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Wittgenstein and many others have said that our language gives the appearance of truth to some nonsense.

Do you think the very simple "This sentence is written in English." is such nonsense which seems true?

It seems true, but if you translate it into French it becomes "Cette phrase est écrite en anglais." which seems false. It seems to me that these sentences are both nonsense because a truth should be true independently of the language used to express/encode it.

For the same reason, in mathematics and logic, I think you should not have a reference in the semantics to the syntax. I think to have such a reference can only produce nonsense.

What do you think about this?

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    A truth about expressing something in a language need not be true independently of the language used to express it. So this is not what Wittgenstein had in mind by linguistic "nonsense". He had in mind philosophers applying expressions whose use is established in ordinary contexts so far beyond those contexts that they become senseless. As for your French translation, it is incorrect. The meaning of "this" shifts, the translated pronoun must still point to the original sentence in English. It always happens when translating self-referential sentences.
    – Conifold
    Jul 7 at 12:50
  • There are philosophers who believe that natural language statements can only be objectively true or false if they express language-independent propositions, see the discussion of "classical semantic theories" here which says whether they are true or false depends on what information they encode or express. This “information” is often called “the proposition expressed by the sentence”. So this example might pose a genuine puzzle for that type of view.
    – Hypnosifl
    Jul 7 at 22:15
  • One might also want to consider whether the sentence This sentence is written in English can be paraphrased as The sentence "This sentence is written in English" is written in English without changing the English-language meaning--for the latter sentence one could translate the part outside the quotation marks into a different language without changing the truth-value, so perhaps one could conceive of a proposition that has as its object a particular English-language statement.
    – Hypnosifl
    Jul 7 at 22:22
  • 'This sentence is written in the language it's written in.' is not nonsense, it's redundant. If you define nonsense as "foolish or unacceptable behavior." then yes. If it's, "denoting verse or other writing intended to be amusing by virtue of its absurd or whimsical language." then I don't find it "amusing" "absurd" or "whimsical". Definition 1: "spoken or written words that have no meaning or make no sense." speaks more about this question itself than any statement made in it.
    – Mazura
    Jul 8 at 1:01
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    For the logical fun and games you can play with self-referential sentences, read Gödel, Escher, Bach by Douglas Hofstadter. Jul 8 at 18:06

8 Answers 8

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"This sentence" is an indexical term. An indexical is a term like "I", "today", or "this city" where the reference of the term depends on the context of the sentence--who said it, when it was said, etc. So for example, if Joe Biden were to say, "I am president of the United States", he would be uttering a true proposition, but if I were to utter the exact same sentence, I would be uttering a false proposition. The difference is in who utters the sentence, which is part of the context.

Indexicals have lots of strange properties. For example, the sentence "I am speaking", when spoken, seems to be necessarily true in some sense, but it doesn't seem to be a logical truth. This category of a necessarily true sentence that is not a logical truth is difficult to square with traditional ideas of logic.

What an indexical term refers to is not decided in the same way as for other types of noun phrases. Your question offers a clever example of this difference. If you translate, for example, "The singing man fell off the ladder" to French, you translate the definite description "the singing man" to French by producing a phrase with the same meaning, and the phrase then has the same referent (the thing that it refers to). For definite descriptions the meaning fixes the referent.

For indexicals like "This sentence", the meaning does not fix the referent. In the sentence "This sentence is written in English", the "this sentence" refers to the English version of the sentence. If, as you point out, you translate the meaning into French, the sentence becomes false, and the reason it becomes false is because the referent of "this sentence" is different in the French translation than it was in the English original.

So the answer to your question: yes, the sentence is meaningful, but it doesn't have the simple mapping from meaning to referent that most sentences have.

As to whether you can have a consistent language where a sentence can refer to its own meaning: yes, you can, but you have to be careful how you do it. Indexicals in general are a common source of trouble.

