Knowra Law of identity Law of identity The principle that every entity is identical to itself, commonly expressed as A = A. It is a basic law of classical logic and a metaphysical claim about identity.
Identity (philosophy) : The relation each thing bears only to itself, and the question of what makes something the same thing over time. The law states identity in its most basic form; philosophy asks what that relation entails.
Classical logic : The standard system of logic built around principles such as excluded middle and noncontradiction. The law is one of the basic principles assumed in classical reasoning.
Identity relation : The binary relation that holds between an object and itself, and between no distinct objects. This relation gives the formula A = A its formal interpretation.
Law of noncontradiction : The principle that a proposition and its negation cannot both be true in the same respect at the same time. It is another foundational logical law, distinct from self-identity.
Principle of individuation : An account of what makes one individual distinct from another. The law presupposes identifiable entities, while individuation explains what distinguishes them.
Propositional logic : A formal system that studies how propositions combine through logical connectives. Its formulas can instantiate identity, though identity between objects needs richer logic.
Reflexive relation : A relation is reflexive when every element bears it to itself. Identity is a special case of reflexivity, though reflexivity alone does not make a relation identity.
Law of excluded middle : The principle that every proposition is either true or false. It is often grouped with identity, but concerns truth alternatives rather than sameness.
Personal identity : The philosophical problem of what makes a person the same person over time. It tests how identity applies when an entity changes across time.
First-order logic : A formal system with variables, predicates, quantifiers, and often an identity symbol. Its identity symbol lets the law be stated for objects within a formal language.
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