Logical truth

Logical truth is one of the most fundamental concepts in philosophical logic, and there are different theories on its nature. A logical truth is a statement which is true and remains true under all reinterpretations of its components other than its logical constants. It is a type of analytic statement.

A logical truth was considered by Ludwig Wittgenstein to be a statement which is true in all possible worlds. This is contrasted with synthetic claim (or fact) which is true in this world, as it has historically unfolded, but which is not true in at least one possible world, as it might have unfolded. Later, with the rise of formal logic a logical truth was considered to be a statement which is true under all possible interpretations.

Logical truths (including tautologies) are necessarily true. One theory is that a proposition such as “If p and q, then p” and the proposition “All husbands are married” are logical truths because they are true due to their inherent meanings and not because of any facts of the world. They are such that they could not be untrue. No situation could arise which would cause us to reject a logical truth.

The existence of logical truths is sometimes put forward as an objection to empiricism because it is impossible to account for our knowledge of logical truths on empiricist grounds.

Logical truths and analytic truths

Main article: Analytic-synthetic distinction

Logical truths, being analytic statements do not contain any information about any matters of fact. Other than logical truths, there is also a second class of analytic statements, typified by "No bachelor is married." The characteristic of such a statement is that it can be turned into a logical truth by substituting synonyms for synonyms salva veritate. "No bachelor is married." can be turned into "No unmarried man is married." by substituting 'unmarried man' for its synonym 'bachelor.'

In his essay. Two Dogmas of Empiricism, the philosopher W.V.O Quine called into question the distinction between analytic and synthetic statements. It was this second class of analytic statements that caused him to note that the concept of analyticity itself stands in need of clarification, because it seems to depend on the concept of synonymy, which stands in need of clarification. In his conclusion, Quine rejects that logical truths are necessary truths. Instead he posits that the truth-value of any statement can be changed, including logical truths, given a re-evaluation of the truth-values of every other statement in one's complete theory.

Logical truths and tautologies

Main article: Tautology (logic)

All tautologies are logical truths, but not all logical truths are tautologies. There are several senses in which the term "tautology" is used. In one sense, they are synonymous. In this sense, a tautology is any type of formula or proposition which turns out to be true under any possible interpretation of its terms (may also be called a valuation or assignment depending upon the context).

However, the term "tautology" is also commonly used to refer to what could more specifically called "truth-functional tautologies." Whereas a "tautology" or "logical truth" is true solely because of the logical terms it contains in general (e.g. "every", "some", and "is") , a truth-functional tautology is true because of the logical terms it contains which are logical connectives (e.g. "or", "and", and "nor").

See also

• Validity
• Theorem