Any time you're thinking you can settle a synthetic question by clear logic rather than by observation, it's a red flag that you're probably making a mistake.
I'm not sure what a "synthetic" question is, but I know when people throw in unnecessary and meaningless jargon to try to dress up their bad ideas.
"Synthetic" is the opposite of "analytic". An analytic question is a question about math, logic, the relationships between concepts, the definitions of the words you're using, and so forth. A synthetic question is a question about what's going on out in the real world.
You must not comprehend the point. It is all derived from the most simple observations.
There is a process of animal communication. Animals use gesture and sound and other modalities to convey specific information to other members of the species. The sounds and the gestures are universal across the species.
This is a finite process. Somehow "programmed" into the brain the way nest building is "programmed" into birds.
Then there is the process of human language. Really a "program" to create a language.
Yes. A
finite program. You can get a finite program from a simpler finite program by taking small steps.
It is not a finite process. In theory infinite different "languages" could arise, each containing infinite phrases or sentences. I agree understanding this this takes some extrapolation from observation, but not much.
You have
a theory that infinite different languages could arise. That's why you keep saying "in theory". How do you know your theory is right? What observations imply human language is an infinite process? You're right, it takes some extrapolation from observation. How much extrapolation? It takes
infinite extrapolation from observation. That's how much you're calling "not much".
If you have a finite process you can add to it and add to it and add to it.
It will never become an infinite process.
Okay, if you say so. But "an infinite process" and "a finite process that's infinite
in theory" are not the same thing. Therefore you don't have grounds to assume that what's true of one must be true of the other. What reason do you have to claim that "If you have a finite process you can add to it and add to it and add to it but it will never become a finite process that's infinite
in theory."? That's not at all obvious.
In fact, the contrary is obvious: it's obvious that you can incrementally add to a finite process and eventually it will become a finite process that's infinite
in theory. Consider the finite process of shooting rockets into the sky. You shoot one up at 5,000 mph. It hits the ground and stops. So you shoot one up at 10,000 mph. It hits the ground and stops. So you shoot one up at 15,000 mph. It hits the ground and stops. So you shoot one up at 20,000 mph. It hits the ground and stops. So you shoot one up at 25,000 mph. It never hits the ground. It just keeps going and going.
In theory it will keep going for ever and you have incrementally reached an infinite process. Of course in practice something will interrupt the process; but we're talking about what happens
in theory.
"Exactly" how many atomic diameters high is the Eiffel Tower? Wait, you can't tell me? Whoa! It must be infinitely many atomic diameters high!
So you're saying that there is in theory some limit, not merely the limits of time and the effects of aging, to the number of books you could read.
After some number of books your brain will stop functioning.
Absurd!!!
With what do you back that clear nonsense up with?
But I didn't say any such nonsense. You make up nonsense and impute it to me because you have no answer to what you actually read. I said there's a limit to how many different sentences you can understand. After some number of books, either the books will start repeating things you already read, or else they will start saying things you can't understand. You can't understand a one-million-word sentence, no matter how long you live, and no matter how successfully future medical science prevents your brain from deteriorating.