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Ideas for 'fragments/reports', 'fragments/reports' and 'A Survey of Metaphysics'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics

4240	It might be argued that mathematics does not, or should not, aim at truth [Lowe]
	Full Idea: It might be argued that mathematics does not, or should not, aim at truth.
	From: E.J. Lowe (A Survey of Metaphysics [2002], p.375)
	A reaction: Intriguing. Sounds wrong to me. At least maths seems to need the idea of the 'correct' answer. If, however, maths is a huge pattern, there is no correctness, just the pattern. We can be wrong, but maths can't be wrong. Ah, I see…!

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

4241	If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe]
	Full Idea: The Peano postulates imply an infinity of numbers, but there are probably not infinitely many concrete objects in existence, so natural numbers must be abstract objects.
	From: E.J. Lowe (A Survey of Metaphysics [2002], p.375)
	A reaction: Presumably they are abstract objects even if they aren't universals. 'Abstract' is an essential term in our ontological vocabulary to cover such cases. Perhaps possible concrete objects are infinite.