PHIL 250: Introduction to Symbolic Logic

tennant.9@osu.edu

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Choose Destination My web-page Teaching PHIL 250 PHIL 650 Basic concepts and techniques Truth tables Universal-Introduction Universal-Elimination Existential-Introduction Existential-Elimination Negation-Introduction Negation-Elimination Conjunction-Introduction Conjunction-Elimination Disjunction-Introduction Disjunction-Elimination Conditional-Introduction Conditional-Elimination Absurdity rule Classical reductio Double negation elimination Law of Excluded Middle Dilemma

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ELIMINATION RULE FOR NEGATION (¬E)

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A

¬A

_______________

⊥

Explanation in words: In order to infer from a negative premiss ¬A, one must prove the "unnegated" minor premiss A. By taking the indicated step of negation elimination, one thereby blames the resulting absurdity (⊥) on the combined assumptions on which the contradictory premisses A and ¬A respectively rest.

Compare the corresponding introduction rule for ¬

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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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