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The law of identity can be expressed as (=), where x is a variable ranging over the domain of all individuals. In logic, there are various different ways identity can be handled. In first-order logic with identity, identity is treated as a logical constant and its axioms are part of the logic itself. Under this convention, the law of identity ...
The law of identity: 'Whatever is, is.' [2]. For all a: a = a. Regarding this law, Aristotle wrote: First then this at least is obviously true, that the word "be" or "not be" has a definite meaning, so that not everything will be "so and not so".
Identity (philosophy) – Relation each thing bears to itself alone; Masked-man fallacy – Formal fallacy when one makes an illicit use of Leibniz's law in an argument, a fallacious use of this principle; Ship of Theseus – Thought experiment about identity over time
In metaphysics, identity (from Latin: identitas, "sameness") is the relation each thing bears only to itself. [1] [2] The notion of identity gives rise to many philosophical problems, including the identity of indiscernibles (if x and y share all their properties, are they one and the same thing?), and questions about change and personal identity over time (what has to be the case for a person ...
To express the fact that the law is tenseless and to avoid equivocation, sometimes the law is amended to say "contradictory propositions cannot both be true 'at the same time and in the same sense'". It is one of the so called three laws of thought, along with its complement, the law of excluded middle, and the law of identity.
Identity (philosophy), the relation each thing bears only to itself; Law of identity, that each thing is identical with itself; Personal identity, the numerical identity of a person over time; Identity (social science), qualities etc that characterize a person or group; Political identity
The law of identity has deep impact on Aristotle's ethics as well. In order for a person to be morally praiseworthy or blameworthy for an action, he or she must be the same person before the act as during the act and after the act. Without the law of identity, Aristotle notes, there can be no responsibility for vice
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. [1] [2] It is one of the three laws of thought, along with the law of noncontradiction, and the law of identity; however, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens ...