Copernicus
Industrial Grade Linguist
What is the syntax error that you are referring to? All of the sentences under discussion are syntactically well-formed.
You could actually mention Kurt Gödel's name, if you are going to talk about completeness. He was a mathematical logician, but he was still working within the limitations of a closed context free symbolic system that simply lack presuppositions. Gödel proved that such systems are inherently incomplete. Expressions in such languages cannot be self-referential.
Natural languages are fundamentally different. They represent context sensitive systems in which the meaning of words and word combinations can be inherently vague and ambiguous. They can only be understood (disambiguated) in the context of experiences that the sender and receiver of the signal have in common. That is, presuppositional knowledge is inherent in the encoding and decoding of messages. Natural language is a system of signals, just like symbolic systems, but they are far more efficient at conveying information precisely because presuppositions act as natural mechanisms for signal compression. Because people associate words with a wide variety of experiences grounded in bodily interactions with reality, those experiences can be used to compress the number of words and word combinations needed to convey information. As I said in the original post that you took issue with, the meaning of logical and mathematical symbolic expressions cannot adequately express the full meaning of sentences without the construction of extremely complex formulae. That's because all of the meaning in such expressions must be explicitly represented in the symbolic logical "signal".
Natural language is far more efficient at conveying complex ideas. Natural linguistic expressions can also be self-referential. They can give rise to paradoxical ideas that can sometimes be useful. At the very least, they help to keep philosophers employed.
Contradictions can be used to prove anything. Tautologies prove nothing. Both are extremely useful in natural language communication, however. To understand why, I refer you to the brilliant work of the philosopher Paul Grice on conversational implicature. If you are unfamiliar with the nature of presuppositional implicatures, I'll leave it to you to do your own research on the subject rather than bother with trying to explain it here. If you don't care, that's your business. I used to be paid to explain such things. Now I'm retired. My pension and annuities don't require me to do that kind of work.
I think you are saying roughly the same thing I was saying--that logical symbolic expressions must exhaustively represent the full meaning of such expressions. Presuppositions are not missing references. They exist in the minds of speakers and hearers as shared knowledge surrounding acts of communication. Natural language expressions can therefore be "compressed" to convey lots more information than logical and mathematical formulae. You can also use natural language as a metalanguage to describe natural language. That's what teachers do in classes on language.
Do you really not understand how LLMs work? They are grounded in Claude Shannon's information theory, which is only capable of identifying concentrations of information in terms of entropy values assigned to units of a signal. They create "summaries"--strings of symbols--that represent the most "relevant" syntropic concentration of information distribution in the textual material that they were trained on. That's why they can "hallucinate" when they calculate syntropic concentrations of text incorrectly for the purposes of the user that creates those prompts. They don't actually understand the expressions they display, but they use expressions created by people who do understand what they wrote about.
Actually, that is the very point that Ordinary Language philosophers tried to make. Linguists take a somewhat different approach to paradoxes--that linguistic expressions can fail to make sense and still be meaningful. Even nonsensical sentences can be grammatically well-formed. I think we've both proven that from time to time in our lives.
Speaking purely as a linguist, I could agree with that, subject to some quibbles. All linguistic systems contain identifiable flaws that hinder communication--for example, the requirement that 3rd person singular pronouns require English speakers to choose between masculine animate, feminine animate, and inanimate references. Reality is much messier than that. So languages that lack gender reference in those personal pronouns (e.g. Hungarian and Turkish) are arguably superior in allowing more flexibility.
Good. I'm not interested in that either.
Last edited:
