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. |
5692 | Introspection is not perception, because there are no extra qualities apart from the mental events themselves [Rosenthal] |
Full Idea: Introspection cannot be a form of perceiving, since that invariably involves sensory qualities, and no qualities occur in introspection other than those of the sensations and perceptions we introspect; there are no additional qualities. | |
From: David M. Rosenthal (Instrospection [1998]) | |
A reaction: This sounds pretty conclusive. Presumably introspection is best described as meta-thought rather than perception, which means that it involves beliefs and judgements, rather than new perceptual qualities. It has to be conceptual, and probably linguistic. |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |