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This article is about arguments in logic.

In logic, an argument is a set of statements known as the premises, and another statement known as the conclusion in which it is asserted that the truth of the conclusion follows from (is entailed by) the premises. A valid argument is one in which the premises cannot be true and the conclusion false. The validity or an argument depends on its form.   The form of argument can be shown by the use of symbols. An argument-form is valid if and only if all arguments of its form are valid. For each argument-form, there is a statement, a corresponding conditional, and an argument-form is valid if and only its corresponding conditional is a logical truth. A statement is a logical truth if it is true under all interpretations. It can be shown to be a logical truth by either (a) showing that it is a tautology or (b) by means of a proof procedure.

Logic is concerned with the validity of an argument, not with the truth or falsity of its premises or conclusion. (Many authors however describe a sound argument as a valid argument with true premises; a sound argument being both valid and having true premises must have a true conclusion.)

Each premise (there must be at least one) of an argument and its conclusion is a statement, capable of being true or false and nothing else. (Some authors use the term proposition or sentence instead of statement, but which ever term is used, each premise and the conclusion must be capable of being true or false and nothing else.)

Non arguments

First the premises and the conclusion must be statements, capable of being true and false. Secondly it must be asserted that the conclusion follows from the premises. In English the words "therefore" and "so" typically separate the premises from the conclusion of an argument, but this is not necessarily so. Thus: "Socrates is a man, all men are mortal therefore Socrates is mortal" is clearly an argument (a valid one at that), because it is clear it is asserted that that "Socrates is mortal" follows from the preceding statements. However "I was thirsty and therefore I drank" is NOT an argument, despite its appearance. It is not being claimed that "I drank" is logically entailed by "I was thirsty". The "therefore" in this sentence indicates "for that reason" not "it follows that".

Validity

It should be carefully noted that there is nothing to stop a valid argument having a false conclusion; this may be the case if the premises are false. Nor is the anything to stop an invalid argument from having a true conclusion. In fact all combinations are possible accept one: it is not possible to have a valid argument with true premises and a false conclusion

Truth

Statements are either true or false; arguments are either valid or invalid. (In Logic statements are never referred to as being valid or invalid, and arguments are either referred to as being true or false.)

Proof

A proof is a demonstration that a statment is a logical truth (see Proof procedure).

(See also Validity, Soundness, true, Soundness_theorem).

For further reading:

More on Arguments:

Wesley C Salmon, Logic, Prentice-Hall, New Jersey 1963 (Library of Congress Catalog Card no. 63-10528)

More on Logic:

Aristotle, Prior and Posterior Analytics, ed. and trans. John Warrington, Dent: London (everyman Library) 1964

Benson Mates, Elementary Logic, OUP, New York 1 972 (Library of Congress Catalog Card no.74-166004)

Elliot Mendelson, Introduction to Mathematical Logic,, Van Nostran Reinholds Company, New York 1964