Trying to Better understand Intuitionistic Logic, to argue against it
As far As I been researching Intuitionistic logic does not use True or false values, Denies Law of excluded middle, and Has the True and not provable system. From these I got that it does not accept proof by contradiction, pierce law, -(-p)=p, and such. Seems so far, this axiomatic system conflates ability to actively prove and Truth together. Anyone able to inform me more, for I intend to have a discussion about how The Three Classical laws are true, therefore anything others that conflict is not true.
Comments (22)
https://plato.stanford.edu/entries/logic-intuitionistic/
So how come you apply (in the other thread) truth to the 3 laws of logic, which are unproven?
If you need to understand intuitionistic logic better in order to argue against it effectively, how do you already know that you will want to argue against it once you do better understand it? Perhaps understanding it better will lead you to realize that it makes perfect sense on its own terms, even though it is inconsistent with classical logic--which, by the way, absolutely no one denies. Everything that conforms to intuitionistic logic also conforms to classical logic, but certain results of classical logic do not obtain in intuitionistic logic. In that sense, it is a more modest formal system, like non-Euclidean geometry relative to Euclidean geometry--one fewer axiom.
Well that is entirely illogical.
Truth is defined and I assume is defined as what is, or another way of saying, what exists.
What exists must be in compliance to the three laws. You can extrapolate the three laws from the very concept of the meaning exist.
But, "The stone in your backyard", I would say needs to be said as There is the stone in your backyard. This would be a truth. Just stone would not provide any distinction of what you are saying.
Infinity is more so a concept, so it would not be strange that something that is true such as in a finite system , to not apply in a non finite system. Infinite Hotel being an example, full but can hold more people.