A compiled computer program is certainly a rigorous description of something, God knows what, certainly not the programmer.

This is just funny:

"I think computer science has a tremendous amount to offer the fields of logic and mathematics. Specifically, I think that requiring all formulas to be executable by a finite, deterministic system (a computer program) could lead to a great increase in the level of rigor of these fields, would make it easier for students to learn existing results, would make it easier for practitioners to develop new results, and might possibly suggest whole new approaches...*

Also he keeps refering to computers as finite. I can only assume he means in a physical sense that there are a non-infinite amount of atoms making up his CPU.

I suppose I should critic his argument seriously but it's just too far away from any actual reality.