Logical truth is one of the most fundamental

concept A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs. Concepts play an important role in all aspects of cognition. As such, concepts are studied within such disciplines as linguistics, ...

s in

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent

proposition A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky ...

s. 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 logical constants). 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 Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statement (logic), statements that hold true when one statement logically ''follows from'' one or more stat ...

. 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 possible worlds. 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

fact A fact is a truth, true data, datum about one or more aspects of a circumstance. Standard reference works are often used to Fact-checking, check facts. Science, Scientific facts are verified by repeatable careful observation or measurement by ...

s (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

s 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 Knowledge is an Declarative knowledge, awareness of facts, a Knowledge by acquaintance, familiarity with individuals and situations, or a Procedural knowledge, practical skill. Knowledge of facts, also called propositional knowledge, is oft ...

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.

Logical truths and analytic truths

Logical truths, being analytic statements, do not contain any information about any matters of

. 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

synonym A synonym is a word, morpheme, or phrase that means precisely or nearly the same as another word, morpheme, or phrase in a given language. For example, in the English language, the words ''begin'', ''start'', ''commence'', and ''initiate'' are a ...

y, 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.

Truth values and tautologies

Considering different interpretations of the same statement leads to the notion of

truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in ...

. 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 term ''tautology'', it is any type of

formula In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwe ...

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). This is synonymous to logical truth. However, the term ''tautology'' is also commonly used to refer to what could more specifically be 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"). Not all logical truths are tautologies of such a kind.

Logical truth and logical constants

Logical constants, including logical connectives and quantifiers, can all be reduced conceptually to logical truth. For instance, two statements or more are logically incompatible '' if, and only if'' their conjunction is logically false. One statement logically implies another when it is logically incompatible with the

negation In logic, negation, also called the logical not or logical complement, is an operation (mathematics), operation that takes a Proposition (mathematics), proposition P to another proposition "not P", written \neg P, \mathord P, P^\prime or \over ...

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.

Logical truth and rules of inference

The concept of logical truth is closely connected to the concept of a

rule of inference Rules of inference are ways of deriving conclusions from premises. They are integral parts of formal logic, serving as norms of the Logical form, logical structure of Validity (logic), valid arguments. If an argument with true premises follows a ...

Logical truth and logical positivism

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, but

nonsense Nonsense is a form of communication, via speech, writing, or any other formal logic system, that lacks any coherent meaning. In ordinary usage, nonsense is sometimes synonymous with absurdity or the ridiculous. Many poets, novelists and songwri ...

Non-classical logics

Non-classical logic is the name given to

formal system A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in ma ...

s which differ in a significant way from standard logical systems such as propositional and

predicate logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables ove ...

. 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 of

and logical truth. Theodore Sider, (2010). ''Logic for philosophy''

References

External links

* * * {{Common logical symbols Philosophical logic Concepts in logic

Truth Truth or verity is the Property (philosophy), property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth, 2005 In everyday language, it is typically ascribed to things that aim to represent reality or otherwise cor ...

Truth Philosophy of logic ca:Valor vertader