Again we commend to your attention, our series of essays regarding
Realism in mathematics, the outline of whose program begins here:
We have just updated that statement as follows:
It is not our goal, as José Ferrerós
remarked anent 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.
Enjoy.
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