PHIL 110 Lecture 12: Note 7
16 Mar 2017
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Dr mc"s philosophy 110 (1171) part notes 7#1 . Announcements, etc. (you should try this without my helpful justifications: p [(q r) v s, (q r) ~p, t ~s. Using cp: p [(q r) v s, (q r) ~p, t ~s. / a (b a) p / a (b c) We can apply cp twice in the same proof (if we"re careful!: c. Nested assumptions are fine, provided that the further assumptions are discharged before your first one). (lines cannot intersect: c. There are no undischarged premises, so the conclusion is a theorem. You could prove it from scratch a theorem is a law of logic . Show that, by assuming something, you can derive an absurdity . (i. e. an explicit contradiction) Thus, you"ve shown that assumption (given the premises) to be false. This form of proof is also called: reduction as absurdum . Assume the negation of the conclusion you want, and derive an explicit contradiction.
