🚀 go-pugleaf

Newberry wrote:
>
> Issues with van Fraassen's Paper
> 
> 1. Presuppositions
> 
> Bas C. van Fraassen used the Logic of Presuppositions to solve the
> Liar paradox. van Fraassen (1968: Presupposition, Implication, and
> Self-Reference, http://www.jstor.org/pss/2024557, The  Journal of
> Philosophy, pp. 136-152)
> 
> Let
> X = �This sentence is false�
> Y = �This sentence is not true�
> 
> Van Frassen concludes that the Plain Liar can is solved when ~T(X) &
> ~T(~X). He further claims that ~T(Y) necessitates Y, and as result the
> Strengthened Liar is unsolvable except by dropping the requirement
> that T() be bivalent. But why does ~T(Y) necessitate Y? We will re-
> examine this claim.
> 
> Van Frassen's definitions are below. The negation of sentence A is
> true if (respectively, false) iff A is false (respectively, true.)
> 
> 1. A presupposes B if and only if
> (a) if A is true then B is true
> (b) if ~A is true then B is true
> 
> 2. A necessitates B iff whenever A is true then B is true
> From 1 and 2 we obtain:
> 3. A presupposes B if and only if
> (a) A necessitates B
> (b) ~A necessitates B
> 
> Truth:
> a) if P is true then T(P) is true, otherwise T(P) is false
> b) If the second level sentence is A is false, then ~A is true, and if
> A is true then ~A is false.
> c) If either A is true or B is true, then (A v B) is true, otherwise
> (A v B) is false.
> 
> 2. The Plain Liar Paradox
> 
> Van Fraassen observes that X and T(~X) necessitate each other.
> a) if ~X is true then T(~X) is true [d3]
> b) if X is true then T(~X) is true  [e1]
> Therefore X presupposes T(~X)
> But T(~X) cannot be true. Hence X does not have a truth value.
> 
> 3. The Strengthened Liar Paradox
> 
> Van Fraassen claims that ~T(Y) necessitates Y. We can indeed show
> this, as well as that T(Y) necessitates ~Y, by a relatively simple
> argument using the principle that if two different sentences mean the
> same thing and one is true then the other one is also true:
> 
> Principle 1
> Assumption         A means B
> Premise            T(B)
> Conclusion         T(A)
> 
> Let us assume that Y and ~T(Y) have the same meaning.
> 
> (1)  Assumption                        Y means ~T(Y)
> (2)  Premise                           T~(T(Y))
> (3)  Tarski's principle from 2        ~T(Y)
> (4)  Principle 1 from 1,3              T(Y)
> 
> (1)  Assumption                        Y means ~T(Y)
> (2)  Premise                           T(T(Y))
> (3)  Tarski's principle from 2         T(Y)
> (4)  Principle 1 from 1,3              T(~Y)
> 
> We have indeed proven that ~T(Y) necessitates Y, but we have also
> proven a contradiction in the process. Neither ~T(Y) not T(Y) can be
> the case. If Y and ~T(Y) mean the same thing then one cannot be
> trivalent and the other bivalent.
> 
> By the definition of necessitation if Y is N then ~T(Y) must not be T.
> Analogically if T(Y) necessitates ~Y and Y is N then T(Y) must not be
> T.
> 
> Van Fraassen suggests that �The Strengthened Liar paradox is averted
> if we hold that T(Y) and T(~Y) are themselves neither true nor false.
> From this it follows immediately that the sentence ~T(Y) & ~T(~Y) also
> is neither true nor false.� But this is implausible. If ~T(Y) & ~T(~Y)
> is the case then by Tarski's principle T(~T(Y) & ~T(~Y)).
> 
> 4. The Plain Liar Again
> 
> The same argument can can be used against the Plain Liar.
> 
> (1)  Assumption                         X means T(~X)
> (2)  Premise                            T(~T(~X))
> (3)  Tarski's principle from 2         ~T(~X)
> (4)  Principle 1 from 1,3               T(~X)
> 
> Neither T(~X) nor ~T(~X) can be the case.
> 
> Haim Gaifman pointed out that: �The contradiction returns also if the
> sentence says of itself that it is false: If it lacks a truth value,
> then it is not false; but it says of itself that it is false, hence it
> is false after all.� Gaifman (Pointers to Propositions ,
> http://www.columbia.edu/~hg17/gaifman6.pdf, Columbia University, p.
> 16) There is no essential difference between the Plain Liar and the
> Stregngthened Liar.
> 
> 4. Conclusion
> 
> What is wrong with the argument is of course the assumption that Y
> means ~T(Y). We have in front of us is a proof by contradiction that Y
> is not the same as ~T(Y). And if ~T(Y) is the only thing Y could
> possibly mean then Y is meaningless, and ~T(Y) says that Y is not
> true.
> 
> http://members.lycos.co.uk/neologic/Issue_vanFraasen.pdf

I've read VF's paper, I've read HG's paper, I've read your post.

1) I tend to agree with you.
2) This stuff about the Liar really makes my head hurt.
3) I fail to really see what interests you so much about it.

--
hz