Validity (logic)

In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.

The validity of an argument can be tested, proved or disproved, and depends on its logical form.

[3] In logic, an argument is a set of related statements expressing the premises (which may consists of non-empirical evidence, empirical evidence or may contain some axiomatic truths) and a necessary conclusion based on the relationship of the premises.

The above arguments may be contrasted with the following invalid one: In this case, the conclusion contradicts the deductive logic of the preceding premises, rather than deriving from it.

The premise 'All men are immortal' would likewise be deemed false outside of the framework of classical logic.

However, within that system 'true' and 'false' essentially function more like mathematical states such as binary 1s and 0s than the philosophical concepts normally associated with those terms.

In the third example, the initial premises cannot logically result in the conclusion and is therefore categorized as an invalid argument.

[3] Model theory analyzes formulae with respect to particular classes of interpretation in suitable mathematical structures.