Sensory-motor expression of concepts is primitive, yes, they become abstracted --- and yes the semantics of those abstractions can be abstract. I'm not talking semantics, i'm talking genesis.
How does one generate representations whose semantics are the structure of the world? Not via text token frequency, this much is obvious.
I dont think the thinnest sense of "2 + 2 = 4" being true is what a mathematician understands -- they understand, rather, the object 2, the map `+` and so on. That is, the proposition. And when they imagine a sphere of radius 4 containing a square of length 2, etc. -- I think there's a 'sensuous, mechanical, depth' that enables and permeates their thinking.
The intellect is formal only in the sense that, absent content, it has form. That content however is grown by animals at play in their environment.
Sensory-motor expression of concepts is primitive, yes, they become abstracted --- and yes the semantics of those abstractions can be abstract. I'm not talking semantics, i'm talking genesis.
How does one generate representations whose semantics are the structure of the world? Not via text token frequency, this much is obvious.
I dont think the thinnest sense of "2 + 2 = 4" being true is what a mathematician understands -- they understand, rather, the object 2, the map `+` and so on. That is, the proposition. And when they imagine a sphere of radius 4 containing a square of length 2, etc. -- I think there's a 'sensuous, mechanical, depth' that enables and permeates their thinking.
The intellect is formal only in the sense that, absent content, it has form. That content however is grown by animals at play in their environment.