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I’m pretty new here. My main focus is logic, so I spend most of my time on the math and philosophy forums.

Chomsky proposed that while “colorless green ideas sleep furiously” is a well-formed sentence in English, it is semantically meaningless. As something of a logician, it seems to me that this sentence indeed does have semantic content, i.e. the same semantic content as “0=1 implies pi is an integer.” That is, it seems to me that not only is there semantic content to this sentence, but that the apparent oddity of it is just the oddity of the Principle of Explosion in disguise. I know that logic is a kind of language, and logics can be invented so that explosion goes away. Given that, is this already something that has been noted? If not, is there something I’m missing at the linguistic level that has priority over pure logic?

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    Poetry is what it is.
    – Lambie
    Commented Nov 7, 2023 at 17:23
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    There is lots in language that has priority over pure logic; in fact, natural languages are rather bad at expressing pure logic, and words and even operators have to be given specialised, unnatural, interpretations to manage it. For example, people sometimes ask whether English "or" means exclusive or inclusive or. I suggest that the answer is either or both, or neither. Much natural language doesn't map well onto formal logic.
    – Colin Fine
    Commented Nov 7, 2023 at 17:34

2 Answers 2

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Chomsky observed (Syntactic structures p. 15) that "Colorless green ideas sleep furiously" and "Furiously sleep ideas green colorless" are both "equally nonsensical", but "any speaker of English will recognize that only the former is grammatical". From this we conclude that "the notion 'grammatical' cannot be identified with 'meaningful' or 'significant' in any semantic sense".

The question of semantic interpretation is orthogonal to this point, and we cannot assume any particular view of "semantics" at the time (his semantic theory only started to develop much later). Under a correspondence theory of meaning, neither string compositionally describes a logically-possible state of affairs. However, like many utterances, the string can be pragmatically interpreted as suggesting some other idea, which is not the same as a literal semantic interpretation (it would be part of broader "meaning"), following pragmatic notions developed after Syntactic structures. Semantic content is not just symbol-manipulation, it is about logical relations between contentful concepts and propositions.

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  • It is clearly false that the sentence in question is impossible. Whatever is a colorless green idea sleeps furiously, unless we’re assuming some sort of Free Logic as our base FOL.
    – PW_246
    Commented Nov 7, 2023 at 17:39
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    @PW_246 What the answer above says is that you can't "bar things like connotation". "Connotation" is the major part of "meaning"; logic is jus a skeleton drawing of syntax.
    – jlawler
    Commented Nov 7, 2023 at 17:52
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    @jlawler that’s fair. It also holds that colorless green ideas dream furiously.
    – PW_246
    Commented Nov 7, 2023 at 17:57
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    orthogonal to this point? Hmm
    – Lambie
    Commented Nov 7, 2023 at 18:00
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    @PW_246 Exactly, Language and grammar have nothing to do with truth, which is a logical concept. If it's grammatical, it doesn't matter what it means or whether it's true.
    – jlawler
    Commented Nov 7, 2023 at 20:35
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First, it should be clear that in natural languages nothing has a rigid definition. To make sense of a sentence is thus to select "definitions" so that the sentence has the intended meaning. This is done through common sense and context.

A core principle of communication is to be relevant. A obvious tautology defies this principle, as there is no information conveyed. Whoever interprets the semantics of a sentence to be a tautology usually just discards this interpretation, as it normally turns out to be just a misunderstanding. If the intended meaning is a tautologies, they, e.g. unreal conditions, are always marked ("If I were a boy").

When confronted with "colorless green ideas sleep furiously" the "logician's" meaning is immediately discarded, and the hearer looks for increasingly unrealistic interpretations of the words, until they eventually will give up, since without context, this sentence just can't be interpreted in a sensible way.

Without context, it is impossible to decide whether the meaning is "all colorless green ideas sleep furiously" or "there are colorless green ideas that sleep furiously" or "the way colorless green ideas sleep is (always?/usually?/sometimes?) furiously.". If a quantifier is a ∀ or a ∃ is usually decided by context. And if green ideas can't be colorless, then the above sentences are either right or wrong depending on the quantifier.

That is what he meant with nonsensical: There is just no obvious parsing into a logical statement.

Side note: When delving into metaphors, one could almost use this sentence: There are good ideas, let's call them "green", and bad ideas, let's call them "red"... Some ideas don't have an obvious color you can see; they are colorless. But what if they were, in reality, green? Colorless green ideas sleep furiously, annoyed at how you don't invoke them because you can't see their value. (in this contrived example, the sentence is not a tautology)

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  • It’s pretty standard to take the quantifier as the universal, since universal quantification is usually over conditionals in practice.
    – PW_246
    Commented Nov 9, 2023 at 3:23
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    @PW_246 That reminds me of the "brown cows in Scotland" joke, see e.g. neatorama.com/2007/01/22/a-mathematical-cow-joke . The logician assumes universal quantification, but this was not really what is meant, since most humans have not seen every single object of a category to conclude a universal property with certainty.
    – Dodezv
    Commented Nov 9, 2023 at 9:16
  • pretty much all conditionals operate like a universal quantifier, so if there is any leeway, it’s in the direction of muddled or mixed meaning. Perhaps most people omit the “ceteris paribus” clause before stating a conditional, but that doesn’t remove the universal aspect of the quantifier involved.
    – PW_246
    Commented Nov 9, 2023 at 17:10

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