Intro to Logic notes18

Intro to Logic notes18 - 18 Wednesday, August 08, 2007...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 18 Wednesday, August 08, 2007 10:21 AM Derivation rules for PL These follow the same rules as for SL. 1 2 3 1 2 3 SHOW: Fa Ga CD Fa As SHOW: Ga SHOW:~ x Fx&Gx ID x Fx&Gx As SHOW:X We need to introduce rules for dealing with quantifiers. 1 2 3 1 2 3 UD O ~ O I O ~ O O vF v x Rax Sx any and all This says that we can replace any free term with any constant we like. Example 1: 1 2 3 4 5 x Fx Hx Pr Fc Pr SHOW:Hc DD Fc Hc 1, O Hc 2,4, O Example 2: 1 2 3 4 5 6 7 x Sx Px Pr x Sx&Px Dx Pr Sm Pr SHOW:Dm DD Sm Pm 1, O Pm 3,5, O Sm&Pm Dm 2, O Intro to Logic Page 1 8 9 Sm&Pm 3,6,&I Dm 7,8, O I Example 1: 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 x Fx Hx Pr Fa Pr SHOW: xHx DD Fa Ha 1, O Ha 2,4, O xHx 5, 1 x Gx Hx Pr Gb Pr SHOW: x Gx&Hx DD Gb Hb 1, O Hb 2,4, O Gb&Hb 2,5,&I x Gx&Hx 6, I x~Rxa ~ xRax Pr ~Raa Pr SHOW: ~Rab ID Rab As SHOW:X DD x~Rxa 2, I ~ xRax 1,6, O xRax 4, I X 1 2 3 4 5 6 7 x yRxy yRxy Pr Raa Pr SHOW:Rab DD yRay yRay 1, O yRay 2, I yRay 4,5, O Rab 6, O Intro to Logic Page 2 ...
View Full Document

This note was uploaded on 04/07/2008 for the course PHILOSOPHY 201 taught by Professor Morgan during the Spring '08 term at Rutgers.

Ask a homework question - tutors are online