References to Irving Copi, Symbolic Logic, are to the fifth edition, Macmillan, 1979.

I include the translation exercises, but not the derivation exercises, that Copi answers himself in the back of the book.

Remember that there are many ways to prove a valid argument valid with a derivation. If my way differs from your way, yours may still be perfectly good.

I welcome corrections.

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Table of Contents

• Translations at pp. 88-89
• Derivations at pp. 103-04
• Translations + derivations at pp. 104-05

1. If anything is damaged, someone will be blamed. (x)[Dx (y)(Py · By)]
   • These variations seem acceptable but are not: (x)[Dx (y)(Py · By)], and (x)(y)[Dx (Py · By)]. The reason is that they are existentially quantified conditionals. (To see why existentially quantified conditionals are usually undesirable, see comments to exercise 2, below. ) The same is true for analogous variations on the exercises below.
   • However, if we take the first of these unacceptable translations and limit the scope of the first quantifier, then we no longer have an existentially quantified conditional: (x)Dx (y)(Py · By). Is this acceptable now? This says: if at least one thing is damaged (but not necessarily for all damaged things), some one will be blamed. This is close but not as close as my translation above, which says: for all things that are damaged (if any, but with no exceptions), some one will be blamed.
2. If anything is damaged, the tenant will be charged for it. (x)(Dx Cx)
   • Paraphrase: All things that are damaged are charged to the tenant.
   • Note that this proposition is not multiply general; it has only one quantifier.
   • Copi wanted an existential quantifier in exercise 1; by analogy one might want one here. But like most existentially quantified conditionals, (x)(Dx Cx) does not mean what we want it to. It is equivalent to (x)(~Dx Cx), which says that there is something that is either not damaged or charged to the tenant. It commits us to the existence of that something; the English does not. Moreover, it is satisfied (made true) by my chalk, since it is undamaged; and this is certainly not intended by the speaker.
   • But (x)(Dx · Cx) is clearly worse, for it asserts that there is something that is damaged that has been charged to the tenant. Hence I prefer the universal quantifier here.
3. If nothing is damaged, nobody will be blamed. (x)~Dx (y)(Py ~By)
   • This is equivalent to ~(x)Dx (y)(Py ~By).
4. If something is damaged, but nobody is blamed, the tenant will not be charged for it. (x)[[Dx · (y)(Py ~By)] ~Cx]
   • See comment to exercise 2, above. Here the "if something" initially pushes us to use an existentially quantified conditional; but since such expressions don't mean what we want them to, we retreat to a universal quantifier. Hence the paraphrase underlying our translation is: All things that are damaged when nobody is blamed will not be charged to the tenant. Or: Nothing which is damaged when nobody is blamed will be charged to the tenant.
5. If any bananas are yellow, they are ripe. (x)[(Bx · Yx) Rx]
   • Paraphrase: All yellow bananas are ripe.
   • See comments to exercises 2 and 4, above.
6. If any bananas are yellow, then some bananas are ripe. (x)(Bx · Yx) (y)(By · Ry)
   • Note this is not an existentially quantified conditional. It is an unquantified conditional with an existentially quantified antecedent and consequent.
7. If any bananas are yellow, then if all yellow bananas are ripe, they are ripe. (x)[(Bx · Yx) [(y)[(By · Yy) Ry] Rx]]
   • Paraphrase: All yellow bananas if all yellow bananas are ripe are ripe.
   • See comments to exercises 2 and 4, above. Making the x quantifier existential is tempting, but then we'd have an existentially quantified conditional.
8. If all ripe bananas are yellow, some yellow things are ripe. (x)[(Bx · Rx) Yx] (y)(Yy · Ry)
9. If all officers present are either captains or majors, then either some captains are present or some majors are present. (x)[(Ox · Px) (Cx Mx)] [(y)(Cy · Py) (z)(Mz · Pz)]
10. If any officer is present, then either no majors are present or he is a major. (x)[(Ox · Px) [(y)(My ~Py) Mx]]
    • Paraphrase: For all present officers, either none are majors or that one is a major.
    • See comments to exercises 2 and 4, above. The x quantifier cannot be existential, for then we'd have an existentially quantified conditional.
11. If some officers are present, then if all officers present are captains, then some captains are present. (x)(Ox · Px) [(y)((Oy · Py) Cy) (z)(Cz · Pz)]
    • Note that this is not an existentially quantified conditional; it is an unquantified conditional with an existentially quantified antecedent.
