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I initially posted this in Linguistics, but wanted to get philosophers' opinions on this as well. (And someone over there is complaining that it's a philosophical rather than a linguistic question... who knew that meaning isn't the concern of linguistics?)

I think it's regarded as common knowledge in linguistics—since Chomsky—that there can be grammatical sentences that are nevertheless meaningless. The standard example trotted out for this is

 Colourless green ideas sleep furiously.

Whether or not there can be meaningless but grammatical sentences, this doesn't seem to me like an example of one. To me, it simply seems meaningful, but false. It seems to me to wear its truth-conditions on its sleeve: for it to be true, there'd have to be ideas that are colourless, green, and sleep furiously. But these conditions aren't met: ideas aren't green, and since they don't sleep, they certainly can't sleep furiously. So the sentence just seems false—indeed, necessarily false, since it's impossible for something to be both green and colourless. But for a sentence to be false, it must be meaningful. So the sentence is meaningful.

Essentially the same question was raised in the Linguistics forum previously, although both the question and answer there seem a bit muddled, with the poster bringing in logic and Explosion when they seem beside the point. A similar question was also posted previously in this forum, but it's more specifically to do with Carnap on "Caesar is a prime number".

I found a similar discussion in Quine's Theories and Things, where he outlines a position similar to mine, in opposition to Ryle, Russell, and Carnap:

Many... predicates will be useless in application to attributes; thus it would be false, at best, to affirm, and useless, at best, to deny, that an attribute is pink or divisible by four. Ryle branded such predications category mistakes; he declares them meaningless and so did Russell in his theory of types. So did Carnap.
 Over the years I have represented a minority of philosophers who preferred the opposite line: we can simplify grammar and logic by minimizing the number of our grammatical categories and maximizing their size. Instead of agreeing with Carnap that it is meaningless to say 'This stone is thinking about Vienna', and with Russell that it is meaningless to say 'Quadruplicity drinks procrastination', we can accommodate these sentences as meaningful and trivially false. Stones simply never think, as it happens, and quadruplicity never drinks. (Theories and Things, 1981, p. 110)

Quine's position seems to me to be quite right, and, applied to "Colourless green ideas...", to lead to my above conclusion. However, Quine says that his position was a minority among philosophers during his time; is it still a minority position today? In the Carnap on "Caesar..." thread, philosopher Stephen K. McLeod is quoted as saying something similar about that issue, so it seems like there's still at least one contemporary defender of this view.

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There's a subtle distinction here between truth-value and semantic-value, one that harkens back to the Russell/Frege debate about 'denotation' and 'sense'. In short, truth-value deals with (bare) facts about the world, while semantic-value deals with impressions of the world. These two often overlap, particularly in analytic and scientific utterances, but they don't overlap by necessity. There was a strong push in the early-to-mid 20th century — peaking with Russell — to ground philosophy in the type of reasoning that the physical sciences use, but by Quine's time that effort had imploded on itself.

As the old joke goes, there are two kinds of analytic philosophers left in the world: those who don't understand Wittgenstein, and those who won't understand him. Ha ha ha…

At any rate, the problem is as follows. We can assign truth-value to any utterance whatsoever based on its conformance to real-world objects or concepts: its capacity to denote. But as often as not that is merely arbitrary, asserting an utterance is false merely because it doesn't point at something we can see or touch. But we assign semantic value in a much more sensitive and context-rich manner. Consider the following utterances:

  • The blue door in the garage is locked

This has a specific truth value, and conveys a specific meaning: if true, it means we cannot use the blue door in the garage without the key

  • I should have been a pair of ragged claws scuttling across the floors of silent seas

This utterance conveys an emotional state. It's likely true at the time of its utterance (in the sense that it is a true representation of a feeling), but the meaning is something we must dig out.

  • Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn

Within the Lovecraft universe this utterance has truth-value and meaning, in the sense that dead Cthulhu is, perhaps, factually dreaming in R'lyeh; in universe it's functionally equivalent to 'the blue door in the garage is locked'. But outside the Lovecraft universe it lacks truth-value or meaning, denoting nothing and conveying no sense to anyone.

