PHIL 250: Introduction to Symbolic Logic

tennant.9@osu.edu

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CLASSICAL RULE OF DILEMMA (Dil)

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__(i)

___(i)

A

¬A

:

:

B

B

_________________(i)

B

Explanation in words: In order to infer to a desired conclusion B, it suffices to prove B from the case assumption A, and prove B from the case assumption ¬A. By taking the indicated step of dilemma, one thereby rests the resulting conclusion B on the combination of: (1) the assumptions of the first case proof (other than the case assumption A, which is discharged) and (2) the assumptions of the second case proof (other than the case assumption ¬A, which is also discharged).

The case assumptions A and ¬A are the two 'horns' of the dilemma.

Compare the classical law of excluded middle , which can easily be derived by using dilemma and two steps of disjunction introduction.

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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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