4 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'. |
| 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'). |
| 1472 | The propositions that God is good and omnipotent, and that evil exists, are logically contradictory [Mackie, by PG] |
| Full Idea: There is a contradiction between the propositions that God is wholly good, God is omnipotent, and evil exists, and one of them has got to give way (assuming good eliminates evil, and omnipotence has no limit). | |
| From: report of J.L. Mackie (Evil and Omnipotence [1955], Pref.) by PG - Db (ideas) |
| 1473 | Is evil an illusion, or a necessary contrast, or uncontrollable, or necessary for human free will? [Mackie, by PG] |
| Full Idea: Perhaps evil is an illusion, or it is necessary for good to exist, or in humans it is required because we have free will, or God lacks the full power to control it, but none of these looks convincing. | |
| From: report of J.L. Mackie (Evil and Omnipotence [1955], §B) by PG - Db (ideas) |