[FOM] Another easy solution does not work
Helene.Boucher at wanadoo.fr
Wed Sep 11 17:13:39 EDT 2002
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 (if indeed that's the way
you go). The sequence obviates the objection of
Barwise/Etchemendy/Moss, and certainly looks like it avoids
self-reference. That is, self-referential non-truth ascription is only
a subset of the problem; the real problem is infinitary non-truth
ascription, of which self-reference is only the most spectacular version.
To be honest, I'm not really sure what really changes by refocusing the
problem, since those who wanted to ban self-reference already had to
deal with loops:
The next statement is not true.
The previous statement is not true.
And if banning self-reference "solves" this, then it would seem that one
is just as entitled to "ban" infinitary graphs like (1)-(2)-(3)... as a
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