Class Note for PHIL 110 at UMass(16)
Class Note for PHIL 110 at UMass(16)
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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Massachusetts taught by a professor in Fall. Since its upload, it has received 21 views.
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Date Created: 02/06/15
INTRO LOGIC DAY 19 Translations in PL 5 Review 2 Quantifiers 1 Predicate everyone respects everyone VX Vy RXy someone respects someone EIX Ely RXy no one respects everyone NEIX Vy RXy no one is respected by everyone NEIX Vy RyX everyone respects someone or other VX Ely RXy there is someone Whom everyone R s EIX Vy RyX there is someone who respects no one Elx Ey ny there is someone Whom no one respects Elx Ey Ryx Review 1 Quantifier 1 Predicate Jay respects someone EIX RjX Jay respects everyone VX RjX Jay respects no one N EIX RjX some one respects Kay EIX RXK everyone respects Kay VX RXK noone respects Kay EX RXK New Material 1 quantifier 2 predicates 2 quantifiers 2 predicates 2 quantifiers 3 predicates Example 1 3 Example 3 3 every student respects Kay Jay respects some at least one student IF W are a student there is someone Who is a S whomj respects no matter who you are THyEN you respeCt ay who is a S and whomj R39s no ma erwho X is IF x is a student there is someone x x is a S andj R39s x THEN x respects Kay 3x Sx amp RJX Vx Sx gt ka 5 7 Example 2 D Example 4 D no Student respects Jay noone respects every politician there is no one who respects every politician there is no39one Who is a S and Who R39sj there is no x x respects every politician there is no x x is a S and x R39sj NEIX X respects eVery POIitiCian 3x Sx amp ij Example 4b 3 x respects every politician no matter who you are IF you are P THEN X R39s you IF y is P THEN x R s y Vy Py a ny wax no matter who y is VyPyany 3x Vy Py gt ny Example 5b x R39s someone who is R39ed by X there is someone Vx 8x a there is some y x R39s y Ely ny whom x R39s VxSx gt3nyy 11 Example 5 every Student respects someone or other no matter who you are IF you are S THEN you R someone no matter who x is IF x is 8 THEN x R39s someone Vx Sx x R39s someone Vx Sx a x R39s someone Example 6 there is a politician whom noone respects there is who is a P whom noone R s someone who is P AND whom noone R39s there is some x x is P AND noone R39s x Elx PX amp noone R39s x 3x Px amp noone R39s x 10 12 Example 6b 3 Example 7b no one R39s X every C R39s X there is no one who R s X no matterwho you are if you are Cthen you R X EIX PX amp there is no y y R39s x 3x Px amp no matter who y is if y is C then y R s x Ey RyX Vy Cy Ryx 3XPXamp3yRyX Vyicya Ryx EX PX amp VyCy gt Ryx 13 Example 7 D Example 8 there is a P iiti ian Whom eVery Citizen ReSPeCtS every Citizen Respects some Politician or other there is who is a P whom every C R39s no matter who you are if you are C then you R some P someone who is P AND whom every C R39s no matter who X is if X is C then X R39s some P there is some X X is P AND every C R39s X VX CX X R39S some P EIX PX amp every C R39s X VX CX gt X R39s some P EX PX amp every C R39sx 14 Example 8b x R39s some P who is a P R39ed by x Example 9b 3 x R39s no P there is no who is a P one AND who is R39ed by x 3X CX amp there is noy y ISP AND yIs Red byx yIsP AND xR39sy Nay Py amp ny Ely Py amp ny EXCX amp 3yPy amp ny 19 there is who is a P AND someone who is R39ed byx VX Cxa WhoisP AND Whome39s there is some y y is P AND x R39s y 3y Py amp ny 3y Py amp RXy VXCX gt 3yPy amp ny 17 D Example 9 there is a Citizen who Respects no Politician who is a C who R39s no P there is someone who is a C AND who R39s no P there is some x xisaC AND xR39snoP Elx Cx ampxR39snoP 3xCxampxR39snoP 18
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