Combining Texts

Ideas for 'Parmenides', 'What Price Bivalence?' and 'Causation and Laws of Nature'

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2 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
If a notion is ontologically basic, it should be needed in our best attempt at science [Schaffer,J]
     Full Idea: Science represents our best systematic understanding of the world, and if a certain notion proves unneeded in our best attempt at that, this provides strong evidence that what this notion concerns is not ontologically basic.
     From: Jonathan Schaffer (Causation and Laws of Nature [2008], 3.2)
     A reaction: But is the objective of science to find out what is 'ontologically basic'? If scientists can't get a purchase on a question, they have no interest in it. What are electrons made of?