  • Colourless green ideas sleep furiously

This utterance is tautologically false because the word denotations contradict each other. But it conveys no meaning or impressions. Unlike the 'ragged claws' utterance this is semantically empty.

  • Spleznitzia clabulant displa glor.

This utterance is merely grouped strings of letters. It has no truth-value because none of the 'words' have any denotations, and it is semantically empty because it conveys no impressions.

The tricky aspect of this, of course, is that human mind generates meaning through analog processes like metaphor and simile. That's why the 'ragged claws' utterance has meaning; it evokes a particular set of feelings and imagery. With effort, one can generate meanings for the last two utterances through creative association or some such, and once we've created such meanings we can revisit truth-value. But the point is that these are two distinct processes that are too easily confused.

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    +1 Comprehensive, though I'd upvote just on the basis you're using Lovecraft's fictional domain. It's as fun as exemplifying with Sinadarin or tlhIngan Hol.
    – J D
    Commented Jun 20 at 17:47
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    Could you explain the "old joke". Is there more to it than a laugh at the fact that nobody understands Wittgenstein? Is there a more direct link with his work? (Also it seems implied that the joke i well known but googling didn't immediately turn anything up. Is it an adaptation of a more popular form of the joke?)
    – Kvothe
    Commented Jun 21 at 0:17
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    This answer's a bit thin. We can't assign truth values arbitrarily; we must give a functor. And, incidentally, we also must give a functor when assigning Montague semantics. Perhaps we should expect any notion of meaning to be structure-preserving.
    – Corbin
    Commented Jun 21 at 2:21
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    One detail I'm having trouble with: "Unlike the 'ragged claws' utterance this is semantically empty." For me Chomsly's phrase is just as visual and evocative, if not more so, despite the logical contradiction. So when you claim it lacks meaning or impressions I feel like that simply isn't true for me (even if I can believe it is true for you).
    – Brian Z
    Commented Jun 21 at 2:22
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    @Corbin: We can (and do) assign truth-values arbitrarily when utterances have no proper objective reference. The phrase "unicorns are grumpy" is arbitrarily labelled false on the (unproven) pretext that unicorns don't exist. I could equally argue that "unicorns are grumpy" is true on some other pretext. But we don't want to be using pretexts at all for truth assignments. Commented Jun 21 at 5:17
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You could also argue that it's a vacuous truth in the sense of:

Have you ever seen one of those colorless green ideas? You haven't? Then how do you know they don't actually sleep furiously.

If from A follows B and A is impossible than the implication is still true, though useless.

Also the meaning of words kinda depends on a shared context, though the context (English language) doesn't fit. The grammar seems to be ok, but the semantics makes no sense. Like green is a color, so not colorless, ideas don't require sleep and it's impossible to sleep while being furious so no matter how you twist these words they don't make sense. Meaning to you and your context they are meaningless. Though they could very well be a passphrase or something comparable.

Or for example a green party might conceive a "green idea" which is nonetheless itself colorless as ideas don't have color, which might be revolutionary and furious but not enacted so as of right now "dormant" (sleeping). So in that case it could even be true and meaningful but you'd need a very technical vocabulary that is not obvious or itself provided by that sentence.

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    Maybe it's a vacuous truth, but in that case, it's still meaningful. In any case, if the rest of your answer is just pointing out that there's a contradiction and an impossibility in the sentence, then I agree; but again, for a sentence to describe a contradiction and/or an impossibility, it still must be meaningful.
    – Spailpín
    Commented Jun 21 at 10:45
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It is considered meaningless only to the extent that people generally agree that it conveys no shared understanding when expressed or received. The statement is generally understood to not convey any information from one person to another. As an example it certainly can be part of an larger context that conveys meaning, as is evidenced from this Q&A, but as a proposition in itself, it does not.

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    +1 For drawing to light that a sentence can have meaning both from the composition of its constituents and from existing as a compositional element of a context.
    – J D
    Commented Jun 20 at 17:16
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Why is "Colorless green ideas sleep furiously" considered meaningless?

In the philosophy of language, one has a choice of theories of semantics. So, when you ask, why the sentence is meaningless and expect an explanation, you are asking for a theoretical basis. For starters, every sentence has a syntax and semantics associated with it. The syntax are the rules of construction, and the semantics is what we associate with the meaning. First you must recognize that this a grammatical sentence that doesn't convey a clear complete thought.