    • If we wanted to say "Cx" at the end of this formula, instead of introducing the new quantifier on "z", then we'd have to extend the scope of the first (x) quantifier to the end of the formula. That would turn the whole thing into an existentially quantified conditional, which is a good reason not to do it.
    • If we make the x quantifier universal, then we could put the rest of the formula within its scope, drop the z quantifier, and change Cz and Pz at the end to Cx and Px. The only problem with this approach is a slight clash with the English meaning. It wouldn't say that all officers were present, but it would say that, for all officers that are present, then (if all officers present are captains) they are captains.
12. If some officers are present, then if all officers present are captains, then they are captains. (x)[(Ox · Px) [(y)[(Oy · Py) Cy] Cx]]
    • Paraphrase: All present officers if all present officers are captains are captains.
    • The syntax of this sentence, hence its translation, is identical to that in exercise 7.
    • Here we sorely want to use an existential quantifier: (x)[(Ox · Px) [(y)[(Oy · Py) Cy] Cx]]. The trouble with this, however, is that creates an existentially quantified conditional. This is not one of the rare cases where we really mean what an existentially quantified conditional would say, however. It would say (after a few transformations that preserve equivalence) that there is something that is either not a present officer or that has the property of being a captain if all present officers are captains. But this sentence is satisfied by my chalk, since my chalk is not a present officer.
    • Another tempting solution would be to retain the existential quantifier but let its scope stop after the antecedent, and not envelope the whole conditional: (x)(Ox · Px) [(y)[(Oy · Py) Cy] Cx]]. The problem with this is that the "x" in the final Cx is free; hence we will have produced a propositional function (lacking a truth-value), while the English sentence was a proposition (bearing a truth-value).
    • Notice that both my translation and the English sentence are non-committal on the existence of present officers. This supports the decision to use a universal quantifier.
    • Also notice how the particular-seeming "they" does not compel an existential quantifier. This is true even of the "he" in exercise 20, below. Recall this usage in other, more familiar English sentences. "The horse is a noble animal; she swats flies with her tail. " This is clearly a statement about all horses that would take a universal quantifier.
13. If all survivors are fortunate and only women were survivors, then if there are any survivors, then some women are fortunate. (x)[(Sx Fx) · (Sx Wx)] [(y)(Sy) (z)(Wz · Fz)]
    • We could just as legitimately use, say, (z)(Sz Wz) in place of Sx Wx.
14. If any survivors are women, then if all women are fortunate, they are fortunate. (x)[(Sx · Wx) [(y)(Wy Fy) Fx]]
    • Paraphrase: All women survivors if all women are fortunate are fortunate.
    • See comment to exercise 12, above.
15. If there are any survivors and only women are survivors, then they are women. (x)[[(Sx) · (y)(Sy Wy)] Wx]
    • Paraphrase: All survivors if all survivors are women are women.
    • See comment to exercise 12, above.
16. If every position has a future and no employees are lazy, then some employees will be successful. [(x)(Px Fx) · (y)(Ey ~Ly)] (z)(Ez · Sz)
17. If any employees are lazy, then if some positions have no future, then they will not be successful. (x)[(Ex · Lx) [(y)(Py · ~Fy) ~Sx]]
    • Paraphrase: All lazy employees if some positions have no future will be unsuccessful.
    • See comment to exercise 12, above.
18. If any employees are lazy and some positions have no future, then some employees will not be successful. [(x)(Ex · Lx) · (y)(Py · ~Fy)] (z)(Ez · ~Sz)
    • Note that this is not an existentially quantified conditional. It is an unquantified conditional. Not even the antecedent is quantified; rather it is an unquantified conjunction whose conjuncts are existentially quantified.
19. If any husband is unsuccessful, then if all wives are ambitious, then some wives will be disappointed. (x)(Hx · ~Sx) [(y)(Wy Ay) (z)(Wz · Dz)]
    • Note that this is not an existentially quantified conditional; it is an unquantified conditional whose antecedent is existentially quantified.
20. If any husband is unsuccessful, then if some wives are ambitious, he will be unhappy. (x)[(Hx · ~Sx) [(y)(Wy · Ay) Ux]]
    • Paraphrase: All unsuccessful husbands if some wives are ambitious will be unhappy.
    • See comment to exercise 12, above.

