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3 ideas
| 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…! |
| 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. |
| 8754 | Logic is dependent on mathematics, not the other way round [Heyting, by Shapiro] |
| Full Idea: Heyting (the intuitionist pupil of Brouwer) said that 'logic is dependent on mathematics', not the other way round. | |
| From: report of Arend Heyting (Intuitionism: an Introduction [1956]) by Stewart Shapiro - Thinking About Mathematics 7.3 | |
| A reaction: To me, this claim makes logicism sound much more plausible, as I don't see how mathematics could get beyond basic counting without a capacity for logical thought. Logic runs much deeper, psychologically and metaphysically. |