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Concept
Validity (logic)
Summary
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. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed by means of sentences called well-formed formulas (also called wffs or simply formulas).
The validity of an argument can be tested, proved or disproved, and depends on its logical form.
In logic, an argument is a set of statements expressing the premises (whatever consists of empirical evidences and axiomatic truths) and an evidence-based conclusion.
An argument is valid if and only if it would be contradictory for the conclusion to be false if all of the premises are true. Validity does not require the truth of the premises, instead it merely necessitates that conclusion follows from the formers without violating the correctness of the logical form. If also the premises of a valid argument are proven true, this is said to be sound.
The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a logical consequence of its premises.
An argument that is not valid is said to be "invalid".
An example of a valid (and sound) argument is given by the following well-known syllogism:
All men are mortal. (True)
Socrates is a man. (True)
Therefore, Socrates is mortal. (True)
What makes this a valid argument is not that it has true premises and a true conclusion, but the logical necessity of the conclusion, given the two premises. The argument would be just as valid were the premises and conclusion false. The following argument is of the same logical form but with false premises and a false conclusion, and it is equally valid:
All cups are green. (False)
Socrates is a cup. (False)
Therefore, Socrates is green.
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