I omit the exercises on pp. 92, 100-01, because they are neither translations nor derivations.

1. (x)(Dx Ex) 2. Da Ea 3. Da 4. Ea 5. (y)(Ey Fy) 6. Ea Fa 7. Fa 8. (y)(Ey Fy) Fa 9. Da [(y)(Ey Fy) Fa]

/ Da [(y)(Ey Fy) Fa] 1 UI ass. for CP 2,3 MP ass. for CP 5 UI 4,6 MP 5-7 CP 3-8 CP

1. (x)[Gx (y)(Hy Iy)] 2. Gx (y)(Hy Iy) 3. (x)Gx 4. Gx 5. (y)(Hy Iy) 6. (x)Gx (y)(Hy Iy)

/ (x)Gx (y)(Hy Iy) 1 UI ass. for CP 3 UI 2,4 MP 3-5 CP

1. (x)Jx (y)Ky 2. Jx (y)Ky 3. (x)[Jx (y)Ky] 4. (x)[Jx (y)Ky]

/ (x)[Jx (y)Ky] 1 EI, ass 2 EG 1,2-3 EI

1. (x)(Nx Ox) 2. Px 3. (y)(Py Ny) 4. Px Nx 5. Nx 6. Nx Ox 7. Ox 8. (y)(Py Ny) Ox 9. Px [(y)(Py Ny) Ox] 10. (x)[Px [(y)(Py Ny) Ox]]

/ (x)[Px [(y)(Py Ny) Ox]] ass. for CP ass. for CP 3 UI 2,4 MP 1 UI 5,6 MP 3-7 CP 2-8 CP 9 UG

1. (x)(Qx Rx) 2. (x)(Sx Tx) 3. (x)(Rx Sx) 4. Qz Rz 5. Sz Tz 6. Rz Sz 7. Qz Sz 8. Qz Tz 9. (y)(Qy Ty) 10. (x)(Rx Sx) (y)(Qy Ty)

/ (x)(Rx Sx) (y)(Qy Ty) ass. for CP 1 UI 2 UI 3 UI 4,6 HS 7,5 HS 8 UG 3-9 CP

1. (x)Ux (y)[(Uy Vy) Wy] 2. (x)Ux · (x)Wx 3. (x)Ux 4. (y)[(Uy Vy) Wy] 5. Uy 6. (Uy Vy) Wy 7. Uy Vy 8. Wy 9. Uy · Wy 10. (x)(Ux · Wx) 11. (x)(Ux · Wx)

/ (x)(Ux · Wx) 2 simp 1,3 MP 3 EI, ass 4 UI 5 add 6,7 MP 5,9 conj 9 EG 3,5-10 EI

1. (x)Xx (y)(Yy Zy) 2. (x)(Xx · Yx) 3. Xx · Yx 4. Xx 5. (x)Xx 6. (x)Xx 7. (y)(Yy Zy) 8. Xx · Yx 9. Xx 10. Yx 11. Yx Zx 12. Zx 13. Xx · Zx 14. (y)(Xy · Zy) 15. (y)(Xy · Zy) 16. (x)(Xx · Yx) (y)(Xy · Zy)

/ (x)(Xx · Yx) (y)(Xy · Zy) ass. for CP 2 EI, ass 3 simp 4 EG 2,3-5 EI 1,6 MP 2 EI, ass 8 simp 8 simp 7 UI 10,11 MP 9,12 conj 13 EG 2,6-14 EI 2-15 CP

1. (x)(y)(Ex Fy) 2. ~(x)Ex 3. (x)(Ex Fy) 4. (x)~Ex 5. ~Ex 6. Ex Fy 7. Fy 8. Fy 9. (y)Fy 10. (y)Fy 11. ~(x)Ex (y)Fy 12. (x)Ex (y)Fy

/ (x)Ex (y)Fy ass. for CP 1 EI, ass. 2 QN 4 EI, ass. 3 UI 5,6 DS 4,5-7 EI 8 EG 1,3-9 EI 2-10 CP 11 mat imp

1. (x)Gx (y)(Gy Hy) 2. (x)(Ix ~Gx) 3. Gz (y)(Gy Hy) 4. Iz ~Gz 5. (x)(Gx Ix) 6. Gz Iz 7. Gz ~Gz 8. ~Gz ~Gz 9. ~Gz 10. (y)(Gy Hy) 11. (x)(Gx Ix) (y)(Gy Hy) 12. (x)(Gx Ix) (y)(Gy Hy)