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  • "This sentence has five words." and "Cette phrase a cinq mots." An example of a sentence which maintains its truth when translated into another language (though maybe not every language). Jul 8 at 16:06
  • @DarrelHoffman certainly not every language. Jul 8 at 16:44
  • @DarrelHoffman A few examples where it doesn’t maintain its truth: Irish Tá cúig fhocal san abairt seo and Greek αυτή η πρόταση έχει πέντε λέξεις both have six words, while Japanese この文には五つの単語があります kono bun-ni wa itsutsu no tango ga arimasu has eight (or nine, depending on how you chop them up). Jul 8 at 20:26
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    @JanusBahsJacquet Fair enough, I'm sure there are countless examples. But just trying to show one example where a self-referential sentence could survive translation. Maybe a better example would be "This sentence describes itself" A statement which is recursively true (if not particularly useful) in any language. Though there may still be some where this cannot be translated at all. There's just so many different languages each with their own idiosyncrasies that it's probably impossible to come up with any statement that will be true in all of them. Jul 8 at 20:41
  • @DarrelHoffman, "This sentence describes itself" could be consistently viewed as either true or false. This is the kinds of issue I had in mind when I said that you have to be careful adding a "this sentence" sort of construct to a formal language. Jul 8 at 22:22
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This sentence is written in english.

Cette phrase est écrite en anglais.

These are different sentences; they have different words to each other. An accurate translation of the first sentence into French would be:

La phrase « This sentence is written in English. » est écrite en anglais.

“This” in the first sentence refers to the first sentence, and “Cette” in the second sentence does not refer to the first sentence: each word refers to the sentence it is in. Therefore, one sentence is true and the other is false.

Unless, of course, the first sentence was really written in (the fictional) Sinister English: a language that uses the same words and grammar as English, but with completely different meanings. In this case, we can't really know whether the sentence was written in English, just from that. Instead, consider:

This sentence is a meaningful English sentence.

which would still be true when interpreted as English, even if it were intended as a Sinister English sentence when it was written.

For the same reason, in mathematics and logics, I think you should not have a reference in the semantics to the syntax. I think to have such a reference can only produce nonsense.

In mathematics, we have the distinction between first-order logic (no self-reference) and higher-order logics (less well-behaved, but can express proofs about proofs). Neither are meaningless.

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    Re: your final paragraph, it's famously not true that first-order logic prevents self-reference. Jul 7 at 23:15
  • @NoahSchweber That's not self-reference; that's constructing a lower copy of the first-order logic and proving stuff about it, But I get what you mean; I don't know that higher-order logics particularly allow for that either, so the distinction I made is probably wrong.
    – wizzwizz4
    Jul 7 at 23:38
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    I'm not sure what your distinction between self-reference and "constructing a lower copy" is exactly. But certainly the proof of Godel's incompleteness theorem (or completeness theorem, for that matter), which lives entirely in first-order logic, is a "proof about proofs" (re: your final parenthetical). Jul 7 at 23:42
  • @NoahSchweber Things like Russell's Paradox don't exist in first-order logic, but they do in naïve set theory (which I think is a second-order logic). By my "proofs about proofs" remark I intended the kind of difference between an emulator and self-modifying code; first-order logic can represent the rules of first-order logic, but the objects within the meta-proof are not the same level of object as are used to construct the meta-proof.
    – wizzwizz4
    Jul 8 at 8:51
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    @NoahSchweber One distinction between self-reference and "constructing a lower copy" is that the "lower copy of the logic" can have different properties than the original logic - for example, assuming say ZFC is consistent, it follows that also ZFC+"ZFC is not consistent" is also consistent; in that theory, although the logic itself is consistent, the "lower copy of logic" you get by "proofs about proofs" is not consistent
    – user49822
    Jul 8 at 11:37
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"This sentence" and "cette phrase" refer to different phrases, one being English, the other being French. If you wrote "The second sentence of my English translation of "War and Peace" is written in English", that would stay true if you translated it into French. But if I say "The first book on my bookshelf is "War and Peace"" and you say the exact same sentence, it is possible that one of us says the truth and the other doesn't, because they refer to different books.

