PHIL 279 Lecture 6: Phil 279 Week 6.docx

• School: University of Calgary
• Department: Philosophy
• Course: PHIL 279
• Professor: John James Mac Intosh

Document Summary

A set is consistent if and only if it is satisfiable. We can prove inconsistency by showing that we can derive a contradiction (any sentence and its same sentence s negation) {p -> p, q -> p, r -> (q s), r s} (this set is not satisfiable, therefore it is not consistent) To derive, we must treat these as premises! Depends on the line change (the sentence number it is justified from) Changing a conditional to a disjunction and vice versa. 2 (1) a b (2) a (3) a (4) b (5) a->b. 1 (6) b (7) b->b (8) b (9) a -> b. 1 (1) a -> b (2) ( a b) (3) a (4) a b (5) a (6) b (7) a (8) a b. In line 2, we want a b. Either not a or b ( a b) So: if a then b ( a b.