/ (x)(Gx Ix) (y)(Gy Hy) 1 EI, ass 2 UI ass. for CP 5 UI 6,4 HS 7 imp 8 taut 3,10 DS 5-11 CP 1,3-11 EI

1. (x)Jx (y)Ky 2. (x)(Jx Kx) 3. ~(y)Ky 4. (x)Jx 5. Jz 6. Jz Kz 7. Kz 8. (y)Ky 9. (y)Ky 10. ~(y)Ky · (y)Ky 11. (y)Ky

/ (y)Ky ass. for IP 1,3 DS 4 EI, ass 2 UI 5,6 MP 7 EG 4,5-8 EI 3,9 conj 3-10 IP

1. (x)(Lx Mx) 2. (x)(Mx Nx) 3. (x)Lx 4. Lz 5. Lz Mz 6. Mz Nz 7. Lz Nz 8. Nz 9. (y)Ny 10. (y)Ny 11. (x)Lx (y)Ny

/ (x)Lx (y)Ny ass. for CP 3 EI, ass 1 UI 2 UI 5,6 HS 4,7 MP 8 EG 3,4-9 EI 3-10 CP

1. (x)[Ux · (y)(Vy Wy)] 2. (x)[Ux [(y)(Xy · Wy) Yx]] 3. (y)(Xy · Vy) 4. Xz · Vz 5. Uw · (y)(Vy Wy) 6. Uw 7. (y)(Vy Wy) 8. Uw [(y)(Xy · Wy) Yw] 9. (y)(Xy · Wy) Yw 10. Vz Wz 11. Vz 12. Wz 13. Xz 14. Xz · Wz 15. (y)(Xy · Wy) 16. Yw 17. (x)Yx 18. (x)Yx 19. (x)Yx 20. (y)(Xy · Vy) (x)Yx

/ (y)(Xy · Vy) (x)Yx ass. for CP 3 EI, ass. 1 EI, ass. 5 simp 5 simp 2 UI 6,8 MP 7 UI 4 simp 10,11 MP 4 simp 13,12 conj 14 EG 9,15 MP 16 EG 1,5-17 EI 3,4-18 EI 3-19 CP

1. (x)[Ax [(y)By Cx]] 2. (x)[Cx [(y)Dy Ex]] 3. (x)(Bx · Fx) 4. (y)(Fy Dy) 5. Bw · Fw 6. Au [(y)By Cu] 7. Cu [(y)Dy Eu] 8. Fw Dw 9. Fw 10. Dw 11. (y)Dy 12. [Cu · (y)Dy] Eu 13. [(y)Dy · Cu] Eu 14. (y)Dy (Cu Eu) 15. Cu Eu 16. Bw 17. (y)By 18. [Au · (y)By] Cu 19. [(y)By · Au] Cu 20. (y)By (Au Cu) 21. Au Cu 22. Au Eu 23. (z)(Az Ez) 24. (z)(Az Ez) 25. (y)(Fy Dy) (z)(Az Ez) 26. (x)(Bx · Fx) [(y)(Fy Dy) (z)(Az Ez)]

/ (x)(Bx · Fx) [(y)(Fy Dy) (z)(Az Ez)] ass for CP ass for CP 3 EI, ass 1 UI 2 UI 4 UI 5 simp 8,9 MP 10 EG 7 exp 12 com 13 exp 11,14 MP 5 simp 18 EG 6 exp 18 com 19 exp 17,20 MP 21,15 HS 22 UG 3,5-23 EI 4-24 CP 3-25 CP

1. (x)(y)(Gx · Hy) 2. (x)(Gx · Hy) 3. Gx · Hy 4. Gx 5. (x)Gx 6. Hy 7. (y)Hy 8. (x)Gx · (y)Hy 9. (x)Gx · (y)Hy

/ (x)Gx · (y)Hy 1 EI, ass 2 UI 3 simp 4 UG 3 simp 6 EG 5,7 conj 1,2-8 EI

1. (x)(y)(Ix Jy) 2. (y)(Ix Jy) 3. Ix Jy 4. (x)(Ix Jy) 5. (x)(Ix Jy 6. (y)(x)(Ix Jy)

