I am reading Graham Priest's In Contradiction (p.14) and he mentioned that the semantic rules of 'this sentence' and 'is True' overdetermine and underdetermine the Liar Paradox and its counterpart respectively.

What did he mean? He didn't elaborate on exactly what rules did he appeal to to make these assertions, but to me 'this sentence' just refers to (1) or (2), while the predicate refers to their truth values - what rules are there to discuss?

PS: For context, Priest is defending against opponents against his inference rule as detailed in this other question who are assuming truth value gaps.

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Recall that (see also your previous post) Graham Priest is a dialetheist, i.e. a proponent of the view that there are true contradictions.

Priest's discussion of the Liar starts rejecting the view that there are (truth-value) gaps and supporting the view of gluts.

If we analyze the "classical Liar" (sentence (2)) in terms of truth values, we conclude that (2) is True iff (2) is False.

Thus, (2) is bot True and False, i.e. the Truth value of (2) is overdetermined.

(2) would therefore seem plausible candidate for a Truth value "glut".

If instead we consider (1), we cannot conclude with a specified truth value: if we assume that (1) is True, we have no contradiction. And if we assume that (1) is False, we have no contradiction either.

This means that the Truth value of (1) is underdetermined.

Such a sentence is an obvious candidate for a Truth value gap.

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  • Thank you so much; you've put it so clearly that I feel stupid asking this question – Daniel Mak Jun 19 at 12:39
  • 1
    @DanielMak - you are welcome :-) – Mauro ALLEGRANZA Jun 19 at 12:48

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