On Truth and Truthmakers I/?
- Posted by Andrew Bailey on Sunday, June 12, 2005 at 9:43 PM
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1 Comments |
Analysis recently made available online a forthcoming article, Peter Milne's Not every truth has a truthmaker. Milne advances a Gödelian argument against truthmaker theory. I began a critical response to Milne this evening; the following proof of his argument is the first step (my argument against Milne shall be to offer reason to reject P2--not as a false statement, but as a meaningless one).
Under truthmaker theory, I take the proper analysis of a locution like, “p has a truthmaker” to be “there is some truth p, there is some truthmaker q, and Tpq,” where T is a two-place predicate signifying the relation a truth stands in to its truthmaker. This just is the difference between there being a truthmaker and some p having that truthmaker. Understanding this, I shall abbreviate claims of the form, “there is some truth p, there is some truthmaker q, and Tpq” as merely “Tp.”
Letting M denote the sentence, "This sentence has no truthmaker," Milne's argument can be proved as follows:
P1: M ≡ Tm (ass, truthmaker theory)
P2: Tm (ass)
P3: M ≡ ~Tm (ass, meaning of M)
C1: Tm ⊃ M (Bioconditional elimination, P1)
C2: M ⊃ ~Tm (Bioconditional elimination, P3)
C3: Tm ⊃ ~Tm (Hypothetical MP, C1, C2)
C4: ~Tm (MP, P2, C3)
C5: ~Tm & Tm (&I, P2, C4)
C6: ~Tm (RAA, P2, C5)
C7: M (MP, P2, C1)
C8: M & ~Tm (&I, C6, C7)
Sometime this week, I plan on finishing the paper off. I'll sit on it for a while and seek feedback; by the time Analysis publishes Milne's piece, I just might have a response worth submitting for review.
1 Comments:
at 10:28 PM said... His argument seems more than unsound.
Except for The Deity, when didn't something have a mother? So to speak...something that gave birth to it.
I may be entirely wrong; for it is late, and I only skimmed his article.
"There is a way which seems right to man, but it's end is the way of death"-Proverbs 14:12
