7 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. |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |
| 2596 | Maybe mind and body are parallel, like two good clocks [Leibniz] |
| Full Idea: Two clocks in perfect agreement must be by natural influence, or the control of a craftsman, or their perfect construction at the beginning. Only the third way (of "preestablished harmony" by God) is possible. | |
| From: Gottfried Leibniz (The Nature and Communication of Substance [1690], p.121) | |
| A reaction: Presumably 'natural influence' would cover the possibility that (unnoticed by you, apparently) one clock is attached to the other clock at the relevant points. If they are unconnected, presumably they are quite unaware of one another's existence. |
| 2595 | If the universe is a perfect agreement of uncommunicating substances, there must be a common source [Leibniz] |
| Full Idea: The perfect agreement of so many substances which have no communication whatever with each other can only come from a common source. | |
| From: Gottfried Leibniz (The Nature and Communication of Substance [1690], p.120) |