# Ten proofs with recorded commentary

Proofs using all 18 rules, from Hurley 9th ed. pp. 376-378

1.

1. Q ⊃ (F ⊃ A)

2. R ⊃ (A ⊃ F)

3. Q ∙ R / F ≡ A

2.

1. (J ∙ R) ⊃ H

2. (R ⊃ H) ⊃ M

3. ~(P v ~J) / M ∙ ~P

3.

1. F ⊃ (A ∙ K)

2. G ⊃ (~A ∙ ~K)

3. F v G / A ≡ K

4.

1. T ⊃ G

2. S ⊃ G / (T v S) ⊃ G

5.

1. S v ~N

2. ~S v Q / N ⊃ Q

6.

1. (E ⊃ A) . (F ⊃ A)

2. E v G

3. F v ~G / A

7.

1. (F ∙ H) ⊃ N

2. F v S

3. H / N v S

8.

1. C ⊃ (~L ⊃ Q)

2. L ⊃ ~C

3. ~Q / ~C

9.

1. K ≡ R

2. K ⊃ ( R ⊃ P)

3. ~P / ~R

10.

1. A ≡ W

2. ~A v ~W

3. R ⊃ A / ~(W v R)

• Solutions to those ten proofs

Render these in propositional notation and write the proofs.  Be careful to show negations with a tilde whenever they are explicit.

11.    The visual cortex is part of the brain. If it isn’t stimulated, there is no visual sensation. But if visual sensation occurs only if the visual cortex is stimulated, and if the visual cortex is part of the brain, then visual sensation is dependent on the brain. And if that is true and visual sensation is a function of the mind, then the mind is necessarily dependent on the brain. Therefore if visual sensation is a function of the mind, then the mind is necessarily dependent on the brain.

12.   If the soul is nonmaterial, then it has no parts, and if it has no parts, then it can’t “come apart” or disintegrate. If it can’t come apart or disintegrate, then if nothing can destroy it, then it’s immortal. But the soul can be destroyed only if God destroys it, and God does not destroy souls. Therefore if the soul is nonmaterial, it’s immortal.

11.

B
~S > ~V
((V > S) . B ) > D
(D . F) > M / F > M
12.

(~M > ~P) . (~P > ~(C v D))
~(C v D) > (~T > ~O)
(T > G) . ~G / ~M > ~O

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