Wednesday, 25 May 2011

Symbolic Logic, D. Jacquette, Wadsworth, 2001, Chpt. 8, IV(17), p. 436

The argument:

"If Annie is elected, then everything we worked to achieve in the last 4 years will be destroyed. Either Annie or Sara will be elected. But it's definitely not going to be Sara. Whatever is destroyed must be rebuilt from scratch. Hence, everything we worked to achieve in the last 4 years must be rebuilt from scratch."

The proof:
  1. Ea ⊃(x)(Wx ⊃Dx)
  2. Ea ∨Es
  3. ¬ Es
  4. (x)(Dx ⊃ Rx)
  5. ∴(x)(Wx ⊃ Rx)
  6. Ea ......... 3,2 DS
  7. (x)(Wx ⊃Dx) ......... 6,1 MP
  8. Wx ⊃Dx ......... 7 UI x/x
  9. Dx ⊃ Rx ......... 4 UI x/x
  10. Wx ⊃ Rx ......... 8,9 HS
  11. (x)(Wx ⊃ Rx) ......... 10 UG

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