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3 ideas
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
| From: Plato (Parmenides [c.364 BCE], 144a) | |
| A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
| 17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
| Full Idea: Benacerraf argues that realists about mathematical objects have a nice normal semantic but no epistemology, and anti-realists have a good epistemology but an unorthodox semantics. | |
| From: report of Paul Benacerraf (Mathematical Truth [1973]) by Mark Colyvan - Introduction to the Philosophy of Mathematics 1.2 |
| 9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
| Full Idea: The principle defect of the standard (platonist) account of mathematical truth is that it appears to violate the requirement that our account be susceptible to integration into our over-all account of knowledge. | |
| From: Paul Benacerraf (Mathematical Truth [1973], III) | |
| A reaction: Unfortunately he goes on to defend a causal theory of justification (fashionable at that time, but implausible now). Nevertheless, his general point is well made. Your theory of what mathematics is had better make it knowable. |