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Law of identity
In logic, the law of identity states that each thing is identical with itself, or symbolically a = a. It applies to singular terms, and is a tautology.
Identity was discussed since antiquity in philosophy, but as a principle in logic was not discussed until much later.
William Hamilton offers a history of the so called "laws of thought". About the law of identity he states "it was not explicated as a coordinate principle till a comparatively recent period. The earliest author in whom I have found this done, is Antonius Andreas, a scholar of Scotus, who flourished at the end of the thirteenth and beginning of the fourteenth century. The schoolman, in the fourth book of his Commentary of Aristotle's Metaphysics – a commentary which is full of the most ingenious and original views – not only asserts to the law of Identity a coordinate dignity with the law of Contradiction, but against Aristotle, he maintains that the principle of Identity is the one absolutely first. The formula in which Andreas expressed it was Ens est ens. Subsequently to this author, the question concerning the relative priority of the two laws of Identity and of Contradiction became one much agitated in the schools; though there were also found some who asserted to the law of Excluded Middle this supreme rank." [From Hamilton LECT. V. LOGIC. 65–66]
Gottfried Wilhelm Leibniz claimed that the law of identity, which he expresses as "Everything is what it is", is the first primitive truth of reason which is affirmative, and the law of noncontradiction is the first negative truth (Nouv. Ess. IV, 2, § i), arguing that "the statement that a thing is what it is, is prior to the statement that it is not another thing" (Nouv. Ess. IV, 7, § 9). Wilhelm Wundt credits Gottfried Leibniz with the symbolic formulation, "A is A."
Another law known as Leibniz's Law rather than merely expressing identity, defines identity; that if two objects have all the same properties, they are in fact one and the same: Fx and Fy iff x = y.
John Locke (Essay Concerning Human Understanding IV. vii. iv. ("Of Maxims") says:
[...] whenever the mind with attention considers any proposition, so as to perceive the two ideas signified by the terms, and affirmed or denied one of the other to be the same or different; it is presently and infallibly certain of the truth of such a proposition; and this equally whether these propositions be in terms standing for more general ideas, or such as are less so: e.g., whether the general idea of Being be affirmed of itself, as in this proposition, "whatsoever is, is"; or a more particular idea be affirmed of itself, as "a man is a man"; or, "whatsoever is white is white" [...]
Afrikan Spir proclaimed the law of identity as the fundamental law of knowledge, which is opposed to the changing appearance of the empirical reality.
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Law of identity AI simulator
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Law of identity
In logic, the law of identity states that each thing is identical with itself, or symbolically a = a. It applies to singular terms, and is a tautology.
Identity was discussed since antiquity in philosophy, but as a principle in logic was not discussed until much later.
William Hamilton offers a history of the so called "laws of thought". About the law of identity he states "it was not explicated as a coordinate principle till a comparatively recent period. The earliest author in whom I have found this done, is Antonius Andreas, a scholar of Scotus, who flourished at the end of the thirteenth and beginning of the fourteenth century. The schoolman, in the fourth book of his Commentary of Aristotle's Metaphysics – a commentary which is full of the most ingenious and original views – not only asserts to the law of Identity a coordinate dignity with the law of Contradiction, but against Aristotle, he maintains that the principle of Identity is the one absolutely first. The formula in which Andreas expressed it was Ens est ens. Subsequently to this author, the question concerning the relative priority of the two laws of Identity and of Contradiction became one much agitated in the schools; though there were also found some who asserted to the law of Excluded Middle this supreme rank." [From Hamilton LECT. V. LOGIC. 65–66]
Gottfried Wilhelm Leibniz claimed that the law of identity, which he expresses as "Everything is what it is", is the first primitive truth of reason which is affirmative, and the law of noncontradiction is the first negative truth (Nouv. Ess. IV, 2, § i), arguing that "the statement that a thing is what it is, is prior to the statement that it is not another thing" (Nouv. Ess. IV, 7, § 9). Wilhelm Wundt credits Gottfried Leibniz with the symbolic formulation, "A is A."
Another law known as Leibniz's Law rather than merely expressing identity, defines identity; that if two objects have all the same properties, they are in fact one and the same: Fx and Fy iff x = y.
John Locke (Essay Concerning Human Understanding IV. vii. iv. ("Of Maxims") says:
[...] whenever the mind with attention considers any proposition, so as to perceive the two ideas signified by the terms, and affirmed or denied one of the other to be the same or different; it is presently and infallibly certain of the truth of such a proposition; and this equally whether these propositions be in terms standing for more general ideas, or such as are less so: e.g., whether the general idea of Being be affirmed of itself, as in this proposition, "whatsoever is, is"; or a more particular idea be affirmed of itself, as "a man is a man"; or, "whatsoever is white is white" [...]
Afrikan Spir proclaimed the law of identity as the fundamental law of knowledge, which is opposed to the changing appearance of the empirical reality.