Back to the point though: The axiom of the excluded middle isn't provable in constructive logic, and you can not use constructive logics to prove theorems with it without explicitly assuming it. You can use constructive logic to prove that other logics prove theorems using it.
It seems to be a good approximation when we say that are no fundamental disagreements between mathematicians. There seem to be merely different areas and levels of expertise. In my view, philosophy is a culture (or several ones), because philosophers have tremendous disagreements
-
-
As for "mathematicians don't have fundamental disagreements" - Gödel's theorems came from a disagreement between him and hilbert. Forcing came from the dissatisfaction with the continuum hypothesis as an axiom which and is still contentious.
-
The disagreement between Gödel and Hilbert was a mathematical and not a cultural one, and it was resolved by mathematics, not by culture.
- 4 more replies
New conversation -
-
-
You appear to be disagreeing with my definition of culture and not with the fundamental point my usage of the word culture and subsequent definition was intended to convey, which is not particularly interesting or insightful.
-
I am in disagreement with what looks like postmodernism to me. Math is not a social construct. Much of philosophy is, but not the good parts.
End of conversation
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.