Intuituionism I: Brouwer's CONSTRUCTIVISM ⟨06,05⟩—optional скачать в хорошем качестве

Intuituionism I: Brouwer's CONSTRUCTIVISM ⟨06,05⟩—optional

Intuitionism makes a radical departure from classical logic and mathematics. Instead of treating logic and math as means of discovering mind-independent truths, Intuitionism emphasises proof as a means of creating mental constructions. Thus, for intuitionism, logic and math are explorations of mind, not of some external, mind-independent realm of Platonist ideas. This has significant implications for the way we think about logic. Here, I set out the intellectual background: Schopenhauer's claim about the relationship between mathematics and time, and his idealism—briefly, the view that we only directly know our mental representation of the world, not the world independent of the mind per se. These views had a profound influence on the mathematician LEJ Brouwer who—apart from inventing modern topology—established Intuitionism. Brouwer thinks mathematics is grounded in our perception of the flow of time, which comes in two irreducible forms: the continuous (i.e. the smooth flow of time itself) and the discrete (i.e. the distinguishable objects and events we encouter in time).