in the wider area of geometric topology, for instance in the proof of theorem 1.1 …
- 5,575