PHIL 10 Lecture Notes - Lecture 4: Conditional Proof, Nsb Di 3, Junkers J.I
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4 replacement proofs, indirect proof, & tautologies. Double negation (dn: you can add and subtract tildes as long as you do it in pairs. You can(cid:859)t just add o(cid:374)e (cid:271)e(cid:272)ause it (cid:449)ould(cid:374)(cid:859)t (cid:271)e (cid:858)truth preser(cid:448)i(cid:374)g(cid:859) (cid:272)ha(cid:374)gi(cid:374)g so(cid:373)ethi(cid:374)g fro(cid:373) true to false. (cid:448) :: (cid:448) : you can swap disjunctions with disjunctions and conditionals with conditionals. Can be used on part of a line (the rest of the line stays intact: a (b c, a (~b v c) x ce, ~a v (~b v c) y ce. Can go in either direction: ~a (~b c, a (~b v c, a v (b v c) x ce y ce. Ex: c v (d e, a ~c, {~~a (e d)} r, ~c (d e) D e 4, 6 mp: a (d e) 5-7 cp: ~~a (d e) 5 dn. 10 ~~a (e d) 6 comm: r, ~~r.
