Monday, December 20, 2010


 Synopsis/Zusammenfassung/ précis :

            Beginning with a parsimonious outset of only two Postulates,

            (1)   Die ganzen Zahlen hat der liebe Gott gemacht … [Kronecker]
            (2) …visibilium omnium et invisibilium [the Credo]

we conclude to the Realist position in mathematics, associated with Cantor and Gödel. We note the nice fit with theism.

Der hlg. Cantor
Der hlg. Gödel

More broadly, we distinguish the Truth of mathematics, from human mathematical practice.  Our Realist position applies only to the former;  our view of mathematical praxis is historical.
In parallel, our view of the Creator is Realist, but we take a historical position as regards the practice of the various religions.

It is not our goal, as José Ferrerós remarked regarding Hilbert’s program, “to employ Kroneckerian means for a justification of modern, anti-Kroneckerian methodology” (in Timothy Gowers, ed., The Princeton Companion to Mathematics (2008), p. 151)  First, we could scarcely hope to succeed where the Hilbertians failed.  More to the point, our argument is essentially epistemological, rather than deductive, constructive, or even properly mathematical.  We contend, and hope to make plausible, along a meandering path of insights and fables, that our knowledge of the (eternal) truths behind the (contingent) practices of mathematicians, is not discontinuous in kind from the way in which we come to know anything which we know not directly or experientially but only inferentially:  the reality of atoms -- of quarks -- of Mars -- of Novosibirsk -- of the Pelopponesian War -- of Other Minds -- or … coffee cups.

[To begin the thread, click here.]

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