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- W1904777694 abstract "This article provides an appraisal of Popper's criticism of L. E. J. Brouwer's intuitionist mathematics. Despite the extensive scholarship on Popper, his engagement with Brouwer's thought has largely been overlooked. Through his critical engagement with Brouwer, Popper provides an eloquent overview of some of the innovative features of his own later objectivist evolutionary epistemology. For Brouwer, the intuitional ground of mathematics completely separates mathematics from mathematical language. Intuitionistic mathematics is an essentially languageless activity of the mind. The mathematician is prioritised as the ultimate source of authority over the formalised representation of mathematics. Popper, while appreciating the important role of intuitions in identifying problems and deriving solutions was highly critical of Brouwer's subjectivist orientation. Popper reconstructed the problem of intuition in terms of evolutionary cognition as the problem of unconscious expectations or knowledge. This background knowledge does not derive from some pristine source of truth in the subject, but is the result of previous problem solving attempts, which become built into our cognitive apparatus and unconsciously inform our actions in the form of conjectures. What is crucial for Popper, is the way we externalise our knowledge in the form of conjectures, which both enables it to be criticised, as well as potentially lay bare hitherto unseen implications. For Popper, this was crucial to the way knowledge grows, and is necessary for the development of the self, which is dependent upon linguistic communication." @default.
- W1904777694 created "2016-06-24" @default.
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- W1904777694 date "2015-08-18" @default.
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- W1904777694 title "L. E. J. Brouwer and Karl Popper: Two Perspectives on Mathematics" @default.
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