10 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. |
| 16383 | Puzzled Pierre has two mental files about the same object [Recanati on Kripke] |
| Full Idea: In Kripke's puzzle about belief, the subject has two distinct mental files about one and the same object. | |
| From: comment on Saul A. Kripke (A Puzzle about Belief [1979]) by François Recanati - Mental Files 17.1 | |
| A reaction: [Pierre distinguishes 'London' from 'Londres'] The Kripkean puzzle is presented as very deep, but I have always felt there was a simple explanation, and I suspect that this is it (though I will leave the reader to think it through, as I'm very busy…). |
| 22709 | We should first decide what are the great works of art, with aesthetic theory following from that [Murdoch] |
| Full Idea: Our aesthetic must stand to be judged by great works of art which we know to be such independently. …So let us start by saying that Shakespeare is the greatest of all artists, and let our aesthetic be the philosophical justification of this judgement. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.205) | |
| A reaction: She offers this view in specific contradiction of Tolstoy, which says we should first have a theory, and then judge accordingly. I take Murdoch to be entirely right, but it means that our aesthetic theory will shift over time. |
| 22715 | Great art proves the absurdity of art for art's sake [Murdoch] |
| Full Idea: The work of the great artists shows up 'art-for-art's-sake' as a flimsy frivolous doctrine. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.218) | |
| A reaction: She keeps referring to tragedy (as the greatest art), but it is hard to see how we learn love and morality from a great pot or a great abstract painting. Wilde makes the doctrine frivolous, but I think it contains a degree of truth. Music. |
| 22714 | Because art is love, it improves us morally [Murdoch] |
| Full Idea: It is of course a fact that if art is love then art improves us morally, but this is, as it were, accidental. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.218) | |
| A reaction: Is an enhancement of one's love necessarily a moral improvement? Love is a fine feeling, but how does it motivate? Has no wickedness ever been perpetrated in the name of love? 'All's fair in love and war'. |
| 22712 | Art and morals are essentially the same, and are both identical with love [Murdoch] |
| Full Idea: Art and morals are (with certain provisos) one. Their essence is the same. The essence of both of them is love. Love is the perception of individuals. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.215) | |
| A reaction: The idea that art, morals and love are all just a single thing seems unhelpful. What about satire? What about duty without love? What about pure abstract painting? What about Stravinsky's highly formal view of his music? |
| 22713 | Love is realising something other than oneself is real [Murdoch] |
| Full Idea: Love is the extremely difficult realisation that something other than oneself is real. | |
| From: Iris Murdoch (The Sublime and the Good [1959], p.215) | |
| A reaction: I suspect that this is a necessary condition for love, but not the thing itself. The realisation she describes may not be love. You would attain her realisation if you shared a prison cell with a terrifying psychopath. |