Ps10-2
.pdf
School
Langara College**We aren't endorsed by this school
Course
PHIL 1102
Subject
Mathematics
Date
Dec 18, 2024
Pages
4
Uploaded by DoctorBook2793
11ViAll2VyB(y)2I FyAYBD2Aln)A(n)-Elim:1A(n)vB(n)VIntroi35B(n)YElim:25x(A(x)vB(x))-Intro:46B(n)1A(n)1 Intro:4,565x(A(x)vB(x))-Elim:2,3-57Fz(B(z)mA(z))Intro:3-67zB(z)8nB(n)A(n)vB(n)VIntroigT5x(A(x)~B(x)-Intro:9115x(A(vB(u)JElim:7,8-10125,/A()vB(x))VElim:1,2-6,7-131J,7y(A(x)mA(y)n+B(x,y)4177 Al2Vicky((A(x)mA(yl)->B(x,y))2AnIn)Alm)nA(n)m-B(m,n)A(n)iiA(m)1A(n)&Elim:3E7xA(x)=>Intro:37B(m,n)&Elim:3↓↓Intro:1,46(A(m)-A(n))->B(m,n)-Elim:26<A(n)7Intro:3-4B(m,n)>Elim:4,67Up<AkIntroi2-6·t1Intro:5,7↓-Elim:1,3-81-EicFy((A()vA(yl)->B(x,y))<Intro:2 - a5 7./SameShape(1,a) nCube(x)L(Tet(alvDodec(a)J,(P(x,a)1Q(x)-7(R(a)vStal)-J../SameShape(1,a) rCube(x)L(Tet(alvLarge(a)#
61 J../SameShape(1),a) nCube(x)2TetlalvDodec(alISameShape(n,a)rCube(n)iCube(a)->Elim:A8,3Tet(a)6Cube(a)n Tetfal1Intro:4,5TFx(Cube(c)nTet(y)-Elim:6g↓1Intro:7,A,9Dodec(a)10Dodec(al1Cubela)1Intro:4,911-(Dodec(i)1Cube(c))JElim:1012↓↓Intro:A3,1113↓VElim:2,5-8,9-1214↓7Elim:113-14L(Tet(alvDodec(a)7Intro:2-14717x(A(x)1B(x))2Fafy((A(x)- Alyl)>x=y)3A(m)- B(m)4A(m)1Elimi5B(m)1Elimi6#7(A(m)1A(n))->m=nVElim:28A(n)A(m)1A(n)1Intro:4,S↑m=n->Elim:7,911A(n)->m=n->Intro:8-1012Fy (A(y)+m=y)-Intro:6-113A(m)+Yy(A(y)>m=y)B(m)~Intro:4,5,1214Fx(Ak)nfy(A(y)+(=y)1B(x))-Intro:1315Fx(A()nfy(Aly)+(=y)1B(x1)JElim:1,3-14g1Vic(5y((x,y->((x,6)2((c,b)aFC3< ((a,a)4a=c5((a,b)=Elim:2,467 y((a,y)-Intro:57by ((a,y)>(la,c)VElim:18((a,c)->Elim:6,79L(a,a)=Elim:4,910+↓Intro:3,911a+C-Intro:4-10
Philosophy 1102 Instructor: Richard Johns Problem Set 10 Hand in your answers during class on Wednesday, November 27. [Please write your proofs neatly, using enough paper so that each proof is all in one place. Use only the rules provided in the handout “Rules of F+”.] 1. Show that the argument below is FO con by giving a formal proof.[6 marks]2. Show that the argument below is FO con by giving a formal proof. [6 marks]3. Show that the argument below is FO con by giving a formal proof. [6 marks] [N.B. you can eliminate the xand yquantifiers in one step if you like, since they’re touching.] 4. Show that the argument below is FO con by giving a formal proof. [6 marks]
5. Show that the argument below is notFO con, by doing the following: [5 marks] (a) Write the argument as it appears through FO goggles (b) Provide a counter-example set of predicates to replace the nonsense predicates used in part (a), and (c) Draw a counter-example world, for the new argument (with the new predicates) 6. By giving a formal proof, show that the argument in Qu. 5 becomes FO con when suitable shape axioms (see below) are added as premises. (Cite the axioms as ‘A1’, ‘A2’, etc.)[7 marks] Shape Axioms A1. x (Cube(x) Tet(x)) A2. x (Tet(x) Dodec(x)) A3. x (Dodec(x) Cube(x)) A4. x (Tet(x) Dodec(x) Cube(x)) A5. x y ((Cube(x) Cube(y)) →SameShape(x, y)) A6. x y ((Dodec(x) Dodec(y)) →SameShape(x, y)) A7. x y ((Tet(x) Tet(y)) →SameShape(x, y)) A8. x y ((SameShape(x, y) Cube(x)) →Cube(y)) A9. x y ((SameShape(x, y) Dodec(x)) →Dodec(y)) A10. x y ((SameShape(x, y) Tet(x)) →Tet(y))7. Show that the argument below is FO con by giving a formal proof.[7 marks] 8. Show that the argument below is FO con by giving a formal proof. [7 marks] [Make sure you understand what the first premise says. An important question then is: Does Celine love Celine?]