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The sentence "This sentence is false." is a paradox (called the "liar's paradox) as even though being well formed it is a contradiction.

While logicians can call this a case of un-decidability what would be the take from a linguistics perspective?

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  • It seems like impossible to run in a programming grammar, such as: "var a = unknown; if(a == false) then a = false;", because a is not well prepared when using a; – archenoo Sep 26 '13 at 14:46
  • @archenoo, Your example is flawed because imperative languages require you to be explicit about order of operations meaning the two used of a are not the same, but declarative languages often don't. MS Excel is one such declarative language. Try putting =NOT(A1) in the cell A1 in a spreadsheet. You won't get an answer, but you will have expressed the liar's paradox. This is also expressible in Verilog which is imperative-ish but is more nuanced re time than JavaScript. – Mike Samuel Sep 26 '13 at 23:11
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    @archenoo, Actually, I was wrong about imperative-ness being the problem. You need recursive reference which you don't get with var. Here's how you express it in JavaScript: function lies() { return !lies(); }; Python: def lies(): return not lies(); OCaml: let rec lies () = not lies (). Iow, it's the fixed-point combinator that lets you express the liar's paradox, and, as a result, allow you to produce programs that fail to halt. – Mike Samuel Sep 26 '13 at 23:23
  • @MikeSamuel, Hi! Thanks for your reply, I am not good at programming and your advice is very useful! – archenoo Oct 4 '13 at 15:23
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I would say that there is no "typical linguistic response" here. The paradox is interesting mostly for philosophical semantics, but much less for many of the linguistic semantics perspectives. For instance, one view is that the sentence in question turns out to be a paradox if we assume a referential theory of meaning, and if we assume that the indexical "this" refers to the sentence itself. When we analyze this sentence taking into account a given context of utterance, then we might have a sentence that perhaps does not refer to itself. The point here is that any sentence from natural language that matters for linguistics is a sentence that has content, its relevant in a given context, and its related to the world in some way or another.

If we see the liar's paradox from the perspective of truth-conditional semantics, I would say that what we want to understand is the truth conditions of the proposition expressed by the sentence, and we need to consider the state of affairs or particular model of reality it describes in a given context. Here it is important to know the difference between truth conditions and truth value, because we can know the meaning of a sentence without knowing if it is true or false. So, for the proposition expressed by "This sentence is false", what we know is that its meaning is whatever makes the sentence true or false depending on the model. If the sentence is uttered in a model or a possible world where the context states that "this" refers to any sentence, we just have to check what sentence are we talking about to evaluate its truth value. If the model states that the sentence refers to itself, then we are moving from the domain of linguistics to the domain of philosophy, and we have different options. One is that this is a problem of confusing hierarchy levels: language and metalanguage (Russellian view); another one is that we are just uttering a pointless sentence, where nothing true or false is really being said (Strawsonian view). There are other alternatives, but again, they are philosophical approaches to the logic of language, and are far from the scope of most linguistic theories of meaning in natural language.

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  • For resolution to Russels paradox/Liar paradox see here – ARi Oct 2 '13 at 7:20
  • The above though is from a Logical/set theoretic perspective – ARi Oct 2 '13 at 7:39
  • @ARi Partially it is, but that's how modern formal linguistic semantics works. And even in other approaches within linguistic semantics, the idea that meaning is anchored to the world and context-sensitive is fundamental to undertand semantic relations in natural language. – edominic Oct 2 '13 at 15:06
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The typical linguistic response is that much like Chomsky's famous "Colourless green ideas sleep furiously", the liar sentence is well-formed but meaningless.

If you insist on evaluating the truth value of the sentence, and posit it is not meaningless in a simple way like "The present King of France is bald" (we can't evaluate the truth-value of this sentence since we are referring to something that doesn't exist) but saying that "This sentence" is a proper self-reference (note that in formal systems, saying 'this sentence' or a similar reference is much more involved) then the alternative way out for the linguist is to say that language is simply inconsistent and the sentence is both true and false.

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  • A sentence cannot be defined as true or false without a proper definition of truth. Considering sentences as meta-signs (from the Sossurian perspective) we might define a true statement as that of a meaningful metasign. This, however, does not exclude the concept of metaphors and/or koans which are 'meaningless', but true. – Manjusri Sep 26 '13 at 21:24
  • If you do away with the excluded middle as intuitionist logic does, then you can say that "this sentence" is referential, and that the sentence is neither evidently true nor evidently false. – Mike Samuel Sep 26 '13 at 23:30
  • "A proposition is a truth-function of elementary propositions." Wittgenstien – ARi Sep 27 '13 at 5:17
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    @Artem_Kaznatcheev I agree partially with the answer given here, although i disagree that the sentence is meaningless. To take your point of comparison first, nobody thinks "the king of france is bald" is meaningless. We all know what it means, and under which conditions it would be true and felicitous. Russell actually thought it was false, Strawson thought it was truth valueless. Nobody thinks it's meaningless. The sentence being asked about is more difficult. It doesn't feel like a presupposition failure. In lieu of more thought, i'd say it has a sense but no reference, in Frege's terms. – P Elliott Sep 28 '13 at 10:04
  • Btw it should be "The present King of France is bald." – Alex B. Oct 2 '13 at 15:11

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