David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Mind 107 (426):305-347 (1998)
The paper scrutinizes Frege's Euclideanism - his view of arithmetic and geometry as resting on a small number of self-evident axioms from which non-self-evident theorems can be proved. Frege's notions of self-evidence and axiom are discussed in some detail. Elements in Frege's position that are in apparent tension with his Euclideanism are considered - his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that understanding is closely associated with inferential abilities. The resolution of the tensions indicates that Frege maintained a sophisticated and challenging form of rationalism, one relevant to current epistemology and parts of the philosophy of mathematics.
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Declan Smithies (2015). Ideal Rationality and Logical Omniscience. Synthese 192 (9):2769-2793.
John Symons (2008). Intuition and Philosophical Methodology. Axiomathes 18 (1):67-89.
Stewart Shapiro (2009). We Hold These Truths to Be Self-Evident: But What Do We Mean by That? Review of Symbolic Logic 2 (1):175-207.
Denis Buehler (2014). Incomplete Understanding of Complex Numbers Girolamo Cardano: A Case Study in the Acquisition of Mathematical Concepts. Synthese 191 (17):4231-4252.
Stephen Yablo (2008). Carving Content at the Joints. Canadian Journal of Philosophy 38 (S1):145-177.
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