5 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reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date.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. |
| 15785 | Our commitments are to an 'ontology', but also to an 'ideology', or conceptual system [Hintikka] |
| Full Idea: We must distinguish between what we are committed to existing in the actual world or a possible world ('ontology'), and what we are committed to as a part of our ways of dealing with the world conceptually, as a part of our conceptual system ('ideology'). | |
| From: Jaakko Hintikka (Semantics for Propositional Attitudes [1969], p.95), quoted by William Lycan - The Trouble with Possible Worlds 02 | |
| A reaction: I think this is the most illuminating idea I have read on the subject of ontological commitment. I'm fighting for the idea that what we think is true should be kept separate from what we think exists. Ideology is a nice addition to the mix. |
| 15786 | Commitment to possible worlds is part of our ideology, not part of our ontology [Hintikka] |
| Full Idea: Quantification over members of one particular world is a measure of ideology, quantification that crosses possible worlds is often a measure of ideology. | |
| From: Jaakko Hintikka (Semantics for Propositional Attitudes [1969], p.95), quoted by William Lycan - The Trouble with Possible Worlds 02 | |
| A reaction: I like this. See Idea 15785 for the underlying distinction. It leaves the question open of what we might mean by 'ideological commitment'. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |