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Peter Milne, Omniscient beings are dialetheists, Analysis, Volume 67, Issue 3, 1 July 2007, Pages 250–251, https://doi.org/10.1093/analys/67.3.250
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Although self-referential, there is nothing self-stultifying about the sentence S below. If no omniscient being exists, it is, quite straightforwardly, true.
S: No omniscient being knows that which the sentence S expresses.
And, with a little more work, we see that S is true irrespective of whether there are (or are not) any omniscient beings. For suppose its contrary, i.e. suppose that some omniscient being knows that which the sentence S expresses; then it is known by some omniscient being that no omniscient being knows that which the sentence S expresses (for that is what S says), and since that which it says is known we have that no omniscient being knows that which the sentence S expresses. In supposing S's contrary we have derived S itself, from which we may infer that no omniscient being knows that which the sentence S expresses –S is true. But now, let X be an omniscient being. Being omniscient X must know what we have just established, namely that no omniscient being knows that which the sentence S expresses, and hence knows that which S expresses (for that no omniscient being knows that which the sentence S expresses is what S says). Thus at least one omniscient being knows that which the sentence S expresses. But that there be an omniscient being who knows that which the sentence S expresses contradicts what we established above, namely that no omniscient being knows that which the sentence S expresses. The supposition that X is an omniscient being implies, then, that there is a truth of the form P & ¬P. This truth is known to X and it is known to X that she knows a truth of this form (for X is omniscient): X is, then, a dialetheist. This suffices to demonstrate, using means acceptable to dialetheist and classical logician alike, that every omniscient being is a dialetheist. What further inference is to be drawn from this conclusion I leave to the reader.1,2