So not only can a translation be false when the original is true, but the same sentence, uttered by different people, can be true at times and false at other times.

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Disclaimer: I'm not intimately familiar with Wittgenstein and like many philosophers he uses language quite deliberately so that "nonsense" isn't just "rubbish", but where he distinguishes between sense and reference and between "not making sense" and "nonsense".

That being said as this sentence is self-referential and not connected to a real thing or a relation between things but is more of a tautology I'd say it's nonsense.

In terms of it's truth value. Well yeah "this sentence is written in English" and "Cette phrase est écrite en anglais.", can both be true, "cette phrase" would just not be self-referencing but referencing "cette phrase (qui a été écrite avant celle-ci)". Also you could argue that "English" in that first sentence is not just a word but a reference to the language of the phrase so it's more of a variable [language that the rest of the sentence is written in] that when written is evaluated to it's current value, but when translated must be reevaluated as such.

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Self reference isn't a simple on/off thing. The more self-referential something is, the more it is prone to paradox. For example, "This sentence is false," can't be resolved into true or false, whereas, "All Cretans are liars," is somewhat self-undermining if a Cretan says it, but can have a logically consistent meaning.

"This sentence is written in English," would cease to be true if translated literally. Yet it's perfectly easy to understand in its current form. One thing that makes it feel nonsensical is that it carries very little meaning, since I already knew it was written in English by reading the first couple of words. But we can have a similar sentence that is somewhat self-referential and actually useful.

For example, I could be addressing a group of French speakers, and say, "I'm sorry I'm speaking to you in English, but I didn't have time to get any of this translated into French." There's a sentence that is useful, but only accurate in English.

We have to accept that some phrases are true only for specific uses. A sentence like, "My name is François," isn't as consistent as, "0 + 1 = 1", because its truth value depends on who's saying it.

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It's a mistake to think that there are such things as simple propositions and these remain eternally true because they are outside of time altogether. Some propositions are outside of time and always true, but the vast majority are not. Which is why Ibn Sina temporalised logic because he wanted to ensure that logic took notice of the world around it and time there of course an essential factor. The same point is made in Buddhist logic where propositions by themselves are empty.

The sentence you mention refers to it's context and hence to remove it from its context by translating it is simply to falsify it. There's nothing particularly insightful here that's going on. It's akin to the sentence:

what happens when an irresistible force meets an immoveable object.

which everyone knows because it is phrased is such an eye-catching way. But of course it means very little and in fact it is the less eye-catching proposition:

a force is that which causes change in object

This is Aristotle's definition of force and which was reified into Newton's mechanics. It's less eye-catching but far more substantially useful.

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In addition to the many excellent points others have raised, it’s not at all obvious that every English sentence must have at least one corresponding French translation with the exact same meaning, or even the same truth value under all circumstances. Or that, if it did, this would be a literal translation with no added qualifiers or footnotes.

It’s possible that you’re implicitly working in a paradigm where this can be assumed. Does Wittgenstein anywhere say this?

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+100

If I may: I think Wittgenstein, being Wittgenstein, would be very likely to believe it was not nonsense, and if you can show that his theory of language games rely on it being nonsense, he would apologise and retract them (though of course there may be no consensus on his theory of propositions etc., in which case you'd have rubbished only some interpretations).

a truth should be true independently of the language used to express/encode it

This is a powerful expression! However, in analytic philosopher you often see philosophers add extra ingredients to clarify (they would see it as an equivocation I suppose) a problem.

One way of doing so here is to say that the "truth value" of the proposition is independent of the language used to express it, but not its being true.

Another, is simply that translation need not "preserve self reference", which is the better dissolution (and the latter is deeper, and you can google the phrase, though I haven't).

If you want to learn more about this, you might want to start with Davidson's 'On saying that', and work from there

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