12 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. |
| 15561 | The events that suit semantics may not be the events that suit causation [Lewis] |
| Full Idea: There is no guarantee that events made for semantics are the same as events that are causes and effects. | |
| From: David Lewis (Events [1986], I) | |
| A reaction: This little cri de couer could be a motto for a huge amount of analytic philosophy, which (for some odd reason) thought that mathematics, logic, set theory and formal semantics were good tools for explaining nature. |
| 15565 | Events have inbuilt essences, as necessary conditions for their occurrence [Lewis] |
| Full Idea: Events have their essences built in, in the form of necessary conditions for their occurrence. | |
| From: David Lewis (Events [1986], III) | |
| A reaction: Revealing. He thinks the essence of an event is something which precedes the event. I take it as obvious that if an event has an essence, it will be some features of the event that occur in it and during it. They need to be intrinsic. |
| 15566 | Events are classes, and so there is a mereology of their parts [Lewis] |
| Full Idea: If events are classes, as I propose, then they have a mereology in the way that all classes do: the parts of a class are its subclasses. | |
| From: David Lewis (Events [1986], V) | |
| A reaction: Lewis says events are properties, which he regards as classes. It is not clear that events are strictly mereological. Could one happening be two events? Is WWII a simple sum of its parts? [see p.260] |
| 15567 | Some events involve no change; they must, because causal histories involve unchanges [Lewis] |
| Full Idea: Not all events involve change. We cannot afford to count the unchanges as nonevents, for the unchanges may be needed to complete causal histories. | |
| From: David Lewis (Events [1986], VI) | |
| A reaction: You end up calling non-changes 'events' if you commit to a simplistic theory that all causal histories consist of events. Why not allow conditions as well as events? Lewis concedes that he may be abusing language. |
| 15564 | An event is a property of a unique space-time region [Lewis] |
| Full Idea: I propose to identify an event with a property, or in other words with a class, a unique spatio-temporal region corresponding to where that event occurs. | |
| From: David Lewis (Events [1986], II) | |
| A reaction: [I've run together two separate bits, on p.244 and 245] Lewis cites Montague's similar view, that events are properties of times. |
| 15563 | Properties are very abundant (unlike universals), and are used for semantics and higher-order variables [Lewis] |
| Full Idea: Properties are abundant, numbering at least beth-3 for properties of individuals alone; they are suited to serve as semantic values of arbitrarily complex predicates and gerunds, and higher-order variables. (If there are universals, they are sparse). | |
| From: David Lewis (Events [1986], II n2) | |
| A reaction: To me this is an outrageous hijacking of the notion of property which is needed for explaining the natural world. He seems to be talking about predicates. He wants to leave me with his silly universals - well I don't want them, thank you. |
| 23221 | The brain, and all the mental events within it, consists entirely of sensitive and rational matter [Cavendish] |
| Full Idea: Sensitive and rational matter …makes not only the Brain, but all Thoughts, Conceptions, Imaginations, Fancy, Understanding, Memory, Remembrance, and whatsoever motions are in the Head or Brain. | |
| From: Margaret Cavendish (Philosophical Letters [1664], p.185), quoted by Matthew Cobb - The Idea of the Brain 2 | |
| A reaction: Judging by the date of this, and that she is a Cavendish, the influence of Hobbes must be strong, which was brave in 1664. A very strong statement of reductive physicalism, making sure that nothing is left out. |
| 15562 | Causation is a general relation derived from instances of causal dependence [Lewis] |
| Full Idea: Causation is the ancestral of causal dependence: event c causes event e iff either e depends on c, or e depends on an intermediate event which in turn depends on c, or.... | |
| From: David Lewis (Events [1986], I) | |
| A reaction: This is Lewis making sure that we don't postulate some huge bogus thing called 'Causation' which is supposed to be in charge of Nature. Good point. |