3 ms·
In the philosophy of mathematics, intuitionism is an approach where mathematics is considered to be purely the result of the constructive mental act
by mg 3y ago
In the philosophy of mathematics, intuitionism
is an approach where mathematics is considered
to be purely the result of the constructive
mental activity of humans rather than the
discovery of fundamental principles claimed
to exist in an objective reality
Wouldn't that mean that not only mathematics is pure mental activity, but every thought?
When we say (or think) "Joe and Sue went to the grocery", it seems inherent to this statement that there are two distinct actors. Joe and Sue. But that is already math, isn't it? I have the feeling to avoid math, we would have to avoid "something" in the first place. As it already implies that "something" is in a category, consists of a collection of other things etc. So we could not talk about anything anymore.
- constantcrying 3y ago>Wouldn't that mean that not only mathematics is pure mental activity, but every thought? That statements seems very obviously true.
- mg 3y ago"pure mental activity" as opposed to "mental activity related to a reality outside of the mental activity".
- constantcrying 3y agoI don't see how you could distinguish those. Even the purest form mathematics involves things like rules and symbols and those have to exist in reality (certainly they are at least as real as any emotion).
- BSEdlMMldESB 3y agocounterpoint: remove all blackboards and chalk, and paper and pencils. can you still do math?
- constantcrying 3y agoSure, it just takes a lot of remembering. But the point is that still that isn't "pure" mental activity. I am still imagining symbols and rules, those exist in reality at least as much as emotions do.
- BSEdlMMldESB 3y agohmm, but imagining rules and symbols IS a pure mental activity, isn't it???
- constantcrying 3y agoThey are very similar to language, which cettainly is part of reality.
- haswell 3y agoMy first foray into math involved counting with my fingers.
- simonh 3y agoI think both are descriptive. Mathematics is a descriptive language, and thoughts are descriptions of the world, ourselves, our intentions, etc or maybe the process of forming those descriptions.