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Is there a formal or semantic difference between these sentences?

  1. This sentence is false.

  2. The sentence containing these words is false.

EDIT: It seems the question is too ambiguous to be answered. I don't know how to make it less so. Perhaps someone could add an edit. I wnat to say the two sentences are equivalent but first I want to check my reasoning as I'm not a logician. If someone stated these sentences are equivalent what would be your response?

  • SEP's entry about the [Liar Paradox](https://plato.stanford.edu/entries/liar-paradox/) presents many variants odf it with a detailed analysis of the "basic ingredients" (that are quite few) needed to produce the contradiction. – Mauro ALLEGRANZA May 05 '20 at 12:26
  • @Mauro - Yes, but what about the question? –  May 05 '20 at 12:33
  • Both sentences are ambiguous & if the ambiguity were removed by the communicator using specific details then there would be no paradox. The point of a paradox is Rhetoric not logic. Does false refer to the real world content of the sentence or does it refer to a truth table kind of truth? If Mathematical logic is about form how is this a question? Logic alone would not tell us anything about sentences. The reader would need to KNOW MORE than just the sentences in front of him. So semantically this is already a set up for rhetorical questions not real mental enquiries. – Logikal May 05 '20 at 14:25
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    "The sentence is containing these false words" contains the same words, but is a different sentence. Are you trying to get to the sentence/proposition distinction? If so, 2. is too ambiguous to do it. In general, descriptions with the same intended referent (like the evening and the morning star) still have different senses, which comes out when substituting into [intensional contexts](https://philosophy.stackexchange.com/q/46361/9148). But it looks like all you (try to) do is use two different indexicals for self-reference. – Conifold May 05 '20 at 15:04
  • The question is very simple and I see no reason to complicate it. From the comments so far I can gain no impression of what the answer is thought to be. It's not a trap, just a simple question. –  May 05 '20 at 15:17
  • @Conifold - You say they are different, but you do not mention how they differ. If they are different, what's the difference? You say S2 is 'too ambiguous' for some purposes, but in what way is it more ambiguous than the first? –  May 05 '20 at 15:22
  • For one thing, "false" predicates different objects. 2. is ambiguous because it picks out multiple sentences. – Conifold May 05 '20 at 15:28
  • @Conifold - How odd. It seems to me that In both cases the word 'false' predicates the sentence containing the word 'false', and that both sentences pick out just one sentence as being false. I wonder why you see it differently. –  May 05 '20 at 15:34
  • To be honest I'm in some despair. How can this question deserve a down-vote? On what possible grounds? I don't care about the rankings but I'm beginning to question my sanity. Why is it so difficult to give a straight answer to this question? It can be just an opinion if you like. I cannot tell them apart,but I'm not such a fool as to state they're equivalent without a prior reality-check. I had no idea it would be a difficult question or annoy people. It is a perfectly innocent an simple question and I'm not completely sure of the answer. I was hoping someone here would be. . . –  May 05 '20 at 17:04
  • I meant your 2 and my variant of it, in the latter "false" predicates "words", not "sentence". And because there can be multiple sentences with the same words the "containing these words" indexical is ambiguous. My guess about the downvote (not mine) is that the question's context and motivation are murky. There are obvious differences in formulation, list of words used, etc., and it is unclear what you are looking for beyond that. The title suggests that this is supposed to do something regarding the Liar. Perhaps, you could spell out what that is. – Conifold May 05 '20 at 22:39
  • @Conifold - I added an edit. I won't respond to your comment because I'm confused about your intreduction of a different sentence. I'll only comment here on answers from now on. After this I'll post a note on the meta-forum and retire from the site. –  May 06 '20 at 12:52
  • I’ve upvoted the question! I think you’re hinting at something interesting about sentential self reference that can and should be addressed; however, I think the weight given to the “liar-like” nature of these two sentences is a bit distracting from the main issue of the question, which is about indexical language and sentence identity. I’ll try my hand at an interesting answer =) – Sofie Selnes May 06 '20 at 14:01

2 Answers2

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Let’s pull this apart from the liar phenomenon for a moment and look at it just as a question about the identity of sentences.

