Question

Why is the Law of Excluded Middle (LEM) rejected in intuitionistic logic?

A) Because intuitionism denies the existence of mathematical objects.
B) Because intuitionism views mathematical truth as a mental construct.
C) Because intuitionistic logic is inherently contradictory.
D) Because LEM is universally rejected in all branches of mathematical philosophy.

Answer 1

Intuitionistic logic rejects the Law of Excluded Middle because it views mathematical truth as a mental construct and allows for statements that are undecidable or unknown.

Step-by-step explanation:

The Law of Excluded Middle (LEM) is rejected in intuitionistic logic because intuitionism views mathematical truth as a mental construct and rejects the idea that all statements must be either true or false. Intuitionistic logic allows for statements that are neither true nor false, but rather are undecidable or unknown.

This is in contrast to classical logic, which accepts the Law of Excluded Middle and assumes that every statement must be true or false.