On 2/4/2013 6:45 AM, Alan Smaill wrote: > fom <fomJUNK@nyms.net> writes: > >> On 2/2/2013 1:16 PM, Virgil wrote: >>> In article >>> <email@example.com>, >>> WM <firstname.lastname@example.org> wrote: >>> >>>> WMatheology § 207 >>>> >>>> Towards the end of his Address on the Unity of Knowledge, delivered at >>>> the 1954 Columbia University bicentennial celebrations, Weyl >>>> enumerates what he considers to be the essential constituents of >>>> knowledge. At the top of his list comes >>>> ?intuition, mind's ordinary act of seeing what is given to it. >>>> (Weyl 1954, 629) >>> >>> I would hardly call the mind's seeing what is given to it, "intuition" >>> as every creature with a brain at all has it. >>> >> >> There is a long history behind references of that >> kind. Although the intuitionists were not actually >> Kantian or Neo-Kantian, a statement like that is >> certainly influenced by the philosophy of Kant and >> possibly Husserl. The word "intuition" here has very >> definite professional jargon attached to it. > > Brouwer explicitly claims links to the Kantian tradition, > eg in "Intuitionism and Formalism": > > re the invention of non-Euclidean geometries, he writes: > > " However weak the position of intuitionism seemed to be > after this period of mathematical development, it has > recovered after abandoning Kant's apriority of space > but adhering more resolutely to the apriority of time. " > >
Intuitionism is now broader than Brouwer, of course. I am currently looking at Sanin who explains certain divergences of his constructivism from Brouwer's original ideas. And, my particular statement paraphrased Mehlberg's position in his 1960 paper "The Present Situation in the Philosophy of Mathematics" reprinted by Blackwell. Since he footnotes a meager remark with a mention of Kant's "Prolegomena to Any Future Metaphyisics," I presume he is basing his distinction on Kant's descriptions relating mathematics to "visualization".