law of excluded middle
principle of excluded middle

The law of excluded middle is true at every possible world.

A significant divide is provided by the law of excluded middle.

Law of excluded middle: "Everything must either be or not be."

A typical example is intuitionistic logic, where the law of excluded middle does not hold.

Three of the topics involve the law of excluded middle.

Constructivists will be interested to work in a topos without the law of excluded middle.

One can see that the law of excluded middle cannot hold from the following basic theorem:

(That is, natural deduction without the Law of excluded middle.)

In this way Peirce's law implies the law of excluded middle.

In the above argument, the assertion "this number is either rational or irrational" invokes the law of excluded middle.

We therefore seem to have a violation of the Law of Excluded Middle.

In particular, the law of excluded middle, "A or not A", is not accepted as a valid principle.

It is not the same as the law of excluded middle, however, and a semantics may satisfy that law without being bivalent.

Improper descriptions raise some difficult questions about the law of excluded middle, denotation, modality, and mental content.

It is sometimes and rather simplistically characterized by saying that its adherents refuse to use the law of excluded middle in mathematical reasoning.

Many modern logic systems reject the law of excluded middle, replacing it with the concept of negation as failure.

However, its various proofs are non-constructive, as they depend on the law of excluded middle, and therefore rejected by intuitionists.

The law of excluded middle is the thesis that for all propositions p, p p is true.

In classical two-valued logic both the law of excluded middle and the law of non-contradiction hold.

He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle.

Aristotle wrote of the Law of Excluded Middle:

Bertrand Russell asserts a distinction between the "law of excluded middle" and the "law of noncontradiction".

For instance, Heisenberg's indeterminacy principle has been held to be a reason to reject the Law of Excluded Middle.

One reason that Peirce's law is important is that it can substitute for the law of excluded middle in the logic which only uses implication.

The proof by resolution given here uses the law of excluded middle, the axiom of choice, and non-emptiness of the domain as premises.