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Is there a term that means "A self referential statement which is true if (and because) it is true and false if (and because) it is false"?

"This sentence is a lie" is a paradox in the sense of "paradox(noun) A self-contradictory statement, which can only be true if it is false, and vice versa." (Source: Synonyms.com.)

I'm looking for the opposite of that.

I found the following on Everything2:

So we have reached the extraordinary result that the statement is always consistent, regardless of whether or not it is true!

Which notes that it is interesting, but doesn't give a name.

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    They both belong to the "category" of self-referential statements. The sentence S="S is false" is self-contradictory; for S="S is true" why not : self-confirming ?
    – Mauro ALLEGRANZA
    Feb 19, 2015 at 12:34
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    I have been using this sentence as a self-evident example of meaningless nonsense. (Is there a technical term for "meaningless nonsense?") Then, I would argue that changing "true" to "false" would not suddenly imbue it meaning, thus easily disposing of "This sentence is false" as meaningless nonsense as well.
    – Dan Christensen
    Feb 19, 2015 at 15:53
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    @Tim Smith A xodarap.
    – user4894
    Feb 19, 2015 at 18:56
  • Causa sui i.e. "the cause of itself"
    – Ram Tobolski
    Feb 19, 2015 at 21:39
  • @MauroALLEGRANZA: It is self-confirming - but the interesting thing is it's also self-denying, if you assume it's false it's also false. I'm looking for something that encompasses both properties.
    – Tim Smith
    Feb 23, 2015 at 12:37

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It is difficult to say exactly what the "opposite" of a paradox might be given your definition, because quite obviously all sentences are true if they are true and false if they are false! Perhaps a way to think of your paradox sentences is as sentences that can receive no consistent semantic value, where their opposite would be a sentence that could receive any semantic value consistently (or more liberally, more than one).

Specifically, the sentence you referred to (if it is a sentence!) is sometimes called the Truthteller sentence. A Truthteller sentence is mentioned in Kripke's Outline of a Theory of Truth as an example of an ungrounded sentence - intuitively, a sentence whose semantic value is somehow undetermined by the facts of the world. However, in Kripke's analysis of the Truth predicate, it's important to note that the Liar sentence (and similar paradoxical sentences) is also ungrounded in the sense that he's trying to capture, as a consequence of its self-referential character.

Distinguishing the truth-teller sentence from other ungrounded sentences requires us to have access to a certain amount of semantic technology that it's not clear that we can necessarily expect to have, depending on your theories about the functioning of the Truth predicate. For instance, proponents of Revision Theories of Truth would argue that the most we can say about the truth-teller is that it is neither categorically true nor categorically false, but that it might nonetheless have some truth value, conditional on some background hypothesis, just as with almost any other aspect of semantic interpretation.

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I'm not sure that that particular kind of sentence has a name. This could just be for historical reasons - it's not obvious that there is anything philosophically interesting to say about these kinds of self-referential statements, in the way that there are philosophically interesting things to say about sentences like 'this sentence is false'.

That said, the go-to reference here is Alfred Tarski's "The Semantic Conception of Truth". You can find the whole article online here. The Stanford Encyclopedia of Philosophy is also a very good resource. Here's a relevant link: http://plato.stanford.edu/entries/tarski-truth/.

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There is a great book by the late Jon Barwise, Vicious Circles, which analyzes these sorts of sentences and many others in great detail. I read this book back in the early 90's when I understood very little about logic, and, as I recall, the first half of the book was still very accessible.

These sorts of self-referential statements create all sorts of logical conundrums. My favorite, which I've used in a class I taught on riddles, was that of a librarian creating a catalog of all catalogs which don't list themselves. So, should this catalog list itself? If it does, then it includes a catalog of the sort outside of its definition. If it doesn't, then the catalog doesn't list all such catalogs.

This is just a rewording of Bertrand Russell's paradox about the set of all sets that don't include themselves. And I believe this particular phrasing of the Russell's paradox in terms of librarians is due to Carl Sagen.

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  • It's only a problem if the catalog needs to be prefect.
    – Cheers and hth. - Alf
    May 30, 2015 at 9:25
  • @Cheersandhth.-Alf It's not a problem of perfection. It's a problem that arises because of the meaning of the word "all". If the catalog isn't perfect, then it's not a catalog of "all" such catalogs, but rather something else. At any rate, this example of the librarian isn't supposed to be about a real librarian. Rather it's to illustrate in a bit more accessible way the meaning and problem of Russell's paradox.
    – A.Ellett
    May 30, 2015 at 14:32
  • I would say a catalog missing a single entry was just slightly imperfect. But it can be placed on a more rigorous footing. Let's say that the intended meaning was a catalog of all catalogs, future or past, that don't list themselves. That's clearly not possible, so it must be a catalog of those catalogs that up till a specified time existed (not just strongly suspected of coming into existence, but that actually existed) and did not list themselves. Well, call this catalog C. The specified time is necessarily before the creation of C.
    – Cheers and hth. - Alf
    May 30, 2015 at 15:27
  • @Cheersandhth.-Alf You're missing the story's point. Russell was demonstrating a serious paradox that seemed to arise from a simple definition: a set of all sets that don't include themselves. Mathematically, there is no past, present, or future in the definition. This paradox pointed to a possible hole in mathematical reasoning which quite a few mathematician spent the beginning of the 20th century patching up. Along the way, Goedel proved the incompleteness of any system that could account for arithmetic. And following not too far off was Alan Turing with his eponymous machine. (cont).
    – A.Ellett
    May 30, 2015 at 15:55
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    @Cheersandhth.-Alf I wouldn't mind chatting with you about this, but I'm traveling all today and tomorrow. The comments are probably not the place for this chat, but take a look at Jon Barwise's book. He was quite a lucid writer. :-)
    – A.Ellett
    May 30, 2015 at 16:05
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No sentence exists before it is completed. A self-referential sentence speaks as though it already exists as a sentence -- even before any sentence exists to refer to as "this sentence". Thus it would have to "pre-exist its own existence" in order to be meaningful. So self-referential sentences are meaningless.

