Law of Excluded Middle/Intuitionist Perspective

Law of Excluded Middle: Intuitionist Perspective

The Law of the Excluded Middle is rejected by the intuitionistic school, which rejects the existence of an object unless it can be constructed within an axiomatic framework which does not include the Law of the Excluded Middle.

This is because from the perspective of intuitionism:

an object cannot be known to exist unless it can be constructed in a finite number of steps

a statement cannot be known to be true if its proof needs an argument requiring an infinite number of steps.

Thus:

while it is sufficient to prove a statement is not true by demonstrating that it is not true

it is insufficient to prove a statement is true by demonstrating it is not false.