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. |
| 5122 | Maybe consequentialism is a critique of ordinary morality, rather than describing it [Harman] |
| Full Idea: Consequentialism may be put forward not as an attempt to capture intuitive folk morality but rather as a critique of ordinary tuitions. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.1) | |
| A reaction: It is certainly true that most people are concerned with why an action was performed, and (after initial anger) are prepared to forgive an unintended disaster. We have no moral objections to earthquakes, which have bad consequences. |
| 5123 | Maybe there is no such thing as character, and the virtues and vices said to accompany it [Harman] |
| Full Idea: It may be the case that there is no such thing as character, no ordinary character traits of the sort people think there are, none of the usual moral virtues and vices. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.1) | |
| A reaction: This would be a devastating fact for virtue theory, if it were true. I don't believe it. He thinks patterns of behaviour result from circumstances, but we give accurate and detailed pictures of people's characters (esp. in novels). |
| 5124 | If a person's two acts of timidity have different explanations, they are not one character trait [Harman] |
| Full Idea: If Herbert is disposed to not speak in history class (but not other subjects), and explanation of this is different from his avoidance of roller coaster rides, then these two dispositions are not special cases of a single character trait. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.2) | |
| A reaction: A basic Harman argument for denying the existence of character (and hence of virtues). I just say that character traits are more complex than his caricature of them. If I keep imagining disaster and humiliation for myself, that is a character trait. |
| 5125 | Virtue ethics might involve judgements about the virtues of actions, rather than character [Harman] |
| Full Idea: There are variants of virtue ethics that do not require character traits in the ordinary sense. For example, moral thinking might be explicated by appeal to judgements about whether particular actions are just or courageous or whatever. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.7.1.1) | |
| A reaction: A very interesting proposal (from Judith Jarvis Thomson). This would flatly reject Aristotle, and one presumes that the judgement about the virtue of the action would largely be a matter of pondering cultural conventions (or, perhaps, consequences). |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |