Why does intuitionistic logic not accept every either-or statement as a logical truth?

In the philosophy of logic, intuitionistic logic rejects the universal validity of the law of excluded middle—the principle that for every proposition p, either p or not-p must be true—because it prioritizes constructive knowledge over abstract truth.123

The intuitionist perspective, pioneered by L.E.J. Brouwer, maintains that a statement is only meaningful if it can be proven or established through a constructive method. Consequently, intuitionists refuse to accept "either p or not-p" as a logical truth because, in many cases—particularly those involving infinite sets—we may currently possess no proof for either alternative.132

For an intuitionist, asserting that a disjunction is true requires the ability to actually demonstrate which of the two options holds. If no such construction is available, the statement does not contribute to our knowledge of whether p or not-p is the case, and therefore it cannot be asserted as a logical truth. This approach shifts the focus of logic from a static description of reality to a system concerned with what can be known or verified.13