Clauses in natural language are constituents of a grammar that express "complete thoughts". This sentence has the right syntax, but it does not express a complete thought according to the conventions of language. For instance, it's 'raining cats and dogs' is an idiom that by convention means 'it is raining heavily'. 'Raining cats and dogs' doesn't make sense to someone not familiar with the idiom because cats and dogs do not literally fall from the sky. But the sentence is meaningful because people accept that the idiom is a stand in for the idea of heavy rainfall. Thus meaningful sentences (according to this theory) are constructions in currency in society that convey shared meaning.

Now, let's consider a second source of the origin of meaning: when constituents are polysemous, meaning is derived from context. What does 'sound' mean? Is it the experience of hearing something or is it the vibrations of air? Interestingly, it might be neither. Sailors aboard ships used to sound depths by lowering ropes with weights to gauge how deep water was. And 'sound' might also indicate the shallow body of water that a sailor would perform such an activity in. So, here, the meaning is only clear by the context:

  • The energy of the sound wave was measured by the sound level meter.
  • The sound of the ghost was scary.
  • The ship in the sound ran aground.
  • To avoid running aground, the sailor sounded and reported to the captain.

Lastly, the meaning of sentences can be derived from its constituents in line with the principle of compositionality. In this case, the technical terms are words like lexemes and morphemes. While 'colorless' is meaningful, and 'green' is meaningful, the phrase 'colorless green' seems to be a contradiction. And how do ideas sleep? What does it mean to sleep furiously? None of these are meaningful constructions even if the constituents (words, phrases, and clauses) of a sentence are. Thus, we have a vague sense the sentence has some meaning, but it doesn't express a complete thought.

So, Ted Wrigley pointed out, we can apply two types of semantic theories to this sentence, the truth-conditional semantics (one in which we can simply say the lack of reference results in the declaration of the falsity of the claim), or we can take a richer semantic theory such as that of cognitive semantics. We can understand, for instance that this utterance, or if you prefer, locutionary act, lacks both illocutionary and perlocutionary force. And why would this be? Because there is no conventional meaning, no contextual meaning, nor is there any coherent compositional meaning that we assign to the sentence. And that is why this sentence is generally recognized as meaningless.

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    Thanks for bringing up compositionality; I suppose the main thrust of my argument here is that if the principle of compositionality is true, then I don't see why this sentence shouldn't be meaningful. As I've said many times at this point, something's being contradictory does not show that it's meaningless but instead quite the opposite, since something must be false (and therefore meaningful) in order to be contradictory. Similarly, if ideas' sleeping and sleeping furiously are impossibilities, that shows that those expressions are meaningful, not meaningless.
    – Spailpín
    Commented Jun 21 at 10:50
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    @Spailpín Whether or not it is meaningful is your decision, because like one camp, you are free to make anything meaningful by declaring it to be vacuously false. You would be in good company with many people who agree that it has some form of meaning. If you cite the principle of compositionality, those who disagree can argue, that's it's not just that you have to meaningful parts, but those parts also have to have a meaningful structure. You can have wings, a fuselage, jet engines, and a pilot, but if not assembled in the right configuration, you don't have a plane...
    – J D
    Commented Jun 21 at 14:27
  • But the choice of how to define meaning, your semantic theory is yours alone. :D Good luck!
    – J D
    Commented Jun 21 at 14:28
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"___ is meaningless" is one of the ways out of the problem that "Which ___?" and "Where/when/why/how do ___?" always returns a category error instead of an answer; and that if you take them to be meaningful, both "subject predicate" and "subject not predicate" return false, which is a contradiction.

The other way out is to re-express "subject predicate" so that "subject predicate" denotes "entity is in category: 'subject' and entity does action and action is in 'predicate'". This can be further blown up for compound subjects (colorless green ideas) and compound predicates (sleep furiously). "Entity is in category: 'idea' and entity satisfies quality: 'green' and entity satisfies quality: 'colorless' and entity does action and action is in category: 'sleep' and action has quality 'furious'." Then it can evaluate like any string of claims joined by "and", thus saving certain meaningless statements for use in formal logic. As far as I know, an approach like this was first made well known by Russell in the early 20th century.

