A disjunction lacking a constructive witness—where we cannot currently prove any single disjunct—fails to constitute genuine mathematical knowledge by intuitionist standards, even if classically valid.

?Rate how convincing each reason is below to see the overall strength.

1 reason for

1 reason against

Reasons For

1 perspective

Reason for

1 perspective

Reason against

Based on where you are in your exploration

Constructive witness(what intuitionistic logic requires): An actual, concrete example or proof that demonstrates something is true, rather than just proving that assuming it's false leads to a problem.
classically valid(Contrasted with intuitionistic validity): A formula or inference is classically valid if it holds in all classical models, including by appeal to the vacuous truth of conditionals with false antecedents
disjunct(in logic): One of the options in an 'either/or' statement; in 'either A or B,' both A and B are disjuncts.
disjunction(as used in formal logic): A logical 'or' statement; 'a or b' (written a∨b) is true when at least one of the two parts is true.
intuitionism(Mill's characterisation of a target he rejected; linked to conservative deference to inherited belief): The view that anything a person believes deeply enough must be true, such that conviction itself is taken as justification.
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.): Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.
mathematical knowledge(philosophy of mathematics and epistemology): Truths about numbers, shapes, and abstract objects that mathematicians consider proven and certain.

2 topics