/ (y)(x)(Ix Jy) 1 EI, ass 2 UI 3 UG 1,2-4 EI 5 UG

1. (x)(y)(Kx · Ly) 2. (x)(Kx · Ly) 3. (y)(x)(Kx · Ly) 4. (y)(x)(Kx · Ly)

/ (y)(x)(Kx · Ly) 1 EI, ass 2 EG 1,2-3 EI

1. (x)(Ax ~Cx) 2. Wa · (x)(Wx Cx) 3. Wa 4. (x)(Wx Cx) 5. Wa Ca 6. Ca 7. Aa ~Ca 8. ~Aa 9. [Wa · (x)(Wx Cx)] ~Aa 10. Wa [(x)(Wx Cx) ~Aa]

/ Wa [(x)(Wx Cx) ~Aa] ass. for CP 2 simp 2 simp 4 UI 3,5 MP 1 UI 6,7 MT 2-8 CP 9 exp

1. (x)(Px Gx) 2. (Dx · Ex) · (y)[(Dy · Ey) ~Gy] 3. Dx · Ex 4. (y)[(Dy · Ey) ~Gy] 5. (Dx · Ex) ~Gx 6. ~Gx 7. Px Gx 8. ~Px 9. [(Dx · Ex) · (y)[(Dy · Ey) ~Gy]] ~Px 10. (x)[[(Dx · Ex) · (y)[(Dy · Ey) ~Gy]] ~Px]

/ (x)[[(Dx · Ex) · (y)[(Dy · Ey) ~Gy]] ~Px] ass. for CP 2 simp 2 simp 4 UI 3,5 MP 1 UI 6,7 MT 2-8 CP 9 UG

1. (x)(Ax Gx) 2. (x)(Cx Hx) 3. Az Gz 4. Cz Hz 5. (x)(Gx Cx) 6. Gz Cz 7. Gz Hz 8. Az Hz 9. (y)(Ay Hy) 10. (x)(Gx Cx) (y)(Ay Hy)

/ (x)(Gx Cx) (y)(Ay Hy) 1 UI 2 UI ass. for CP 5 UI 6,4 HS 3,7 HS 8 UG 5-9 CP

1. (x)[(Cx · Bx) (Dx · Rx)] 2. (Cx · Bx) (Dx · Rx) 3. Cx · Nx 4. (y)[(Cy · Ny) By] 5. (Cx · Nx) Bx 6. Bx 7. Cx 8. Cx · Bx 9. Dx · Rx 10. Dx 11. (y)[(Cy · Ny) By] Dx 12. (Cx · Nx) [(y)[(Cy · Ny) By] Dx] 13. (x)[(Cx · Nx) [(y)[(Cy · Ny) By] Dx]]

/ (x)[(Cx · Nx) [(y)[(Cy · Ny) By] Dx]] 1 UI ass. for CP ass. for CP 4 UI 3,5 MP 3 simp 7,6 conj 2,8 MP 9 simp 4-10 CP 3-11 CP 12 UG

1. (x)(Gx Ex) (y)(Gy · Cy) 2. (x)[(Px · Hx) ~Cx] 3. (x)[Gx (Px · Hx)] 4. (x)(Gx Ex) (Gz · Cz) 5. Gw 6. (Pw · Hw) ~Cw 7. Gw (Pw · Hw) 8. Pw · Hw 9. ~Cw 10. Gw ~Cw 11. ~Gw ~Cw 12. ~(Gw · Cw) 13. (x)~(Gx · Cx) 14. ~(Gz · Cz) 15. (x)(Gx Ex) 16. (x)(Gx Ex) 17. (x)[Gx (Hx · Px)] (x)(Gx Ex)

/ (x)[Gx (Hx · Px)] (x)(Gx Ex) ass. for CP 1 EI, ass ass. for CP 2 UI 3 UI 5,7 MP 6,8 MP 5-9 CP 10 imp 11 DeM 12 UG 13 UI 4,14 DS 1,4-15 EI 3-16 CP

