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.

### 4 Responses to All Liar, No Paradox

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

• Jon Awbrey says:

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.

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