Both sentences have a sentence as their subject and share a predicate they’re attributing to that subject, but their noun-phrase names are different. The question is whether those noun phrases are “the same”, given that they both invoke an indexical component.

So, what individuates a sentence? Intuitively we want to be able to say that if two sentences “mean the same thing” then they are in some important sense not distinct. The sense of meaning involved here is more granular than just simple reference, though.

To roll out a classic example, “Superman has saved the day” is a sentence that we intuitively think we understand - “saving the day” means something like averting disaster, defeating a villain, rescuing Jimmy Olsen and so on, and Superman is the flying guy with the square jaw and the red and blue costume. Also, as both we and Superman know, Superman and Clark Kent are the same person, and so anything referring to one also refers to the other.

Nonetheless, we must acknowledge that “Superman saved the day” and “Clark Kent saved the day” are two distinct sentences. This is straightforwardly so, even when both might be true at exactly the same times, because there is an item of knowledge which we as speakers of the English language must have in order to determine the appropriate use of one given the other - namely, that the two names co-refer. If I don’t know Superman’s identity, it would be news to me that Clark Kent saved the day.

Michael Dummett proposed that there are three different views about the granularity of meanings in language use. We have one view which he called Atomism, which is that sentences are individuated on the basis of their words, which are the bearers of meaning. Two sentences are only identical when they compose the exact same words. Another view, which he called Molecularism, is that there are some notions of synonymy, logical form and definition that allow us to identify some sentences as the same; for example, “The bachelor went home” and “The unmarried man went home” would be the same sentence, because it’s an analytic prior of the language that Bachelor just means an unmarried man. The third view, called Holism, is that sentence meaning is determined by whole language practice, and two sentences are the same just in case they serve the same functions in a community of speakers. So, for example, idiomatic variations and slang terms can be different expressions of the same sentence.

So, I propose that your sentences may be differently individuated depending on who you ask. The Atomist will say that the sentences come apart because the words are different. The Holist might say that both are expressions of the Liar, because of how indexicality works in language practice. My instinct is that a Molecularist might interpret indexicality closer to the Atomist, understanding a process of reference that would require the speaker of the second to demonstrate what the words of the sentence are which is not required in the first.

There is a nice SEP article on Meaning Holism if you would like to explore this division a bit more!

https://plato.stanford.edu/entries/meaning-holism/

Sofie Selnes
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    +1 Many thanks Sofie. You usefully raise some of the issues that arise. Note that I do specify formality and semantics as the two relevant measures of difference. It seems I am a holist. Your answer received a down vote and I wonder why. . –  May 06 '20 at 15:02
  • Peter, Holism does come with some challenges in terms of justifying how you can build up the meaning of a sentence from its parts. That’s not to say it can’t work around that - particularly in formal languages we can hand-wave structured semantics as community norms - but it’s definitely worth reading further if formality is a key area of consideration. – Sofie Selnes May 06 '20 at 15:12
  • @PeterJ That is unexpected. I thought your criticism of the Liar came from its meaning not being composable from meanings of its parts. But that would not be an issue for a holist. – Conifold May 06 '20 at 18:53
  • @Conifold - I find your initial comments on questions very useful and of significant benefit to the site. But on this occasion I would have thought answering the question would have been the best approach. –  May 07 '20 at 10:10
  • @PeterJ But how? As you can see, I am still not sure what the question is getting at or what its intended relation to the Liar is. – Conifold May 07 '20 at 20:21
  • @Conifold. Why does it matter? The question is the question. It could hardly be clearer. But it's okay. I've given up on it. –  May 08 '20 at 12:59
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"The sentence containing these words is false." Presumably, "these words" refers back to all the words including "these words." So we could rewrite it as, "The sentence containing the words, 'The sentence containing these words is false,' is false." This looks like what we could do with the original version: "The sentence, 'This sentence is false,' is false."

