Logical truth is one of the most fundamentalconcepts inlogic. Broadly speaking, a logical truth is astatement which istrue regardless of the truth or falsity of its constituentpropositions. In other words, a logical truth is a statement which is not only true, but one which is true under allinterpretations of its logical components (other than itslogical constants). Thus, logical truths such as "if p, then p" can be consideredtautologies. Logical truths are thought to be the simplest case of statements which areanalytically true (or in other words, true by definition). All ofphilosophical logic can be thought of as providing accounts of the nature of logical truth, as well aslogical consequence.[1]
Logical truths are generally considered to benecessarily 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 allpossible worlds. However, the question of which statements arenecessarily true remains the subject of continued debate.
Treating logical truths, analytic truths, and necessary truths as equivalent, logical truths can be contrasted withfacts (which can also be calledcontingent claims orsynthetic claims). Contingent truths are true inthis world, but could have turned out otherwise (in other words, they are false in at least one possible world). Logically truepropositions 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 byempiricism, because they hold that it is impossible to account for ourknowledge 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 thelogical positivists in the early 20th century.
Logical truths, being analytic statements, do not contain any information about any matters offact. 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 synonymssalva veritate. "No bachelor is married" can be turned into "no unmarried man is married" by substituting "unmarried man" for its synonym "bachelor".[citation needed]
In his essayTwo Dogmas of Empiricism, the philosopherW. 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 ofsynonymy, 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.[citation needed]
Considering differentinterpretations of the same statement leads to the notion oftruth value. The simplest approach to truth values means that the statement may be "true" in one case, but"false" in another. In one sense of the termtautology, it is any type offormula orproposition which turns out to be true under any possible interpretation of its terms (may also be called avaluation or assignment depending upon the context). This is synonymous to logical truth.[citation needed]
However, the termtautology is also commonly used to refer to what could more specifically be calledtruth-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 arelogical connectives (e.g. "or", "and", and "nor"). Not all logical truths are tautologies of such a kind.[citation needed]
Logical constants, includinglogical connectives andquantifiers, can all be reduced conceptually to logical truth. For instance, two statements or more arelogically incompatibleif, and only if theirconjunction is logically false. One statementlogically implies another when it is logically incompatible with thenegation of the other. A statement is logically true if, and only if its opposite is logically false. The opposite statements must contradict one another. In this way all logical connectives can be expressed in terms of preserving logical truth. The logical form of a sentence is determined by its semantic or syntactic structure and by the placement of logical constants. Logical constants determine whether a statement is a logical truth when they are combined with a language that limits its meaning. Therefore, until it is determined how to make a distinction between all logical constants regardless of their language, it is impossible to know the complete truth of a statement or argument.[2]
The concept of logical truth is closely connected to the concept of arule of inference.[3]
Logical positivism was a movement in the early 20th century that tried to reduce the reasoning processes of science to pure logic. Among other things, the logical positivists claimed that any proposition that is not empirically verifiable is neither true nor false, butnonsense.[citation needed]
Non-classical logic is the name given toformal systems which differ in a significant way from standard logical systems such aspropositional andpredicate logic. There are several ways in which this is done, including by way of extensions, deviations, and variations. The aim of these departures is to make it possible to construct different models oflogical consequence and logical truth.[4]
| Major fields |
| ||||
|---|---|---|---|---|---|
| Foundations | |||||
| Lists |
| ||||
| General | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Theorems (list) and paradoxes | |||||||||
| Logics |
| ||||||||
| Set theory |
| ||||||||
| Formal systems (list), language and syntax |
| ||||||||
| Proof theory | |||||||||
| Model theory | |||||||||
| Computability theory | |||||||||
| Related | |||||||||
Commonlogical connectives | ||
|---|---|---|
 | ||
| Functional: |  | |
|---|---|---|
| Formal: | ||
| Negation | ||
