3 ideas
| 9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |
| Full Idea: A theory of abstraction is any account that reconstructs mathematical theories using second-order abstraction principles of the form: §xFx = §xGx iff E(F,G). We ignore first-order abstraction principles such as Frege's direction abstraction. | |
| From: R Cook / P Ebert (Notice of Fine's 'Limits of Abstraction' [2004], 1) | |
| A reaction: Presumably part of the neo-logicist programme, which also uses such principles. The function § (extension operator) 'provides objects corresponding to the argument concepts'. The aim is to build mathematics, rather than the concept of a 'rabbit'. |
| 20064 | Actions are not mere effects of reasons, but are under their control [Audi,R] |
| Full Idea: An action for a reason is one that is, in a special way, under the control of reason. It is a response to, not a mere effect of, a reason. | |
| From: Robert Audi (Action, Intention and Reason [1992], p.177), quoted by Rowland Stout - Action 6 'Alien' | |
| A reaction: This modifies Davidson's 'reasons are causes'. Audi has a deviant causal chain which causes trouble for his idea, but Stout says he is right to focus on causal 'processes' (an Aristotelian idea) rather than causal 'chains'. |
| 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'). |