Combining Texts

Ideas for 'Parmenides', 'Does Ontology Rest on a Mistake?' and 'Modern Philosophy:introduction and survey'

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3 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

3907	Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton]
	Full Idea: Could someone have a perfect intellectual acquaintance with numbers, but be incapable of counting a flock of sheep?
	From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.6)

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

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.

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism

3908	If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton]
	Full Idea: If there can be unprovable truths of mathematics, then mathematics cannot be reduced to the proofs whereby we construct it.
	From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.7)