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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Wang, H. To and from philosophy — Discussions with Gödel and Wittgenstein. Synthese 88, 229–277 (1991). https://doi.org/10.1007/BF00567747
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DOI: https://doi.org/10.1007/BF00567747