No new reading for Wednesday. Exam #2 is Friday. Office hours today are cancelled. Rescheduled for tomorrow, 2-4 p.m. Talk today at 3:15 in HUM 1B50. Colin.

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PROOF BY CONTRADICTION

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Presentation transcript:

No new reading for Wednesday. Exam #2 is Friday. Office hours today are cancelled. Rescheduled for tomorrow, 2-4 p.m. Talk today at 3:15 in HUM 1B50. Colin Allen, “A Perceptual Account of Symbolic Reasoning.”

Exam #2: Rough Outline -Use a truth-table to categorize a single statement (as a tautology, contradiction, or contingent statement) -Truth-table test for logical equivalence -Truth-table test for validity (method of exhaustive search) -Constructing an interpretation to test for validity -Proofs One of each type, except proofs (two of these)

~Elimination a 1,…,a n (j) ~q.. b 1,…,b n (k) q.. a 1,…,a n, b 1,…,b n (m) ∧ j, k ~E j > k or j k or j < k

~Introduction j (j) p Assumption.. a 1,…,a n (k) ∧.. {a 1,…,a n }/j (m) ~ p j, k ~I j > k, j k, j < k, or j = k

DN (Double Negation) a 1,…,a n (j) ~~p.. a 1,…,a n (k) p j, DN This rule is needed when you use ~I to derive something “positive” (i.e., something that does not have a tilde as its main connective). Assume the negation of your goal. Use ~I to get two adjacent tildes. Then use DN to arrive at your target.