Introduction To Logic
Introduction To Logic PHIL 110
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This 12 page Class Notes was uploaded by Ms. Jada Ernser on Friday October 30, 2015. The Class Notes belongs to PHIL 110 at University of Massachusetts taught by Gary Hardegree in Fall. Since its upload, it has received 12 views. For similar materials see /class/232334/phil-110-university-of-massachusetts in PHIL-Philosophy at University of Massachusetts.
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Date Created: 10/30/15
INTRO LOGIC DAY 19 Translations in PL 5 Polyadic Predicate Logic Day 2 Old Material 1 quantifier 1 predicates 2 quantifiers 1 predicates New Material 1 quantifier 2 predicates 2 quantifiers 2 predicates 2 quantifiers 3 predicates Review 1 Quantifier 1 Predicate Jay respects someone EIX RjX Jay respects everyone VX RjX Jay respects no one EIX RjX some one respects Kay EIX RXk everyone respects Kay VX RXk noone respects Kay NEIX RXk Review 2 Quantifiers 1 Predicate everyone respects everyone VX Vy RXy someone respects someone EIX Ely RXy noone respects everyone NEIX Vy RXy noone is respected by everyone NEIX Vy RyX everyone respects someone or other Vx Ely ny there is someone whom everyone R s EIX Vy RyX there is someone who respects noone EIX Ely RXy there is someone whom noone respects EIX Ely RyX New Material Example 1 1 o 2 P some Student Respects Jay who is a student there is some one AND lwho respects Jay X is a student there is some X AND X respects Jay 3X SX amp RXj EXSXampRXj Example 2 1 o 2 P every Student Respects Kay you are a student no matter who you are you respect Kay X is a student no matter who X is X respects Kay RXk VX SX VXSX gtRXk Example 3 1 o 2 P Jay Respects no Student there is no one who is a student AND lwhom Jay respects there is no X X is a student AND Jay respects X 3xk SX amp RjX 3XSXampRjX Example 4 2 o 2 P every Student Respects someone or other no matter who you are you are a student you respect someone no matter who X is X is a student X respects someone VXSX X respects someone VX SX gt X respects someone Example 4b IVXSX gt X R39s someone I there is someone whom X R39s there is some y X R39s y 3y ny VXSX Enyy Example 5 2 o 2 P noone Respects every Politician there is no one who respects every politician there is no X EX X respects every politician 3XX respects every politician Example 5b EX X Respects every Politician IF you are P THEN X R s you IF y is P THEN X R s y Vy Py gt ny no matter who you are no matter who y is I EXVyPy gtRq 13 Example 6 2 o 2 P there is a Politician whom noone Respects who is a politician there is some one AND lwhom noone respects X is a politician there is some X AND noone respects X Elx PX amp noone R39sx EX PX amp noone R39s X L Example 6b EXPXamp noone R39sx there is no one who R s X there is no y y R39s X Ey RyX EX PXamp Ey Ryx Example 7 2 o 3 P there is a Politician who Respects every Citizen there is some one who is a politician AND who respects every C there is some X X is a politician AND X respects every C 3X PX amp X respects every C EX PX amp X respects every C L Example 7b 3X PX amp X R39s every C no matter IF you are C who you are THEN X R s you no matter IF y is C who y is THEN X R s y Vy Cy gt ny 3XPX amp VyCy gt ny Example 8 2 o 3 P every Citizen Respects some Politician or other IF you are a citizen no matter who you are THEN you respect some P IF X is a citizen no matterwho X is THEN X respects some P Vx CX xrespectssomeP Vx Cx gt x respects some P Example 8b VXCXgt X R39s some Politician there is someone who isa P AND lwhom X R39s there is some y yisaP AND X R39s y 3y Py amp ny VXCX gt EyPy amp ny Example 9 2 o 3 P there is a Politician whom every Citizen Respects there is some one who is a politician AND whom every C respects there is some X X is a politician AND every C respects X 3X PX amp every C respects X 3X PX amp every C respects X 20 Example 9b 3x PX amp every C R39s X no matter 39F YOU are C Who YOU are THEN you R X no matter 39F y is C WhO y is THEN y R s X Vy M Cy gt Ryx EIXPX amp VyCy gt RyX Example 10 2 o 3 P there is a Citizen who Respects no Politician who is a citizen there is some one AND who respects no P X is a citizen there is some X AND X respects no P EIX CX amp X respects no P EIX CX amp X respects no P 22 Example 10b 3XCXamp xR39snoP who is P AND whom X R39s y is P AND X R s y Ey M Py amp ny there is no one there is no y iaxmx amp EyPy amp ny 3 THE END 24