In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans. That is, given a set of axioms, the only propositions that can exist are those that ...
I've just been reading this question about the existence (or lack thereof) of contradictions in maths. I've been wondering: What if 'proof by contradiction' is not a valid method to (dis)prove a ...
In Wikipedia's Double-negation translation article, I found that any formula in classical logic has its double negation as its intuitionist equivalent: It is also possible to define φN by ...
In this lecture (which is accompanied by these slides), right near the end (so page 9 in the pdf of the slides; I don't think you have to watch the lecture), P. Johnstone refers to the "Penon ...
Consider pairs $(\Phi,n)$ where $\Phi$ is a finite set of statements in Peano arithmetic and $n$ is an integer. Say that $p'=(\Phi',n')$ is an elementary intuitionistic extension of $p=(\Phi,n)$ iff ...
As I was trying to review forgotten knowledge on Vector Spaces in wikipedia, I read that the existence of a basis follows from Zorn lemma, hence equivalently from the axiom of choice. Actually, the ...