7 ideas
| 15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine] |
| Full Idea: Cantor's development of set theory began with his discovery of the progression 0, 1, ....∞, ∞+1, ∞+2, ..∞x2, ∞x3, ...∞^2, ..∞^3, ...∞^∞, ...∞^∞^∞..... | |
| From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite VIII.2 |
| 15911 | Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine] |
| Full Idea: Ordinal numbers are generated by two principles: each ordinal has an immediate successor, and each unending sequence has an ordinal number as its limit (that is, an ordinal that is next after such a sequence). | |
| From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite III.4 |
| 10496 | Monothetic categories have fixed defining features, and polythetic categories do not [Ellen] |
| Full Idea: Many categories are 'monothetic' (the defining set of features is always unique), and others are 'polythetic' (single features being neither essential to group membership nor sufficient to allocate an item to a group). | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.33) | |
| A reaction: This seems a rather important distinction which hasn't made its way into philosophy, where there is a horrible tendency to oversimplify, with the dream of a neat and unified picture. But see Goodman's 'Imperfect Community' problem (Idea 7957). |
| 10497 | In symbolic classification, the categories are linked to rules [Ellen] |
| Full Idea: Symbolic classification occurs when we use some things as a means of saying something about other things. ..They enhance the significance of some categories, so that categories imply rules and rules imply categories. | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.35) | |
| A reaction: I'm afraid the anthropologists seem to have more of interest to say about categories than philosophers do. Though maybe we couldn't do anthropology if philosophers had made us more self-conscious about categories. Teamwork! |
| 10495 | Continuous experience sometimes needs imposition of boundaries to create categories [Ellen] |
| Full Idea: Because parts of our experience of the world are complexly continuous, it is occasionally necessary to impose boundaries to produce categories at all. | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.33) | |
| A reaction: I like it. Ellen says that people tend to universally cut nature somewhere around the joints, but we can't cope with large things, so the sea tends to be labelled in sections, even though most of the world's seas are continuous. |
| 10498 | Classification is no longer held to be rooted in social institutions [Ellen] |
| Full Idea: The view that all classification finds its roots in social institutions is now generally considered untenable. | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.36) | |
| A reaction: And about time too. Ellen (an anthropologist) inevitably emphasises the complexity of the situation, but endorses the idea that people everywhere largely cut nature at the joints. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |