Note 19 for PHIL 110 at UMass
Note 19 for PHIL 110 at UMass
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This 12 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 19 views.
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Date Created: 02/06/15
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 who 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 no matter who you are you are a student you respect Kay no matter who X is X is a student X respects Kay VX SX ka VXSX gtRXk Example 3 1 o 2 P Jay Respects no Student there is no one who is a student AND whom Jay respects there is no X X is a student AND Jay respects X 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 10 Example 4b VX SX gt X R39s someone there is someone whom X R39s there is some y X R39s y Ely ny VXSX gtEy ny 11 Example 5 2 o 2 P noone Respects every Politician there is no one who respects every politician there is no X X respects every politician EX 3X X respects every politician 12 Example 5b X Respects every Politician no matter who you are IF THEN you are P X R s you no matter who y is IF THEN yisP XR sy Vy Py ny EX Vy Py gtny 13 Example 6 ZQ2P there is a Politician whom noone Respects who is a politician there is some one AND whom noone respects Xisap oitician there is some X AND noone respects X 3X PX amp noone R39s X EX PX amp noone R39s X 14 Example 6b EIX PX amp no one R39s X there is no one who R s X there is no y y R39s X Ey RyX EX PXamp Ey Ryx 15 Example 7 2 o 3 P there is a Politician who Respects every Citizen who is a politician there is some one AND who respects every C X is a politician there is some X AND X respects every C 3X PX amp X respects every C EIX PX amp X respects every C 16 Example 7b 3x PX amp x R39s every C no matter 39F YOU are C Who YOU are THEN X R s you no matter 39F y is C WhO y is THEN X R s y Vy Cy gt ny 3XPX amp VyCy gt ny 17 Example 8 2 o 3 P every Citizen Respects some Politician or other you are a citizen no matter who you are you respect some P X is a citizen no matter who X is X respects some P VX CX X respects some P VX CX gt X respects some P Example 8b VXCXgt X R39s some Politician there is someone who isa P AND whom X R39s there is some y yisaP AND X R39s y 3y Py amp ny VXCX gtEy PyampRXY 19 Example 9 2 o 3 P there is a Politician whom every Citizen Respects who is there Is some one 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 1O 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 Cy gt Ryx 3XPX amp VyCy gt Ryx 21 Example 10 2 o 3 P there is a Citizen who Respects no Politician there is some one who is a citizen AND who respects no P there is some X X is a citizen AND X respects no P 3X CX amp X respects no P EIX CX amp X respects no P 22 11 Example 10b 3XCXamp xR39snoP who is P there is no one AND whom X R39s yisP there is no y AND X R s y Ey Py amp ny EXCX amp EyPy amp ny 23 THE END 24 12
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