11 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. |
| 23026 | We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz] |
| Full Idea: It is by the natural light that the axioms of mathematics are recognised. If we take away the same quantity from two equal things, …a thing we can easily predict without having experienced it. | |
| From: Gottfried Leibniz (Letters to Queen Charlotte [1702], p.189) | |
| A reaction: He also says two equal weights will keep a balance level. Plato thinks his slave boy understands halving an area by the natural light, but that is just as likely to be experience. It is too easy to attribut thoughts to a 'natural light'. |
| 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. |
| 13189 | A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz] |
| Full Idea: That which is necessary for something does not constitute its essence. Air is necessary for our life, but our life is something other than air. | |
| From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
| A reaction: Bravo. Why can't modern philosophers hang on to this distinction? They seem to think that because they don't believe in traditional essences they can purloin the word for something else. Same with the word 'abstraction'. |
| 19432 | Intelligible truth is independent of any external things or experiences [Leibniz] |
| Full Idea: Intelligible truth is independent of the truth or of the existence outside us of sensible and material things. ....It is generally true that we only know necessary truths by the natural light [of reason] | |
| From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
| A reaction: A nice quotation summarising a view for which Leibniz is famous - that there is a tight correlation between necessary truths and our a priori knowledge of them. The obvious challenge comes from Kripke's claim that scientists can discover necessities. |
| 19430 | We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz] |
| Full Idea: We use the external senses ...to make us know their particular objects ...but they do not make us know what those sensible qualities are ...whether red is small revolving globules causing light, heat a whirling of dust, or sound is waves in air. | |
| From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
| A reaction: These seems to be exactly the concept of secondary qualities which Locke was promoting. They are unreliable information about the objects we perceive. Primary qualities are reliable information. I like that distinction. |
| 19431 | There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz] |
| Full Idea: It can be said that there is nothing in the understanding which does not come from the senses, except the understanding itself, or that which understands. | |
| From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
| A reaction: Given that Leibniz is labelled as a 'rationalist', this is awfully close to empiricism. Not Locke's 'tabula rasa' perhaps, but Hume's experiences plus associations. Leibniz has a much loftier notion of understanding and reason than Hume does. |
| 21989 | Man is dominated by money, which is the essence of his alienation [Marx] |
| Full Idea: Money is the alienated essence of man's labour and life, and this alien essence dominates him as he worships it. | |
| From: Karl Marx (On the Jewish Question [1844], p.60), quoted by Peter Singer - Marx 3 | |
| A reaction: Presumably this is inherit in the very nature of money, rather than in the wickedness of capitalists who control it. But money is not inherently alienting for the rich, or for the comfortable bourgeoisie (is it?). |
| 20519 | Marxists say liberal rights are confrontational, and liberal equality is a sham [Marx, by Wolff,J] |
| Full Idea: For Marx liberal rights are egoistic rights of separation: they encourage each individual to view others as limitations to his or her freedom. ....Liberals set up a sham community of 'equal' citizens. | |
| From: report of Karl Marx (On the Jewish Question [1844]) by Jonathan Wolff - An Introduction to Political Philosophy (Rev) 4 'Marxist' | |
| A reaction: The point is that equality in law does not ensure equal treatment in daily life. I suppose a liberal right can be seen as an opt-out clause for some aspect of society. |