In particular, the law of the excluded middle does not hold in general, though the induction axiom can be used to prove many specific cases.

Kronecker goes in almost the opposite direction from Poincaré, believing in the natural numbers but not the law of the excluded middle.

Even as a child he was an absolutist, reciting the law of the excluded middle.

Fuzzy logic rejects the law of the excluded middle and allows as a truth value any real number between 0 and 1.

Many modern logic programming systems replace the law of the excluded middle with the concept of negation as failure.

The programmer may wish to add the law of the excluded middle by explicitly asserting it as true; however, it is not assumed a priori.

For example, a particular statement may be shown to imply the law of the excluded middle.

The choice principles that intuitionists accept do not imply the law of the excluded middle.

He claims, in other words, that the law of the excluded middle is not applied in Chinese thought, and that a different standard applies.

("A or not A"), the law of the excluded middle.