> using a finite set of symbols to represent an infinite number of communicable meanings
This always seemed wildly implausible to me. A very large number of communicable meanings, sure, but infinite?
This always seemed wildly implausible to me. A very large number of communicable meanings, sure, but infinite?
This is "trivial" in the boring kind of way. With just digits, we can communicate an infinite set of distinct numbers simply by counting.
https://www.lesswrong.com/posts/HDyePg6oySYQ9hY4i/david-deut...
The whole book is worth reading, though, as it lays it out in more detail.
Mary ran after the dog and the dog was brown and a cat came along and…
I think you're going to find out that no, you can't, and this impossibility is going to trivially demonstrate itself.
Both viewpoints are useful, they can prove general properties that hold for arbitrary long sequence of words and you put a practical bound on that length.
That's clearly false. It's not about some platonic mathematical simplification. Humans patently do not fit the Chomsky criterium for intelligence.
In fact, I'm pretty sure it's physically impossible for any real being to fit it.
Well, yes and no. Constructing this "infinite" sentence will run into some serious problems once the last star burns out, possibly sooner.
The only way you can represent this symbolically is in the trivial sense like you can represent everything, because you can use few symbols to build up natural numbers, and then you can use those numbers to approximate everything else. But I doubt it's what Chomsky had in mind.