Describing the unspeakable and demonstrating the unprovable
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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of (from British Columbia Philosophy Graduate Conference) Despite the apparent polarity between the philosophies of Wittgenstein and G�del, I here seek to demonstrate and consider important similarities in these two allegedly disparate interpretations of mathematical proposition. Wittgenstein asserts that the meaning is comprised by proof, while G�del relegates provability to an intrinsically imperfect status. Each represents metamathematical statements as severely limited, and analysis emphasizing the complementary here yields a rich interpretation of mathematical proposition: invention, but not without a basis for describing these inventions as incomplete. As contrivances that exhibit a necessarily imperfect correlation to hypothetical completeness, the extent to which any one system is comparatively useful is thus a reflection of the degree of imperfection with which it correlates to the otherwise inarticulable qualities that dictate usefulness. Inconsistency produced by our necessarily incomplete systems should therefore be viewed as a natural consequence of the inherent imperfect correlation, and so admits of meaningful interpretation.
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