The latter approach has been criticized for not adequately comporting with the actual use of language. You can find a summary of the argument here.

Note that even if you accept the denoting-by-explosion approach, you still need a category for meaningless statements where the individual words don't mean anything or where the syntax is unintelligible.

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Colourless green ideas sleep furiously

In my favorite dialog about semantics we find

"There’s glory for you!” “I don’t know what you mean by ‘glory,’” Alice said. Humpty Dumpty smiled contemptuously. “Of course you don’t—till I tell you. I meant ‘there’s a nice knock-down argument for you!’” “But ‘glory’ doesn’t mean ‘a nice knock-down argument,’” Alice objected. “When I use a word,” Humpty Dumpty said in rather a scornful tone, “it means just what I choose it to mean—neither more nor less.” “The question is,” said Alice, “whether you can make words mean so many different things.” “The question is,” said Humpty Dumpty, “which is to be master—that’s all.”

If Humpty Dumpty is right, then it seems that we (well, at least he) can also interpret any statement as meaningful (or meaningless) if we can give it a meaning (or rob its meaning from it).

If it is meaningful to assert that colourless green ideas sleep furiously, then it's false. The assertion presupposes

There are ideas that are both green and colourless

which presupposes

There are things that both have color and don't have colour

which is a self-contradiction. If we may assume that no self-contraction can be true, then the original statement must be false. There's glory for you, indeed!

But, wait! How should we interpret "presupposes"? Are we allowed to say

The statement (a linguistic thing) presupposes ...

or

The proposition (that what the statement expresses) presupposes ...

or

The assertion (which somehow links statement and proposition) ...

or

The assertion, if done with assertive force, ...

or

The fact (that what the assertion when done with assertive force putatively refers to) ...

I really don't know. As someone with a formalistic/engineering mindset, I can only deal with this by short-circuiting all this, and asking what does it matter?

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    Oh its more than just that (and I guess you know it). (1) colorless+green — you talked of that much (2) "color" applied to "idea" (3) ideas having the potentiality to sleep (4) adverb furiously modifying verb sleep. That sentene is a work of art in itself!
    – Rushi
    Commented Jun 20 at 17:24
  • @Rushi - You guessed right. Still, to me that sentence is not too different from the poetic example that Ted Wrigley gave. It does evoke a kind of picture. Perhaps because I tend to think of ideas as little lego blocks, that sometimes do seem to sleep furiously when they are giving me logical nightmares.
    – mudskipper
    Commented Jun 20 at 17:41
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    +1 I'm upvoting because you exposed the contradiction, which is a good first step in analysis; you can continue to explore the sentence by broadening your exploration of compositional constituents. You might also be interested in the SEPs presuppositions, which is useful when fanning outwards when exploring an utterance in a context.
    – J D
    Commented Jun 20 at 17:44
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    Veritas, meaning is assigned.
    – Hudjefa
    Commented Jun 21 at 2:49
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+50

It is a matter of labelling, or how you chose to define meaningless. Sentences can exist on a spectrum spanning from utter gibberish to remarkably clear and informative, with no well-defined threshold beyond which the term meaningless is unanimously applied. Any sentence of the form 'verb subject object' will have a literal meaning if each of its constituent words does. Take 'anticlockwise Tibetan nose farmers deplete antagonistic yellow'. You can, if you wish, treat it as having a literal meaning and being false, on the grounds that there are no such things as anticlockwise Tibetan nose farmers or antagonistic yellow, and even if there were, the former are not known to deplete the latter. Or you could take it to be meaningful and vacuously true. However, if you adopt that position, you are rather obliged to consider the question 'Do anticlockwise Tibetan nose farmers deplete antagonistic yellow?' as being a meaningful question. If you take the view that it is a meaningful question, with the answer 'No', then you are also obliged, it seems to me, to consider the question 'Do anticlockwise Tibetan nose farmers not deplete antagonistic yellow?' to be a meaningful question requiring the answer 'Yes', which seems rather stretching the envelope of meaningful.

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  • I agree - kind of. But are we actually free to chose how to define meaningful/meaningless? And if we are then am I free too? If I am, then I could construct a private language. Is Wittenstein's argument against the possibility of private languages invalid? Or does it depend on how we define "possibility" or "private language"? But then we're back at square one. --- It's interesting - and emotionally moving - to see how some poets and philosophers go a very long way on the road(s) to private languages (Paul Celan, Alfred North Whitehead - try reading "Process and Reality").
    – mudskipper
    Commented Jun 25 at 14:37
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    As @mudskipper suggests, we're not entirely free to choose how we define 'meaningless'—at least, not any more than we are any other word—and doing so may well just change the question from what I originally asked. Anyways, re: "Anticlockwise Tibetan nose farmers don't deplete antagonistic yellow": if that just means that it's not the case that ATNF deplete AY, then yes, that's true. But if it's understood as saying that there are such nose farmers, but they don't do that, then that's also false.
    – Spailpín
    Commented Jun 29 at 14:28
  • Hi guys, I disagree that words have well defined and unanimously agreed meanings. There are many examples in philosophy of disagreements at cross purposes owing to conflicting uses of the same word. Also, words that imply something to an extent, such as big, fat, lazy etc, are inherently vague because there is no sharp cut-off for their areas of applicability. When does a person stop being fat, for example? It is not a matter of changing the overall meaning of a word, but of where you draw the line. Commented Jun 29 at 14:55
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"Colourless green ideas sleep furiously" is not absolutely meaningless. Some parts of it are meaningful starting with letters , words and groups of words etc. But it fails to deliver a coherent meaning on the whole because it doesn’t relate to the state of affairs of the world or universe. Natural sentences and their interpreters do not work in classical logical framework. Meanings can be nebulous or vague. Meanings arise like waves. Meanings are build upon meanings. So yes , it is meaningful upto some extent but then it degenerates into meaninglessness.

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Doesn't the statement in question consist of a concatenation of fundamental category errors which render it meaningless or at least impossible to make logical sense of, in the first place?

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  • As I've said numerous times in response to other questions: if by "category errors" you just mean that it's impossible for ideas to be coloured, or to sleep, etc., then I agree; but that doesn't entail meaninglessness.
    – Spailpín
    Commented Jun 29 at 14:29
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Just to give a bit of counter-weight to the orthodox, linguistic kind of overview that others gave ...

From a computational, statistical point of view -- the point of view of distributional semantics -- we can see "meaning" as something that emerges from encoding words (and sequences of words) as multidimensional vectors of floating point numbers (and using those in some dialogue system or natural language understanding task). It does not make sense in this kind of view to speak of "the meaning(s) of a word" except by saying something like "meanings of a particular word, as found in a particular corpus of texts, and as relevant to performing certain natural language understanding tasks, are all encoded in this vector". Similar for phrases and sentences.

So, "meanings" (of words) are just word embeddings. The meaning of a phrase or sentence can then be modeled (for instance - there are different approaches) as a walk through word vector space. Which can itself be seen as a higher-dimensional vector. (It's amazing how powerful even the model of a random walk is. Unfortunately I cannot find the reference I have in mind here, but look for instance at studies by Sanjeev Arora.)

[Ok, speaking more carefully, you would say: We don't know what "meanings of words" are, or how they work, but we model them - whatever they are - by word embeddings. When a model becomes very dominant, we tend to start saying "x is y" instead of "we model x by y". Perhaps at some point we start forgetting that we're using a model and start conflating model and reality.]

Why are some sentences then commonly considered to be "syntactically ok, but semantically meaningless"? That's just because of social habit. They are kind of uncommon. It doesn't really mean very much - though a certain sequence of words "colorless green" might be very uncommon and other parts more common. The perception of "meaningfulness" can slowly change over time and for different groups the "semantic meaning" might be very different. Personally, I would also tend to say that the colorless green ideas sentence is sort of meaningful, but a little self-contradictory, and therefore false - but I don't really know what an "idea" is, so I might reserve judgement... For me that sentence as a whole - because it has been used so numbingly often - has become more like an index (in Pierce's sense of the word), a sign "that signifies its object solely by virtue of being really connected with it", like the symptom of a disease or an actual pointing finger. The "object" in this case would be the lack of imagination of linguists who simply keep paroting Chomsky. (See Pierce, 1885)

[As evidence that the sentence as a whole has become a kind of "index" in the above sense, just type "colorless g" into a search engine - just that, one letter 'g', not the whole phrase. The first thing that comes up is that sentence. If you want to have a more charitable view of linguists, then you could also say that its object is "exemplary sentence illustrating semantic meaninglessness" - so it has become a self-referential sentence - even though a very dull one.]

