PHIL 250: Introduction to Symbolic Logic

tennant.9@osu.edu

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CLASSICAL RULE OF DOUBLE-NEGATION ELIMINATION

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¬¬A

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A

Explanation in words: From the double negation of any sentence A one may infer the sentence A itself. One thereby rests that conclusion A on the same set of assumptions on which its double negation depends.

Since this is neither an introduction rule, nor a genuine elimination rule (dealing with a single dominant occurrence of the operator concerned), there is no rule 'corresponding' to it! The rule of double-negation elimination obliterates any distinction between a sentence and its double negation.

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[¬I] [∧I] [∨I] [→I] [∀I] [∃I]
[¬E] [∧E] [∨E] [→E] [∀E] [∃E]
[EFQ]
[LEM] [Dil] [CR] [DNE]

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