intuitionistic

The idea was as old as intuitionistic logic: by the

Chores 2009

If one wished to satisfy Hilbert's requirements, the task would still remain of showing intuitionistic arithmetic consistent.

Chores 2009

The anti-realist's purported right to give up classical logic in favor of intuitionistic logic has been defended independently.

Fitch's Paradox of Knowability Brogaard, Berit 2009

If, on the other hand, one admits the intuitionistic position as a secure basis in itself, i.e., as a consistent one, the consistency of classical arithmetic is secured by my result.

Chores 2009

The undecidedness paradoxes give the anti-realist even further reason to revise classical logic in favor of intuitionistic logic.

Fitch's Paradox of Knowability Brogaard, Berit 2009

Moreover, some of the intuitionistic consequences of KP are thought to be bad enough.

Fitch's Paradox of Knowability Brogaard, Berit 2009

Owing to a verificationist (or constructivist) reading of negation and existential quantification, intuitionistic logic validates neither the elimination of double negation,

Fitch's Paradox of Knowability Brogaard, Berit 2009

That is because in intuitionistic logic the quantifier exchange rule,

Fitch's Paradox of Knowability Brogaard, Berit 2009

Williamson (1982) argues that Fitch's result is not a refutation of anti-realism, but rather a reason for the anti-realist to accept intuitionistic logic.

Fitch's Paradox of Knowability Brogaard, Berit 2009

There is some debate about whether this consequence is sufficiently troublesome, but the the intuitionistic anti-realist takes solace in the fact that she is not committed to the blatantly absurd claim that all truths are known.

Fitch's Paradox of Knowability Brogaard, Berit 2009