6 ideas
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups. |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties | |
| A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things. |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things. |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5 | |
| A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory. |
| 15049 | Metaphysical realists are committed to all unambiguous statements being true or not true [Dummett] |
| Full Idea: The anti-realist view undercuts the ground for accepting bivalence. ...Acceptance of bivalence should not be taken as a sufficient condition for realism. ..They accept the weaker principle that unambiguous statements are determinately true or not true. | |
| From: Michael Dummett (Realism and Anti-Realism [1992], p.467) | |
| A reaction: [cited by Kit Fine, when discussing anti-realism] I take it be quite an important component of realism that there might be facts which will never be expressed, or are even beyond our capacity to grasp or express them |
| 15456 | Extrinsic properties, unlike intrinsics, imply the existence of a separate object [Kim, by Lewis] |
| Full Idea: Kim suggest that 'extrinsic' properties are those that imply 'accompaniment' (coexisting with some wholly distinct contingent object), whereas 'intrinsic' properties are compatible with 'loneliness' (being un-accompanied). | |
| From: report of Jaegwon Kim (Psychophysical supervenience [1982], 9th pg) by David Lewis - Extrinsic Properties II | |
| A reaction: The aim of Kim and Lewis is to get the ontological commitment down to a minimum - in this case just to objects (and mysterious 'implications'!). I like nominalism, but you can't just deny properties. 'Loneliness' is extrinsic! |