IN THIS STRANGE LITTLE BIT OF LANGUAGE, BROUWER PROVIDES THE ANSWER TO PLATONIST

IN THIS STRANGE LITTLE BIT OF LANGUAGE, BROUWER PROVIDES THE ANSWER TO PLATONISTS.

(emphasis mine)

“…mathematics is an essentially languageless activity of the mind having its ***origin in the perception of a move of time.*** This perception of a move of time may be described as the falling apart of a life moment into two distinct things, one of which gives way to the other, but is retained by memory. If the twoity thus born is divested of all quality, it passes into the empty form of the common substratum of all twoities.” — Brouwer.

Genius.

NELSON’S CRITIQUE

–“Since the advent of digital computers, attention has turned from effective methods — functions computable in principle – to feasible algorithms and programs. There is strong evidence that polynomial time functions provide the correct formalization of the intuitive notion of a feasible computation, and unlike the situation for recursive functions there is a purely syntactical characterization of polynomial time functions. I am convinced that intuitionism reformulated in this context will become a powerful practical method for constructing and verifying feasible algorithms, and that Kleene’s realization predicate will provide an incisive tool for

analyzing problems concerning interactive programs.”– Nelson.

https://web.math.princeton.edu/~nelson/papers/int.pdf

CURT: These are different contracts, for utility not different truths.

As far as I can tell, if it is not computable it is questionable. But I need to learn more.