Question

LAW OF ARISTOTLE..Explain ​

Answer 1

Laws of thought, traditionally, the three fundamental laws of logic: (1) the law of contradiction, (2) the law of excluded middle (or third), and (3) the principle of identity. That is, (1) for all propositions p, it is impossible for both p and not p to be true, or symbolically ∼(p · ∼p), in which ∼ means “not” and · means “and”; (2) either p or ∼p must be true, there being no third or middle true proposition between them, or symbolically p ∨ ∼p, in which ∨ means “or”; and (3) if a propositional function F is true of an individual variable x, then F is indeed true of x, or symbolically F(x) ⊃ F(x), in which ⊃ means “formally implies.” Another formulation of the principle of identity asserts that a thing is identical with itself, or (∀x) (x = x), in which ∀ means “for every”; or simply that x is x.Aristotle cited the laws of contradiction and of excluded middle as examples of axioms. He partly exempted future contingents, or statements about unsure future events, from the law of excluded middle, holding that it is not (now) either true or false that there will be a naval battle tomorrow but that the complex proposition that either there will be a naval battle tomorrow or that there will not is (now) true. In the epochal Principia Mathematica(1910–13) of A.N. Whitehead and Bertrand Russell, this law occurs as a theorem rather than as an axiom That the laws of thought are a sufficient foundation for the whole of logic, or that all other principles of logic are mere elaborations of them, was a doctrine common among traditional logicians. The law of excluded middle and certain related laws were rejected by L.E.J. Brouwer, a Dutch mathematical intuitionist, and his school, who did not admit their use in mathematical proofs in which all members of an infiniteclass are involved. Brouwer would not accept, for example, the disjunction that either there occur 10 successive 7’s somewhere in the decimal expansion of π or else not, since no proof is known of either alternative, but he would accept it if applied, for instance, to the first 10100digits of the decimal, since these could in principle actually be computed

Answer 2

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Michael Pakaluk, Catholic University of America

Aristotle did affirm the existence of a “law of nature,” but he was admired by and influenced the American Founders more for his related views on republican government and the rule of law.
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Some of the Founders—notably, John Adams and James Wilson—refer frequently to Aristotle and show a deep acquaintance with his Politics. Moreover, Aristotle generally enjoyed an authority among the Founders like that which he had exercised over the learned world for centuries beforehand. A passage from Wilson’s treatise, Of the General Principles of Law and Obligation, is illustrative:
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“Why should a few received authors stand up like Hercules’s columns, beyond which there should be no sailing or discovery?” –To Aristotle, more than to any other writer, either ancient or modern, this expostulation is strictly applicable. Hear what the learned Grotius says on this subject. “Among philosophers, Aristotle deservedly holds the chief place, whether you consider his method of treating subjects, or the acuteness of his distinctions, or the weight of his reasons.

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