Thursday, 24 March 2011

Symbolic Logic, Dale Jacquette, Wadsworth, 2001, Chpt. 8, IV(11), p. 435

The argument:

Not everyone has the good fortune to come from Corinth. There are metaphysicians or there are epistemologists only if all have the good fortune to come from Corinth. Thus, there are no metaphysicians.

and the proof:
  1. ¬ (x)Cx
  2. (∃x)(Mx ∨Ex) ⊃(x)Cx
  3. ∴¬ (∃x)Mx
  4. ¬ (∃x)(Mx ∨Ex) ......... 1,2 MT
  5. (x) ¬ (Mx ∨Ex) ......... 4 QC
  6. (x)(¬Mx • ¬ Ex) ......... 5 DeM
  7. ¬Mx • ¬ Ex ......... 6 UI x/x
  8. ¬Mx ......... 7 Simp.
  9. (x) ¬Mx ......... 8 UG
  10. ¬ (∃x)Mx ......... 9 QC

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