5 ideas
| 8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
| Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §1) | |
| A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to. |
| 8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
| Full Idea: The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §3) | |
| A reaction: Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others. |
| 5121 | Basing ethics on flourishing makes it consequentialist, as actions are judged by contributing to it [Harman] |
| Full Idea: Basing ethics on human flourishing tends towards utilitarianism or consequentialism; actions, character traits, laws, and so on are to be assessed with reference to their contributions to human flourishing. | |
| From: Gilbert Harman (Human Flourishing, Ethics and Liberty [1983], 9.2.2) | |
| A reaction: This raises the question of whether only virtue can contribute to flourishing, or whether a bit of vice might be helpful. This problem presumably pushed the Stoics to say that virtue itself is the good, rather than the resulting flourishing. |
| 5120 | What counts as 'flourishing' must be relative to various sets of values [Harman] |
| Full Idea: If we base our ethics on human flourishing, one implication would seem to be moral relativism, since what counts as 'flourishing' seems inevitably relative to one or other set of values. | |
| From: Gilbert Harman (Human Flourishing, Ethics and Liberty [1983], 9.2.1) | |
| A reaction: This remark seems to make the relativist assumption that all value systems are equal. For Aristotle, flourishing is no more relative than health is. No one can assert that illness has an intrinsically high value in human life. |
| 16591 | Prime matter is nothing but its parts [Vanini] |
| Full Idea: The whole of prime matter, considered as prime matter, is nothing other than its parts. | |
| From: Julio Cesare Vanini (Amphitheatrum [1615], Ex 5:p.28), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.2 | |
| A reaction: This is a late scholastic writer rejecting the traditional (and obscure) prime matter with the new corpuscularian approach. It signals the end of the Greek concept of matter. |