Digital infinity

We have somehow in our heads a procedure for constructing an infinite array of structured expressions, each of which is assigned a sound and assigned a semantic interpretation.

Furthermore, these structured expressions have the property of what's called digital infinity.

And by that time, say late 40s, The mathematics of it were well understood.

The theory of computation had been developed, the theory of recursive functions.

You have this system of digital infinity.

It's a procedure of some sort that generates an infinity of structured expressions.

That's a generative grammar, in fact.