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    "No sentence exists before it is completed." Not sure I agree 100%, but it's an interesting point. Is it not possible that sentences "exist" when they begin? For example, a life exists before it is completed (some would argue even that when it's completed, it no longer exists!). Also, musical pieces - a composer can discuss "this piece I'm working on," even if it's not complete (either in the sense that it's not done being written or done being played), and so the piece exists. Why is it different with sentences?
    – James Kingsbery
    Jul 8, 2015 at 19:06
  • >>Why is it different (than life or musical compositions) with sentences?<< I hope you don't think I'm ignoring your question, James, but before I can answer it, we must get together on the word "sentence". After thinking over what I wrote, I think I would have written it differently. Sentences don't "drop down from the sky". They always have authors and audiences. I don't ask "What does a sentence mean?" but instead "What could the author be using "This sentence is true" for? I can't think of a thing, can you? If nobody can mean anything by it, then it's meaningless, right?
    – user8159
    Jul 10, 2015 at 0:42
  • What could a self referential sentence mean? Does a sentence ever refer to itself or does its author only use it to refer to the sentence she has in her mind? Since her sentence already exists in her mind before she writes it or speaks it, she is not really speaking of what she is writing, but only of what's in her head that she's in the process of expressing by her writing or speaking.
    – user8159
    Jul 10, 2015 at 0:55
  • A sentence also can only be interpreted after it has been completed (because before that, we can't know whether something will follow that completely changes its meaning). So at the time we attempt to interpret the sentence, it is already completed, and therefore the self-reference, which comes only about on interpretation, is to a completed sentence.
    – celtschk
    Jan 15, 2018 at 11:15
  • @user8159. Gramatically this is a complete sentence. I also don't see why you say - if this is your view - the 'sentence already exists in her mind before she writes it or speaks it'. She might think it out in the act of writing it on paper or screen or saying it. I appreciate your reflections on the problem sentence. There's no proposition it can be said to express. For if propositions are true or false (bivalence) what does it say that is true or false ? I like your comments. Their angle is original.
    – Geoffrey Thomas ♦
    Jan 16, 2018 at 17:56
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I believe this is called a recursive, or self referential statement. A quick search of the Internet will quickly return such results, undoubtedly.

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Perhaps you mean a "performative utterance"?

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  • If you have a new question, please ask it by clicking the Ask Question button. Include a link to this question if it helps provide context. - From Review
    – Alexander S King
    Jan 14, 2018 at 19:26
  • Welcome to Philosophy.SE. I have edited your answer to add a link. If you know any thing else, please feel free to edit your answer to improve it. You can find some more guidance on How to Answer. I hope you enjoy the site. (@AlexanderSKing I think this was meant as an answer to the question.)
    – user2953
    Jan 14, 2018 at 20:35
  • @gofmane. A performative statement or utterance is one that changes a situation as when I say, 'I promise to return your £5'. This is not a merely statement like an indicative sentence; it changes my and your status. I have become a promisor, you a promisee.
    – Geoffrey Thomas ♦
    Jan 14, 2018 at 21:09
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I claim that technically it is just as meaningless as the liar paradox, because language is temporal. That is, it always takes time to speak, write, hear, or read a sentence. Even if you speak or write very fast, the instant you have spoken "this sentence", there is no sentence for "this sentence" to be speaking of. 'A sentence in the making' is not really a sentence.

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The term is "The Liar's Paradox", and its variants.

Arthur Prior does a weak job of correctly explaining why it isn't a paradox. I'll explain why it's not a paradox in detail if anyone is interested.

The Liar's Paradox illustrates the difference between math, logic, reason, and science, and difference between platonism vs operationalism, and the difference between well formed and malformed statements in colloquial grammar, ordinary language grammar, vs deflationary grammars.

Or stated differently, the grammatical structure of the statement relies on ordinary language grammar, while the question refers to formal, legal,or logical grammar.

For example, you can draw the square root of two, you can apply the square root of two in calculation or construction, but you cannot calculate it itself.

And for the same reason.

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Possibly, the term you're looking for is a tautology.

One of the senses of the word seems to be applicable here. According to google's definition, tautology is

a statement that is true by necessity or by virtue of its logical form.

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    Hi. The statement that was asked about ("this sentence is true") is not a tautology. It could be false, if it has a truth value at all. While a tautology cannot be false.
    – Ram Tobolski
    Feb 20, 2015 at 14:32

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