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Logical truth is one of the most fundamental in logic. Broadly speaking, a logical truth is a statement which is truth regardless of the truth or falsity of its constituent . In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other than its ). Thus, logical truths such as "if p, then p" can be considered tautologies. Logical truths are thought to be the simplest case of statements which are analytically true (or in other words, true by definition). All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence.Quine, Willard Van Orman, Philosophy of logic
Logical truths are generally considered to be necessarily true. This is to say that they are such that no situation could arise in which they could fail to be true. The view that logical statements are necessarily true is sometimes treated as equivalent to saying that logical truths are true in all . However, the question of which statements are necessarily true remains the subject of continued debate.
Treating logical truths, analytic truths, and necessary truths as equivalent, logical truths can be contrasted with (which can also be called contingent claims or synthetic claims). Contingent truths are true in this world, but could have turned out otherwise (in other words, they are false in at least one possible world). Logically true such as "If p and q, then p" and "All married people are married" are logical truths because they are true due to their internal structure and not because of any facts of the world (whereas "All married people are happy", even if it were true, could not be true solely in virtue of its logical structure).
Rationalist philosophers have suggested that the existence of logical truths cannot be explained by empiricism, because they hold that it is impossible to account for our knowledge of logical truths on empiricist grounds. Empiricists commonly respond to this objection by arguing that logical truths (which they usually deem to be mere tautologies), are analytic and thus do not purport to describe the world. The latter view was notably defended by the logical positivists in the early 20th century.
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 , 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.
However, the term tautology is also commonly used to refer to what could more specifically be called Truth function 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 "joint denial"). Not all logical truths are tautologies of such a kind.
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