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 ...
I understand that a lot of statements are just non-nonconstructive in nature (like negative statements), and I understand that a lot of statements are not provable without the axiom of choice. ...
As you all know, the Curry-Howard correspondance provides a link between type theory and predicate logic. Concepts featured in the former, such as $\Pi$-type and $\Sigma$-type can, by the ...
There exist constructive and non-constructive proofs. Sometimes, for a mathematical statement, we can have both non-constructive and a constructive proof. However, are there statements for which ...
Since constructive mathematics allows us to avoid things like Russell's Paradox, then why don't they replace traditional proofs? How do we know the "regular" kind of mathematics are free of paradox ...