Pierce classifies all signs (linguistic and non-linguistic) as 'tokens', 'icons' and 'indices'. A 'token' signifies by arbitrary convention; an 'icon' by similarity of structure; an 'index' by direct/causal connection to the signified. In any discourse (e.g. a mathematical proof) signs of each category are needed. He then says something that is both trivial and deep, and imo goes to heart of the problem of hallucinations in LLMs:

But tokens alone do not state what is the subject of discourse; and this can, in fact, not be described in general terms; it can only be indicated. The actual world cannot be distinguished from a world of imagination by any description.

If you accept this (I do), then you perhaps also accept that a theory of meaning (a model) trained only on text, can never totally capture "meaning" (semantic meaning) since it's a theory without world. But ... where is this world that we pretend to know? Do we have access to the world? Is it possible to compare a fact (that what a true sentence presumably refers to) to the semantic meaning (that what the sentence supposedly says)? If we can compare them it's only because of non-linguistic indices.

To come back to the infamous colorless green ideas. It makes as much sense (now, for us) to call that sentence a meaningful but false sentence as it does to call it a meaningless, neither true nor false, sentence. I can declare it to be meaningful and derive a falsehood (as I did in another answer). But taken as an almost pure index, it doesn't assert anything, it just is. To quote Pierce again:

The index asserts nothing; it only says "There!" It takes hold of our eyes, as it were, and forcibly directs them to a particular object, and there it stops.

[The student, who actually already read a lot of linguistic theory, but is contemplating switching to CS, looks at the professor who just uttered "A classic example of a semantically meaningless sentence is ..." "Oh, no," the student thinks, "I know what's coming..." "...'Colorless green ideas sleep furiously'." "No!," the student thinks, "not again! I'm going to switch."]

Meanings are slippery little critters, scuttling around - furiously or in a haze - on the floor of our minds. Sometimes we break them - and remake them - and sometimes they break or (re)make us.

Symbols become cymbals in the hour of death

(Gerrit Achterberg, Werkster (Charwoman), 1949)

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    Can we not simply extend our understanding of word meaning to sentences?
    – Hudjefa
    Commented Jun 25 at 2:31
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    Depends on what you mean by 'extend'? There are different ways of generating word embeddings and 'extending' those to sentences. In the most simplistic bag-of-words model a sentence acquires its "meaning" just by summing up the word vectors. That's of course pretty primitive and not terribly useful (but still a little). But generally you do want to also encode the order of words in a sentence somehow. (The original transformer models did that in a very elegant, ingenious way.)
    – mudskipper
    Commented Jun 25 at 13:10
  • Si, the meaning of a sentence as (merely) the sum of the meaning of the words is what I was referring to. Notice though, sir/madam, that the meaning of words isn't truth-apt (the meaning of a word can't be true/false), but once we "sum up" the meanings of words in a sentence, it becomes a proposition, a truth-apt entity. Do you have anything to say about that? Thank you.
    – Hudjefa
    Commented Jun 26 at 2:34
  • I don't really have anything to say about that, except to consider Pierce's quote (above) again. (Also, not every sentence expresses a proposition.) If you train an LLM on a task where you want it to learn to distinguish truth from falsehoods, then this possible to some extent (asks ChatGPT if fairies exist or whether it has a concept of truth) - LLMs are trained to provide factual info and be coherent, but this is limited to what they have been fed as factual info and by their reasoning capabilities.
    – mudskipper
    Commented Jun 26 at 2:47
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    No, the word "proposition" is commonly used (n these kind of contexts) to refer only to sentences that are used to express facts - assertions of putative fact. And that's also how I'm using it. Obviously, many sentences do not do that. For instance a recommendation, request, or command does not assert a fact - but obviously those do have (semantic) meaning.
    – mudskipper
    Commented Jun 26 at 15:24

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