Is Language Infinite?

The first line of chapter 2 in Noam Chomsky’s Syntactic Structures serves as the basis for this entire essay. Chomsky says ‘From now on I will consider a language to be a set (finite or infinite) of sentences, each finite in length and constructed out of a finite set of elements.’ This line has much to explore. Already, at the outset, I suspect that this essay will not end with one definite outcome. Rather than be black and white, it will be in greyscales, something more conditional. Regardless, language must first be defined in order to disseminate its bounds.

Language is a tool to convey thought. Arguably (though I am fairly confident of this), language serves no other purpose. Language, as Chomsky says, is constructed out of a finite set of elements. A finite set of elements helps set definitions for each one and thus, create a cohesive linguistic structure to follow when one is trying to make sense. Naturally, something that is comprised of a finite set of elements cannot make up something infinite. Sure, one could keep adding words and phrases and clauses to a sentence, and by that regard, language is infinite. But there are two faults in that. One, if language as defined by Chomsky is a set of sentences, then that one infinite sentence is actually not a sentence. A sentence must have a full stop and we can apply some of Benedict de Spinoza’s arguments in his Ethics to prove this. Quite simply, something can only be limited by something else of the same nature. So, how can the infinite be limited by a full stop, something that is necessarily finite? Two, if language aims to convey thought then language must strive to make sense. An infinite line of words that are being put on in front of the other forever will not make sense and tumbles into lands of incoherency. That goes against the core principle and aim of language, so is this infinite line even language even more? I would argue, no. Now, it is just a pattern of shapes, stretching infinitely across an infinite plain. Another one of Spinoza’s axioms that proves this would be that ‘A substance which is absolutely infinite is indivisible’. According to this, that infinite line cannot be divided into anything, yet language is what the infinite line is made of, and language is most certainly divisible. Letters, letters, letters - one cannot just simply forget of that. So, one may make an incredibly long sentence, but in order to pertain to the rules described, there must be a full stop, thus this sentence was never infinite, and was always finite. But, one can only take this application of Spinoza’s version of the infinite (and God) so far. Because the substances that he describes are inherently different to the tool that language is.

It would seem logical to think that if language is comprised of finite elements, that computes to a finite number of possibilities. That number is likely astronomically high and hard to imagine, perhaps the word to describe such a large value does not even exist [I may be completely wrong, though 26! (26 factorial) as a math function may perhaps be an idea, at least for the English language which may be drawback of this essay: it only considers the English language in terms of specificities]. But this finite nature seems to only apply to the formation of words. However, till now, I have only considered words and the singular sentence. When considering this, there may be finite possibilities (infinite if one is to abandon the goal of coherency). A fixed set computes to a fixed number of possibilities. But what of the possible number of finite sentences put one front of the other? There isn’t a fixed set for that. It could go on and on, perhaps to infinity. What of its coherency? Well, if one were to chronicle time itself - time’s passage through history as - then it would make sense, for it is the examination of the mutable reality around us and it would be a chronicle that spanned from some singular beginning till the end, but with time, and time as the progression of reality, there is no end, it simply goes on, ad infinitum. In this way, language can be infinite, and it also proves Chomsky’s statement, calling language to be a set (finite or infinite) of sentences. To this extent, it seems like we have gone against some of Spinoza’s arguments while trying to prove this. However, there is still some justification in having used Spinoza’s axioms, since sentences, language, and at the end of the day, thought are all fundamentally different things. This will be discussed later on.

Language is infinite in another way as well. What is the main objective of language? Language functions as the distillation of thought. Or, at least, it attempts to distill thought. Language’s objective is to act as a form of communication, and for that communication to be successful, it must be imbued with meaning and that meaning comes from the very fact that it is rooted in thought. Language on its own is meaningless, shapes that fall from one’s sight as the eyes trace the bone white page. So in terms of what language can mean, it is infinite. Because meaning depends on the person. We can interpret Ludwig Wittgenstein’s picture theory to help this argument. Wittgenstein says that words must recall a picture or an object that exists in this world to make sense. Everybody is bound recall something else. A different picture is related to the same word for everybody, because everybody has a different lexical framework that has arisen from different experiences. Experience comes from knowledge and this conduces to different ways of experiencing and understanding other information. And each different picture may correspond to something that exists in this world or examinable universe. Take the word blue. Everybody thinks of a different shade. Somebody may think of the baby blue of the sky, somebody may think of the ultramarine of the ocean. They are different but still exist (though, in what capacity does colour exist? That is a discussion for another essay). So language can be infinite in meaning in that everybody derives something else, but also in that it is directly tied to thought and thought is infinite.

To conclude, we have explored how language is infinite in different ways. But that would go against what Spinoza said. Yet, there some justifications. When we discuss language as being finite in the number of combinations of words or for a single coherent sentence, that is but a physical sequence. That is not language. When we say that language is infinite, it is considering the meaning it possesses and aims to convey. They are different things, and thus different substances. But even if this does not satisfy Spinoza’s conditions, one can still argue that his laws apply to nature while language is man made and unnatural; what is natural about language is that it aims to communicate thought and thought, no matter what, is infinite.

These are the differentiations of language. And I would like to conclude this essay with one question. If thought, which is what language aims to express, is infinite, but the forms of language through which we must express this infinite thought is finite, is that not a limitation of language? And does that not mean for somethings, we can never truly express ourselves, and in that process, we lost some knowledge, or at least the essence of that knowledge? In a way, isn't language fundamentally flawed?