All Liar, No Paradox

Posted on August 1, 2015 by Jon Awbrey

A statement S_0 asserts that a statement S_1 is a statement that S_1 is false.

The statement S_0 violates an axiom of logic, so it doesn’t really matter whether the ostensible statement S_1, the so-called liar, really is a statement or has a truth value.

This entry was posted in C.S. Peirce, Epimenides, Foundations of Mathematics, Liar Paradox, Logic, Logical Graphs, Paradox, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics, Zeroth Order Logic and tagged , , , , , , , , , , , , , , , . Bookmark the permalink.

9 Responses to All Liar, No Paradox

  1. ontologicalrealist says:
    August 1, 2015 at 8:24 pm

    Can you explain that in this case how S0 (the first statement) violates an axiom of logic and what is that axiom?

    Reply
    • Jon Awbrey says:
      August 2, 2015 at 12:00 pm

      I’m preparing to discuss this further in my next few posts. I picked the liar puzzle to illustrate some points in Peirce’s semiotic approach to logic because this hoary old precipitate appears to dissolve relatively quickly when immersed in the pragmatic medium of sign relations. But I’m not sure it works the same way for fish who swim in other seas. So there is an issue of cross-paradigm communication that needs to be discussed along the way.

      Reply

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