Statement that is true regardless of the truth or falsity of its constituent propositions
This article is about propositions which are logically true. For the logical property, see Truth.
Logical truth is one of the most fundamental concepts in logic.[1] Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. 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.[2]
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 facts (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 propositions 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.
^null; et al. (2017). Proceedings of the 5th Unconventional Resources Technology Conference. Tulsa, OK, US: American Association of Petroleum Geologists. doi:10.15530/urtec-2017-2670073. ISBN 978-0-9912144-4-0.
Logicaltruth is one of the most fundamental concepts in logic. Broadly speaking, a logicaltruth is a statement which is true regardless of the truth...
of the possible results of the logical operation that the table represents (for example, A XOR B). Each row of the truth table contains one possible configuration...
logic. Formal logic is the study of deductively valid inferences or logicaltruths. It examines how conclusions follow from premises due to the structure...
[better source needed] In formal languages, truth functions are represented by unambiguous symbols. This allows logical statements to not be understood in an...
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...
study of the laws of thought, correct reasoning, valid inference, or logicaltruth. It is a formal science that investigates how conclusions follow from...
disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated...
is meant to provide accounts of the nature of logical consequence and the nature of logicaltruth. Logical consequence is necessary and formal, by way of...
( ∧ {\displaystyle \wedge } ) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically...
of logical symbols Logic gate § Symbols Logical connective Mathematical operators and symbols in Unicode Non-logical symbol Polish notation Truth function...
statement is a truth function. On the other hand, modal logic is non-truth-functional. A logical connective is truth-functional if the truth-value of a compound...
In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement)...
said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p {\displaystyle p} and q {\displaystyle...
ability to perceive logical or mathematical truth—and the ability to solve mathematical challenges efficiently. Humans apply logical intuition in proving...
Boolean logic, logical NOR, non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That...
true. Negation is thus a unary logical connective. It may be applied as an operation on notions, propositions, truth values, or semantic values more...
statements verifiable through direct observation or logical proof are meaningful in terms of conveying truth value, information or factual content. Starting...
language; in the case of predicate logic more logical axioms than that are required, in order to prove logicaltruths that are not tautologies in the strict...
the truth of their premises does not ensure the truth of their conclusion. In some cases, whether a rule of inference is valid depends on the logical system...
the truths they are concerned with, and as such there is only truth under some interpretation or truth within some logical system. A logicaltruth (also...
through deductively valid inferences that preserve truth from the premises to the conclusion. This logical perspective on argument is relevant for scientific...
rules having the property of preserving truth. The converse of soundness is known as completeness. A logical system with syntactic entailment ⊢ {\displaystyle...
mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used...
propositions are formed by connecting propositions by logical connectives representing the truth functions of conjunction, disjunction, implication, biconditional...
fallacy – Faulty deductive reasoning due to a logical flaw Four-valued logic – Any logic with four truth values Impossible object – Type of optical illusion...
Global Information