"Unlimited" does not mean "all" in this context, it means something more like "inexhaustible" or "infinite." And some infinities can be larger than others: the set of all real numbers is larger than the set of all integers, even though both are infinite in size.

Of course language is limited in terms of its ability to represent reality, Chomsky doesn't deny that. All ways of representing reality are limited, that's pretty much axiomatic in whatever definition of "representation" you mean.

In fact Chomsky is repeatedly on the record of believing there are computational limits to humans.

> How could language express an unlimited array of thoughts when language cannot even fully express the experience of eating a chicken nugget? Can language express all your thoughts when looking at a sunrise? When embracing your lover after a hard day?

I think your attempts at counterexamples are bad.

None of those experiences (modulo being vegetarian so no chicken) seem to me to be hard to express in language. Slow, perhaps, but not hard.

However.

I believe that words are mere references to experiences, and without shared experience the meaning of any given word will generally differ somewhat between any two minds, and therefore while my words can model my experiences I can be sure that those same words will not create in your mind more than a merely similar experience, not even if you can visualise all the same senses, which you may not: if you have aphantasia, me saying "red" will never convey red in quite the same way, and I assume all other senses have equivalents though I do not know their names.

The limit in your examples is more time than language. Ample language could exist to describe a sunset. Language is extremely flexible and good poets constantly find ways to make words describe deeper and deeper concepts. The problem is that you could spend a hundred years expressing your thoughts of a sunset and only scratch the surface.

Your argument seems similar to saying that infinite numbers are "so ridiculous it verges on not even being worthy of being called unfalsifiable" because you can't count that high.

This isn't even consistent. You can't disprove that language can express infinitely many thoughts by showing a thought language can't express. Likewise, the fact you can show that there exist functions a universal Turing machine can't compute doesn't disprove that a universal Turing machine can compute infinitely many functions.

You're also just plainly wrong, e.g. because recursion exists.

There are an infinite number of real numbers, and yet "blue" is not a real number.

A set can be infinite and yet not contain all things.