Compare to the L-form liar sentence, "L: L is false." The "these words" counterpart might be: "L: The sentence containing the term L is false." I suppose it's not quite the same thing but ultimately it looks like it would collapse into the other case (we might say that, "L: L is false," is true if and only if, "L: The sentence containing the term L is false," is true).

EDIT: There are a lot of liar sentences, after all:

The first sentence on this list is false. C.f. ones formed like "the only sentence on this page" or "the first sentence in this essay".

I am lying/I am not telling the truth/I am telling an untruth (falsehood).

This sentence is false.

This sentence is not true.

"L: L is false," and, "L: L is not true."

The liar loop: "(A) Sentence B is false; (B) sentence A is true."

Yablo's paradox [too complicated to sum up right now, haha!].

"Yields falsehood when preceded by its own quotation" yields falsehood when preceded by its own quotation.

This sentence is false or meaningless.

K: K is unknown (the epistemic liar).

Is this sentence false? [Not an assertoric sentence, to be sure, but that just goes to show the fundamental problem with the construction of the liar sentences: they have no erotetic counterparts and would therefore have the surprising property of being unquestionable and hence axiomatic truths, if they were true!]

Don't comply with this sentence (the unfair sentence).

Is this sentence not true?

L: Is L false/not true?

And I might be forgetting at least one or more. Now, for example, true and false are opposites. Being the opposite of something is not the same as being the absence of something, so falsity is not completely and utterly the same thing, as such, as lack of truth. However, in propositional space, for a proposition to lack truth does imply that it is opposite of what is true. "That it is not true that..." implies, "Not that it is true..." So perhaps the liar sentences distinguished from each other by "not true" and "false" are semantically the same while formally different.

Interestingly, "This sentence is false/not true," does have a usage in natural language, but only where "This sentence" is not self-referential (e.g. I'm giving a lecture and write, "2 + 2 = 5," on the board, then point at, "2 + 2 = 5," and say, "This sentence is false," where "This sentence" refers to "2 + 2 = 5"). "The sentence containing these words is false," or, "L: The sentence containing the term L is false," might be a new entry on such a list, a new species or subspecies of the liar genus so to say (I mean, I've never seen it otherwise, though there doesn't seem to be anything wrong with adding it to such a list).

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Kristian Berry
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  • I'm grateful for any answer so thanks for this one, but it does not seem to answer my question. What is the difference between the two sentences? –  May 05 '20 at 16:53
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    You are right, and the OP is "paying" with the (intended) ambiguity of natural language: this is the reason why (IMO), if we are interested to understand the phenomenon we have to use a "formal," analysis, like that available in many resources (SEP's entry included). – Mauro ALLEGRANZA May 05 '20 at 17:01
  • Well, one just refers to sentences, the other to individual words. So they're pragmatically different. But the semantics of the truth predicate (or a truth-theory of semantics, for that matter) would semantically collapse them. So it's not semantic/formal but semantic/pragmatic? – Kristian Berry May 05 '20 at 17:40
  • It should have been "the sentence containing these words in this order is false". I originally thought that the point was to distinguish between pointing to the sentence as a stand-in for a proposition and pointing to it as a mere collection of words. However, to predicate "false" the collection of words would still have to be interpreted as a proposition in the end, so it does not seem to make a difference for the Liar. And I am no longer sure that was the point. What's missing from the OP is the purpose of noting the difference that is there. – Conifold May 06 '20 at 02:39
  • @KristianBerry - By 'semantically-collapse' them I presume you mean they seem semantically identical. It seem so to me also. Are they also logically identical? –  May 06 '20 at 12:56
  • "L: L is false," and, "L: The sentence containing the term L is false," have a similar enough form that they might be logically equivalent but maybe not logically identical? If there is such a thing (maybe logical equivalence _just is_ identity, after all). The way they bind their variable at least seems similar enough. – Kristian Berry May 06 '20 at 15:39
  • @KristianBerry - It seems this way to me also. But a consensus on this looks well out of reach. –  May 07 '20 at 10:12