This is the second post in my series of reading summaries. See the first one for more information on the series.
Mark van Atten, Göran Sundholm. “L.E.J. Brouwer’s ‘Unreliability of the logical principles’. A new translation, with an introduction". November, 2015. arXiv:1511.01113v1 [math.HO].
The intro provides historical context for the paper, both in terms of Brouwer’s other work & that of others, notably, Kronecker, Molk, & the French.
⋆ This is the paper in which Brouwer rejects the law of the excluded middle and doubts the application of logic to the acquisition of knowl.
In geom, from accepted premises, logic gives incontrovertible conclusions. This mistakenly caused it to be used for the rest of human knowledge. But it only works here b/c geom is divorced from human exp. Science by means of induction forms math-l systs to desc. reality. Deducing within this syst may however produce conclusions contradicting observation. So logic unreliable in science. But math divorced from obs. There, syllogism & contradiction are OK. But law of excl. middle is equiv to there being no unsolvable problems, which is unsure. For finite systs, exhaustive check makes LEM OK. For inf systems w/o induction, all bets are off. So LEM not valid in general.