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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INTRODUCTION RULE FOR NEGATION (¬I)

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_(i)_

A

:

:

⊥

____(i)

¬A

Explanation in words: In order to infer to a conclusion with a dominant occurrence of negation, one must assume A and deduce ⊥ (absurdity)---as indicated by the descending dots. By taking the indicated step of negation introduction, one thereby discharges the assumption A. This means that the conclusion ¬A no longer depends on the assumption A. Instead, it depends only on whatever other assumptions might have been used, besides A, to obtain the absurdity.

Compare the corresponding elimination 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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