8 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. |
| 7876 | Even if we identify pain with neural events, we can't explain why those neurons cause that feeling [Levine, by Papineau] |
| Full Idea: Materialists identify pain with the firing of nociceptive-specific neurons in the parietal cortex. Even so, Levine argues, we will still lack any explanation of why nociceptive-specific neurons yield pain. | |
| From: report of Joseph Levine (Purple Haze [2001]) by David Papineau - Thinking about Consciousness 5.1 | |
| A reaction: [Proposed by Levine in 1983] I don't think we need to instantly go dualist when faced with this, but we may all eventually have to concede a bit of mysterianism. The explanation may be holistic (and hence hopelessly complex). |
| 7877 | Only phenomenal states have an explanatory gap; water is fully explained by H2O [Levine, by Papineau] |
| Full Idea: Levine says the explanatory gap is peculiar to phenomenal states. Once water has been identified with H2O, or temperature with mean kinetic energy, we do not continue to ask why H2O yields water, or why mean kinetic energy yields temperature. | |
| From: report of Joseph Levine (Purple Haze [2001]) by David Papineau - Thinking about Consciousness 5.1 | |
| A reaction: Everything is mysterious if you think about if for long enough. What about a representational gap? Why do those neurons represent that tree (if the neurons aren't tree-shaped)? To understand qualia, we must understand the whole brain, I suspect. |
| 7878 | Materialism won't explain phenomenal properties, because the latter aren't seen in causal roles [Papineau on Levine] |
| Full Idea: We cannot give materialist explanations of why brain yields phenomenal properties because phenomenal concepts are not associated with descriptions of causal roles in the same way as pre-theoretical terms in other areas of science. | |
| From: comment on Joseph Levine (Purple Haze [2001]) by David Papineau - Thinking about Consciousness 5.1 | |
| A reaction: I think Papineau has part of the answer, and I certainly like his notion of Conceptual Dualism, but if qualia are physical, there must be a physical account of how they acquire their properties. I think the whole brain needs to be understood first. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |