6 ideas
| 12427 | All of mathematics is properties of the whole numbers [Kronecker] |
| Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers. | |
| From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5 | |
| A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim. |
| 10091 | God made the integers, all the rest is the work of man [Kronecker] |
| Full Idea: God made the integers, all the rest is the work of man. | |
| From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro | |
| A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them. |
| 19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
| Full Idea: A proposition about an item exists only if that item exists... how could something be the proposition that that dog is barking in circumstances in which that dog does not exist? | |
| From: Timothy Williamson (Necessary Existents [2002], p.240), quoted by Trenton Merricks - Propositions | |
| A reaction: This is a view of propositions I can't make sense of. If I'm under an illusion that there is a dog barking nearby, when there isn't one, can I not say 'that dog is barking'? If I haven't expressed a proposition, what have I done? |
| 21991 | The middle class gain freedom through property, but workers can only free all of humanity [Marx, by Singer] |
| Full Idea: Where the middle class can win freedom for themselves on the basis of rights to property - thus excluding others from their freedom - the working class have nothing but their title as human beings. They only liberate themselves by liberating humanity. | |
| From: report of Karl Marx (Contrib to Critique of Hegel's Phil of Right [1844]) by Peter Singer - Marx 4 | |
| A reaction: Individual workers might gain freedom via education, marriage, or entrepreneurship, or by opting for total simplicity of life, but in general Marx seems to be right about this. But we must ask what sort of 'freedom' is needed. |
| 21990 | Theory is as much a part of a revolution as material force is [Marx] |
| Full Idea: Material force must be overthrown by material force. But theory also becomes a material force once it has gripped the masses. | |
| From: Karl Marx (Contrib to Critique of Hegel's Phil of Right [1844], Intro p.69), quoted by Peter Singer - Marx 4 | |
| A reaction: A huge problem, I think, is that every theory (even conservatism) has to be simplified in a democracy if it is to grip the imagination of the majority. My current hatred is labels in political philosophy. They give us a cartoon view of the world. |
| 7128 | Religion is the opium of the people, and real happiness requires its abolition [Marx] |
| Full Idea: Religion is the opium of the people. The abolition of religion as the illusory happiness of the people is required for their real happiness. | |
| From: Karl Marx (Contrib to Critique of Hegel's Phil of Right [1844], Intro) | |
| A reaction: Not being religious myself, I have some sympathy with this ringing clarion-call. However, while opium satisfies an artificial and superficial need, religion certainly seems to speak to something deeper and more central in people. |