[FOM] Another easy solution does not work

[Todd Wilson]

On Wed, 11 Sep 2002, Andrew Boucher wrote:
> Todd Wilson rightly notes that the claim that Yablo's paradox is not 
> self-referential is contested.  This is why I prefer (I believe the 
> older and simpler) infinite paradox:
> 
> (1)  Statement (2) is not true.
> (2)  Statement (3) is not true.
> (3)  Statement (4) is not true.
> ...
> 
> Now this does not lead to a contradiction, as Yablo's paradox does, 
> since either the even (or odd) statements can be true, with the odd (or 
> even) statements not true.  Nonetheless, of course, it is paradoxical in 
> the sense that both statements (1) and (2) are in the same position:   
> namely at the head of an infinite sequence of statements, "Statement .. 
> is not true," and there seems to be no theory of truth which could 
> explain why one is true and the other not true

Actually, under the Barwise/Etchemendy treatment of propositions (at
least what they call "Russellian propositions"), each proposition in
the above infinite list is again just the Liar, and thus is
paradoxical.  The statements above are translated in the B/E formal
language as:

    (1)  - True[that_2]
    (2)  - True[that_3]
    (3)  - True[that_4]
    ...

whereupon each of the associated propositions is equal to

    [Fa [Fa [Fa ...]]] ,

and thus all equal to each other (and to the liar, f = [Fa f]).  Thus,
the analysis that leads to the conclusion that the odd-numbered
propositions must have the opposite truth value of the even-numbered
propositions, under this account, is flawed because it assigns
different truth values to what, after some investigation, are revealed
to be the same propositions.

-- 
Todd Wilson                               A smile is not an individual
Computer Science Department               product; it is a co-product.
California State University, Fresno                 -- Thich Nhat Hanh