To and from philosophy — discussions with gödel and Wittgenstein

Synthese 88 (2):229 - 277 (1991)
Abstract
I propose to sketch my views on several aspects of the philosophy of mathematics that I take to be especially relevant to philosophy as a whole. The relevance of my discussion would, I think, become more evident, if the reader keeps in mind the function of (the philosophy of) mathematics in philosophy in providing us with more transparent aspects of general issues. I shall consider: (1) three familiar examples; (2) logic and our conceptual frame; (3) communal agreement and objective certainty; (4) the transcommunal universality of mathematics; (5) the big jump to the potential infinite; (6) the reconciliation of local creation with the hypothesis of discovery; (7) Platonism as realism plus conceptualism; (8) foundational studies and mathematical practice; and (9) the decomposition of philosophical disagreements. The views of Gödel and Wittgenstein are emphasized in order to add specificity to the discussions.
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Kurt Gödel (1986). Collected Works. Oxford University Press.

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