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If our language was infinite to describe an infinite amount of objects, would it even be possible for any of those concepts to mean anything? My intuition is that the meaning of a word is given to it by its relation to the meaning of other words and so if there was an infinite amount of words each with a particular meaning wouldn't words, and thus meaning itself, become redundant? If my intuition is a good one the meaning of a word would be lost because when any individual object stands in relation to an infinite set of objects it loses its distinctness.

I know people on the forum like to keep the questions focussed and mine are quite vague, but nevertheless responses to this question might help me with an essay. So cheers.

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    I am pretty sure that any answers to questions about the actual infinity of objects (as opposed to formal relations) have to be purely speculative since it is something we cannot even grasp. Words do have a particular, material relation that that constitutes their (normative) meaning, i.e. actual infinity, in that case, is hard to imagine. Since we look for objectively answerable questions and reject purely speculative answers, I ask to alter the question so that it does not rely merely on intuition, i.e. is embedded in specific philosophical frameworks. – Philip Klöcking Feb 11 at 19:08
  • I don't know how else I can frame this question. If it's a nonsense question then I'll take it down. – Banana in a vat Feb 11 at 19:15
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    The rules of syntax allow us to produce a name for every natural number. Thus, in principle, we can have an infinity of number-words. – Mauro ALLEGRANZA Feb 11 at 19:45
  • That the meaning of a word is its relational role in a system is one of the standard semantic theories, it is called inferentialism. But the rest of your intuition is off base, I am afraid. The more relations a word enters the richer its meaning, this does not make it lose distinctiveness, it makes it more and more distinctive. Think of how much more distinctive chemistry made "water". Having an infinite number of relations means that we can not grasp them all at once, but we can grasp ever more for ever better understanding. – Conifold Feb 11 at 21:01
  • @Bananainavat Your question actually means something, it is not nonsense, if I understand , then you mean that if words are infinite then every single word rests on an infinite number of words, definitions and meanings, which makes it impossible for the word to have meaning, since there should be no meaning that rests on infinite meanings, which means that nothing would have meaning, is that right? – SmootQ Feb 11 at 22:25
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Isn't every natural language an infinite language in the sense that it can generate infinitely many sentences and infinitely many word-tokens ? This is the case even if most of these sentences are never uttered and most of the word-tokens do not occur.

A language which employed only infinitely long sentences could not be understood by any realistically likely language user, and hence its words would be meaningless if we take the Fregean view that a word has meaning only in the context of a sentence. Sentences would be cognitively bracketed out.

A language which had an infinitely large vocabulary could be understood, and its words have meaning, if we employed only a fragment of the language. English is not an infinite language in terms of vocabulary but I, like most people, use only a fragment of its vocabulary and yet my words still have meaning in the sentences I formulate. Once the concession is made that meaning is possible when only a portion of a language's vocabulary is employed, I can't see that it makes any difference if the portion left out is small, large or infinite.

Or, to be more cautious, I can't see that if meaning is attenuated the smaller the fragment, e.g. because we have fewer contrastive or ampliative words by which to specify our meaning, words are reduced to meaninglessness in sentences formulated in a fragment of language. Impoverishment of meaning does not entail meaninglessness in a fragment of an infinite language.

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We theoretically speak an infinite language. It even has infinitely many words, in that it includes the Arabic numerals and this mathematical notation easily accommodates an infinite set.

A word may be defined in terms of other defined words, and the integers are surely each defined in terms of the one before it. Each word is not defined in terms of all the words in the language, only some of them. I this case each integer is defined by a given set script of other words, and the previous integer.

Each meaning remains quite distinct in usage, specifying a given quantity that has been counted up to, even if it we cannot naturally relate to each one independently. We will only ever use a finite number of them. But all the rest are in the language, the same way every work constructed by adding 'non-' or 'super-' to any adjective not already constructed that way is in the language, even if most of those constructions are annoying and redundant and will never be used. Those are still words, even if they are never used, because we would recognize it if it were deployed.

There is surely an Nth prime number, for any integer N, and that has meaning.

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