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A non-prime disjunction is one that is true even if none of its disjuncts are; I've seen them come up at least in impossible-worlds talk, but now I'm wondering whether the basic "revenge"1 sentence (relative to the liar paradox), "This sentence is false or meaningless," could be evaluated in terms of being non-prime?

So, then, if, "This sentence is false or meaningless," is evaluated to true, we would normally say that at least one of its disjuncts is true. However, then it would be false or meaningless, neither of which options seems to work properly. But so if it's true without either disjunct being true, does it still avenge, "This sentence is false," as it has before, or does it get its revenge in some other way,2 by leading to a sentence like, "This sentence is false or meaningless or non-prime"?

1For more on the use of this terminology, see J. C. Beall (ed.), The Revenge of the Liar: New Essays on the Paradox, the abstract for which reads:

A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another.

2Cf. the revenge of the so-called Super-Liar in a contextualist approach to the phenomenon:

To many, contextualism seems to capture our pre-theoretic intuitions about the semantic paradoxes; this is especially due to its reliance on the so-called Revenge phenomenon. I, however, show that Super-Liar sentences (where a Super-Liar sentence is a sentence which says of itself that it is not true in any context) generate a significant problem for Burge’s contextual theory of truth.

ADDENDUM: has this question occurred already in the literature, about 40-odd years ago?

Apparently, a certain Chris Mortensen, with Graham Priest no less, wrote a paper published in 1981 (see here for a rather later review/critique) where they use non-prime disjunctions in addressing a "truth-teller paradox" (dual to the liar), but unfortunately all the relevant material is seemingly behind a (JSTOR) paywall, so I'm not sure how this address and the response thereto is fully conducted by these authors (I can see only a preview of either indicated paper).

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    @DavidGudeman it's the common word used for these things. There are 973 results for "revenge of the liar" on philpapers.org alone. Or 970, last I checked, admittedly 22 if you put quotes around the phrase. But Beall's book with this title has been out since 2007 apparently, among other examples. Commented Apr 6, 2025 at 20:26
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    I just found another essay in which the phrase "infamous revenge problem" shows up. I don't know what else to say, this wording is extremely well-known in the literature. Commented Apr 6, 2025 at 21:05
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    @DavidGudeman Apparently you did not read those 973 papers on phil papers that use the phrase "revenge of the Liar"? I thought that anyone who has read even a tiny bit about the Liar paradox will have encountered that phrase. See also SEP: "Expressive power and 'revenge'" (plato.stanford.edu/entries/liar-paradox/#ExprPoweReve) Google scholar also gives hundreds of refs. Commented Apr 6, 2025 at 23:08
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    Can someone please explain in simple words - for pedestrians in logic - what the OP's question is? Commented Apr 7, 2025 at 4:35
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    @KristianBerry - You can freely download the 1981 Mortensen, Priest article "The truth teller paradox" from grahampriest.net/publications/papers. (It's good never to rely only on Google scholar, but simply use DuckDuckGo... :) Commented Apr 7, 2025 at 11:30

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The solution to your problem would seem to depend upon the theory of truth you subscribe to.

If you subscribe to the correspondence theory of truth, the sentence would neither be true nor false, since it does not correspond to anything in reality and is self-referential ... and thus would be absurd ... or meaningless as you put it.

Other theories of truth may give you different results.

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    I have "experimented" with these considerations before, as in comparing, "This sentence doesn't correspond to a fact," to, "This sentence doesn't cohere with an ideal set of other sentences," or, "This sentence isn't at the ideal limit of inquiry." I thought to use these as ways of corroborating one theory of truth more than another inasmuch as one theory might fit to the possibility of the liar sentence more than another. However, my question per this post has more to do with non-primality in light of the revenge problem, so I don't think the appeal to meaninglessness per the correspondence Commented Sep 19, 2025 at 16:42
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    [cont.] theory would be sufficient to address the current matter. Commented Sep 19, 2025 at 16:42
  • Well, then take the pragmatic theory of truth. That which is useful is true, that which not is false. Given that your sentence has no obvious usefulness ... it is false. Here is the thing though, if you are just trying out different theories of truth to figure out this one statement the only thing you prove is that you have no notion of what false (and true) means. The consequence is obvious, I presume? Commented Sep 19, 2025 at 19:34
  • My own "theory" of truth (aside from an evolving commitment to alethic pluralism, about truthmakers and truth-bearers) is a "constitution" version, where a belief (not a sentence or a proposition) is the primary truth-bearer and is true if and only if it is constituted by the fact that it is about (and where constitution is not identity). As for the current question about non-primality, again, this is a specific, other matter, which a successful answer must address. Commented Sep 19, 2025 at 19:37
  • I get the distinct impression that your issue is with the truth, and until that is untangled you will not get anywhere on the current issue (or even on any issue). Unfortunately I cannot help in this endeavor. Commented Sep 20, 2025 at 7:51
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You mean like how "te" is not a word and "xt" is not a word (in English), but "text" is a word?

An intriguing idea, assuming whole sentences function similarly. Remember OR is a logical connective for propositions and so "this sentence is false OR meaningless" is actually (?) "this sentence is false OR this sentence is meaningless". What's the referent for "this"? It looks like "this" is functionally a pronoun like "he" or "she". I can't seem to fix its identity.

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  • Wow! Thus much love! Commented Jun 19, 2025 at 14:48

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