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2 ideas
| 9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
| Full Idea: Field commits himself to a Platonic view of mathematics. The theorems of set theory are held to imply or presuppose the existence of things that don't in fact exist. That is why he believes that these theorems are false. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Charles Chihara - A Structural Account of Mathematics 11.1 | |
| A reaction: I am sympathetic to Field, but this sounds wrong. A response that looks appealing is that maths is hypothetical ('if-thenism') - the truth is in the logical consequences, not in the ontological presuppositions. |
| 13331 | Part and whole contribute asymmetrically to one another, so must differ [Fine,K] |
| Full Idea: The whole identity of a part is relevant to whether it is a part, but the identity of the whole makes a part a part. The whole part belongs to the whole as a part. The standard account in terms of time-slices fails to respect this part/whole asymmetry. | |
| From: Kit Fine (Things and Their Parts [1999], §2) | |
| A reaction: Hard to follow, but I think the asymmetry is that the wholeness of the part contributes to the wholeness of the whole, while the wholeness of the whole contributes to the parthood of the part. Wholeness does different jobs in different directions. OK? |