- I am in a position to know the denial of (1).
Part I: Assume (1). Then I am in a position to know the negation of (1). But I can only be in a position to know something that's true, and if (1) is true, then its negation is not. So it seems we have a rock-solid argument against (1). Part II: But if we have a rock-solid argument against
p, then we are in a position to know the denial of
p. Hence I am in a position to know the denial of (1). But that's what (1) says, so (1) is true, after all.
One move that works here, but not in the original Liar Paradox, however, is that one say that Part II of the argument provides a defeater for the argument in Part I, and ensures that the argument in Part I does not put me in a position to know the denial of (1).
So the original Liar Paradox is more powerful. But there is still some paradoxicality here.
3 comments:
This just happened to coincide with this new entry at SEP: http://plato.stanford.edu/entries/liar-paradox/
That comment coincided with my needing a brief but up-to-date and authoritative review of the Liar Paradox, so many thanks.
I guess my own view as to the Liar is that it requires a more radical revision to the way analytic philosophy thinks of language than any of the proposals surveyed in the SEP entry, but without forcing any revision to the rules of inference of classical logic. What it forces you to do is to deny that two exactly alike non-indexical sentence types are exactly alike in meaningfulness. It also forces you to attribute meaning to sentence tokens not sentence types, even in non-indexical cases. But you can keep all of classical logic, and all of the T-schema.
That's all in my head, and I don't know when I'll get around to writing it up. Maybe when I finally co-write that radical philosophy of language book that has been brewing for years.
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