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by: Dandre Von
Dandre Von
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This 5 page Class Notes was uploaded by Dandre Von on Thursday October 22, 2015. The Class Notes belongs to PHIL 2310 at Texas Tech University taught by Hom in Fall. Since its upload, it has received 124 views. For similar materials see /class/226487/phil-2310-texas-tech-university in PHIL-Philosophy at Texas Tech University.

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Date Created: 10/22/15
Philnsnphy 2310 Spring 2011 Midterm 3 Practice Problems Model Answers Evens 1 Translate the following statements into PQ schemata Be sure to specify the UD and the assignment of predicates to predicate letters NOTE For convenience predicate letters will be left implicit for these answers but this practice is not acceptable on homework quiz or exam questions b Every celebrity despises all actors VXCX D VyAy D ny d Nothing is performed by every actor EIXVyAy D Pyx f Anyone who despises all moves is despised by actors VXPX 39 VyMy 3 ny D VzAz D sz h There is a celebrity in Hollywood who is more famous than any celebrity in New York 3XCX Hx Vyny Ny D M j There is someone who knows everyone who knows himher 3xVyny D ny UDpersons 1 If anyone gets something she does not deserve then not everyone deserves everything she gets 3XPX 39 EbXny 39 NDXy 3 VXPX 3 VYXGXy 3 DXY n If a Laker respects all Celtics who respect him then that Laker is respected by all Celtics VxLx 39 VyCy 39 RyX 3 ny D VyCy 3 RyX p If no Laker respects only Celtics then all Lakers respect every Celtic ElxLx 39 VyRXy 3 Cy 3 VXXLX D VyCy 3 ny r No Laker respects anyone unless everyone adores him 3xLx 3yPy ny vszz 3 Azxu OR VXLX 39 ElyPy 39 ny 3 VzPz D Azx t Celtics who are respected by everyone respect every Laker who respects them VXCX 39 VyPy D Ryx D VzLz 39 sz D sz V Every Celtic who respects Kobe is respected by some Laker who respects Kobe VXCX 39 ka D EIyLy 39 Ryk 39 Ryx x Either Kobe respects every Celtic who respects him or else no Laker is respected VXCX 39 ka D ka v EIXLX 39 ElyPy 39 Ryx z A Laker respects a Celtic just in case he is respected by that Celtic mom 3 WM 3 ltny a Ryxu Philnsnphy 2310 Spring 2011 2 4 Provide interpretations that make the schemata in problem 1a 1ktruefalse Take the UD to be 123 and find non empty extensions where possible b VXCX 3 VyAy 3 ny 1 A2 Dlt12gt Make b false by any of the three ways 1 adding another element to C 2 adding another element to A 3 replacing lt12gt in D with some other ordered pair d 3xVyAy 3 Pyx Plt13gt Make d false by placing lt23gt in P f VXPX VyMy D ny 3 vzAz 3 sz 1 M3 A2 Dlt13gt lt21gt Make f false by removing lt21gt from D by adding another element to A h 3XCx 39 Hx 39 VyCy 39 Ny D ny C12 H 1 N2 Flt12gt Make h false by removing lt12gt from F by removing 1 from H by adding another element to N j 3xVyKyX 3 ny Klt12gt lt21gt Make j false by removing one of the elements in K or by adding lt5 1gt and lt32gt Philosophy 2310 Spring 2011 5 Translate the following schemata into clear idiomatic English Use the following UD and vocabulary UD 2 everything P D is a professor D D deserves to be fired S D is a student of D B D bores b VXPX 39 VySyx D Bxy D Dx Every professor who bores all of her students deserves to be fired d HXXPX VyPy D Bxy Some professor bores every professor 6 Give an interpretation which proves that the premises do not PQ imply the conclusion Provide non empty extensions if possible b 1 3xMx NX 2 3xMx Ox 3 VXOX D Nx Something is in both M and N Something is in both M and 0 Something is in 0 but NOT in N UD123 M12 N1 O2 d 1 VXAX D ElyBy ny 2 3xAx VyBy D ny 3 EIXEyny ny Typo there should be in front of the conclusion Every aardvark cares for at least one beaver Some aardvark despises all beavers Something cares for and despises the same thing UD123 A1 B2 Clt12gt Dlt12gt Philnsnphy 2310 Spring 2011 7 Natural Deduction b Deduce VXHX D Sx from VXHX 3 AK and EIXAX SK 1 1 VXHX 3 AK 2 2 3XXAX 39 SK 1 3 HX 3 AK 2 4 VXAX 39 SK 2 5 AX 39 SK 6 6 HX quotUPNH U U CIOCI HOD 1 126 7 Sx 356 TF 12 8 HX 3 Sx 6 7 D 12 9 VXHX 3 SX 8 UG d Deduce EIXKXX from VzKzz 3 M2 Nz and ElzNz 1 1 vzKzz 3 Mz Nz P 2 2 EIzNz P 1 3 K22 3 Mz Nz 1 U1 4 4 EI XKXX P 4 5 VXKXX 4 CQ 4 6 VXKXX 5 TF 4 7 K22 6 U1 14 8 M2 Nz 37 TF 14 9 Nz 8 TF 14 10 vzNz 9 UG 2 11 VzNz 2 CQ 124 12 vzNz VzNz 10 11 TF 12 13 EIXKXX 3 vzNz VzNz 4 12 D 12 14 EIXKXX 13 TF f Deduce p E VXFX from Vxp E Fx Typo missing FX from first schema 1 1 VXXP E FX P 1 2 p 5 FX 1 U1 3 3 p F 13 4 Fx 23 TF 13 5 VXFX 4 UG 1 6 P 3 VXFX 3 5 D 7 7 VXFX P 7 8 Fx 7 U1 17 9 p 28 TF 1 10 VXFX 3 P 7 9 D 1 11 pa VXFX 610 TF Philnsnphy 2310 Spring 2011 9 Schematize the following argument assuming the UD is restricted to persons and show by deduction that the premises imply the conclusion Premise 1 Alexander was a great leader Premise 2 Every great leader is wise Conclusion Therefore someone is a great leader just in case they are wise 1 1 Gx P 2 2 VxGx D Wx P EIxGx E Wx 2 3 Gx D Wx 2 U1 1 4 Wx D Gx 1 TF 12 5 Gx E Wx 34 TF 12 6 EIxGx E Wx 5 EG Notice that the conclusion can be read as VxGx E Wx but the premises do not imply that conclusion Prove to yourself that implication does not hold by finding an interpretation that is a counterexample Also get clear on exactly why VxGx E Wx could not be line 6 on the proof above


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