TAILIEUCHUNG - The Oxford Companion to Philosophy Part 57

The Oxford Companion to Philosophy Part 57. The book is alphabetized by the whole headings of entries, as distinct from the first word of a heading. Hence, for example, abandonment comes before a priori and a posteriori. It is wise to look elsewhere if something seems to be missing. At the end of the book there is also a useful appendix on Logical Symbols as well as the appendices A Chronological Table of Philosophy and Maps of Philosophy. | 540 logical laws logical laws. Propositions true on logical grounds alone logical truths. For example the laws of non-contradiction identity excluded middle and double negation. In propositional calculus the law of non-contradiction is - p -p It is not the case that both p and not p in predicate calculus Vx - Fx. -Fx For any x it is not the case that x is F and x is not F In propositional calculus the law of identity is p p If p then p in predicate calculus Vx Fx Fx For any x ifx is F then x is F in predicate calculus with identity Vx x x For any x x is x in modal predicate calculus with identity Vx x x Necessarily for any x x is x In propositional calculus the law of excluded middle is p v -p Either p or not p in predicate calculus Vx Fx v -Fx For any x either x is F or x is not F In propositional calculus the laws of double negation are p p Ifnot not p then p and p p Ifp then not not p and in predicate calculus Vx Fx Fx For any x if x is not not F then x is F and Vx Fx Fx For any x ifx is F then x is not not F . Aristotle does not distinguish sharply between logical laws laws of thought and laws ofbeing so the consistent the conceivable and what could exist coincide and the inconsistent the inconceivable and what could not exist coincide. Aristotle s informal statements of the law of non-contradiction include For the same thing to hold good and not to hold good simultaneously of the same thing and in the same respect is impossible Metaphysics r 1005b Vx - Fx. -Fx or arguably Vx - Fx. -Fx and Nor . . . is it possible that there should be anything in the middle of a contradiction 1011b - p . -p . His statement of the law of excluded middle is but it is necessary either to assert or deny any one thing of one thing 1011b Vx Fx v -Fx or arguably D Vx Fx v -Fx . Aristotle says it shows a lack of education to demand a proof of logical laws. He does however bring a self-refutation argument against their putative denial by his Pre-Socratic predecessors Protagoras who .

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