1. (x)[(Bx · Px) Wx] 2. (x)(Wx Cx) 3. (x)(Cx · ~Lx) (y)(Py ~Cy) 4. (x)(Wx · ~Lx) 5. Wx · ~Lx 6. Wx 7. ~Lx 8. Wx Cx 9. Cx 10. Cx · ~Lx 11. (x)(Cx · ~Lx) 12. (x)(Cx · ~Lx) 13. (y)(Py ~Cy) 14. Px ~Cx 15. (Bx · Px) Wx 16. Wx Cx 17. (Bx · Px) Cx 18. Cx ~Px 19. (Bx · Px) ~Px 20. Bx (Px ~Px) 21. Bx (~Px ~Px) 22. Bx ~Px 23. Px ~Bx 24. (y)(Py ~By) 25. (y)(By ~Py) 26. (x)(Wx · ~Lx) (y)(By ~Py)

/ (x)(Wx · ~Lx) (y)(By ~Py) ass. for CP 4 EI, ass. 5 simp 5 simp 2 UI 6,8 MP 9,7 conj 11 EG 4,5-11 EI 3,12 MP 13 UI 1 UI 2 UI 15,16 HS 14 trans 17,18 HS 19 exp 20 mat imp 21 taut 22 trans 23 UG 24 trans 4-25 CP

1. (x)[[(Wx · Lx) Ix] [(Sx · Wx) ~Lx]] 2. Wx · Ix 3. (y)(Wy Sy) 4. Wx Sx 5. Wx 6. Sx 7. [(Wx · Lx) Ix] [(Sx · Wx) ~Lx] 8. [Lx (Wx Ix)] [(Sx · Wx) ~Lx] 9. Ix 10. Ix ~Wx 11. ~Wx Ix 12. Wx Ix 13. (Wx Ix) ~Lx 14. ~Lx (Wx Ix) 15. Lx (Wx Ix) 16. (Sx · Wx) ~Lx 17. Sx · Wx 18. ~Lx 19. (y)(Wy Sy) ~Lx 20. (Wx · Ix) [(y)(Wy Sy) ~Lx] 21. (x)[(Wx · Ix) [(y)(Wy Sy) ~Lx]]

/ (x)[(Wx · Ix) [(y)(Wy Sy) ~Lx]] ass. for CP ass. for CP 3 UI 2 simp 4,5 MP 1 UI 7 com, exp 2 simp 9 add 10 com 11 mat imp 12 add 13 com 14 mat imp 8, 15 MP 6,5 conj 16,17 MP 3-18 CP 2-19 CP 20 EG

1. (x)[(Jx · Mx) [(y)(Sy Hy) Rx]] 2. (x)(Sx · Hx) (y)(Sy Hy) 3. (Jx · Mx) [(y)(Sy Hy) Rx] 4. Jx · Mx 5. (y)(Sy Hy) Rx 6. (y)(Sy · Hy) 7. Sy · Hy 8. (x)(Sx · Hx) 9. (x)(Sx · Hx) 10. (y)(Sy Hy) 11. Rx 12. (y)(Sy · Hy) Rx 13. (Jx · Mx) [(y)(Sy · Hy) Rx] 14. (x)[(Jx · Mx) [(y)(Sy · Hy) Rx]]

/ (x)[(Jx · Mx) [(y)(Sy · Hy) Rx]] 1 UI ass. for CP 3,4 MP ass. for CP 6 EI, ass. 7 EG 6,7-8 EI 2,9 MP 5,10 MP 6-11 CP 4-12 CP 13 UG

1. (x)Lx (y)(Py Ly) 2. (x)Hx (y)(Ly Hy) 3. (x)(Hx · Lx) 4. Hx · Lx 5. Hx 6. Lx 7. (x)Hx 8. (x)Lx 9. (x)Hx · (x)Lx 10. (x)Hx · (x)Lx 11. (x)Hx 12. (x)Lx 13. (y)(Ly Hy) 14. (y)(Py Ly) 15. Lx Hx 16. Px Lx 17. Px Hx 18. (y)(Py Hy) 19. (x)(Hx · Lx) (y)(Py Hy)

/ (x)(Hx · Lx) (y)(Py Hy) ass. for CP 3 EI, ass. 4 simp 4 simp 5 EG 6 EG 7,8 conj 3,4-9 EI 10 simp 10 simp 2,11 MP 1,12 MP 13 UI 14 UI 15,16 HS 17 UG 3-18 CP

This file is an electronic hand-out for the course, Symbolic Logic.

Most of the logic symbols in this file are GIFs. See my Notes on Logic Notation on the Web.

Peter Suber, Department of Philosophy, Earlham College, Richmond, Indiana, 47374, U.S.A.
peters@earlham.edu. Copyright © 1997, Peter Suber.