[FOM] The liar paradox

martdowd at aol.com martdowd at aol.com
Thu Feb 16 23:54:49 EST 2017

 Nik Weaver writes:

  >> This is just to say that I have written a short paper on the subject
  >> titled "The liar paradox is a real problem".  It is available on the
  >> arXiv here
  >>   https://arxiv.org/abs/1702.03875
  >> The key takeaway: "whatever simple idea you have for an easy resolution
  >> of the liar paradox --- we've tried it, and it doesn't work."

Nik's article states that there is no good theory of truth.  It cites Saul Kripke's "Outline of a theory of truth" but does not state what his objection to this, at least as a theory of truth relevant to the liar paradox and related difficulties in the semantics of truth as an object of study.
For formal languages with both a truth modality and a self-reference mechanism there are well formed statements which cannot be assigned a truth value under a sensible semantics.

I have an old paper "A Propositional Modal Logic for the Liar Paradox", available at www.hyperonsoft.com/lrp.pdf, which presents some example formal systems simpler than Kripke's.

Martin Dowd

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