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. |
| 3238 | 'Dead person' isn't a contradiction, so 'person' is somewhat vague [Williams,B] |
| Full Idea: If we say (in opposition to a physical view of identity) that when Jones dies 'Jones ceases to exist' but 'Jones' body does not cease to exist', this shouldn't be pressed too hard, because it would make 'dead person' a contradiction. | |
| From: Bernard Williams (Are Persons Bodies? [1970], p.74) | |
| A reaction: A good point, which nicely challenges the distinction between a 'human' and a 'person', but the problem case is much more the one where Jones gets advanced Alzheimer's, rather than dies. A dead body ceases as a mechanism, as well as as a personality. |
| 3239 | You can only really love a person as a token, not as a type [Williams,B] |
| Full Idea: If you love a person as a type instead of as a token (i.e. a "person", instead of a physical body) you might prefer a run-down copy of them to no person at all, but at this point our idea of loving a person begins to crack. | |
| From: Bernard Williams (Are Persons Bodies? [1970], p.81) | |
| A reaction: Very persuasive. If you love a person you can cope with them getting old. If you own an original watercolour, you can accept that it fades, but you would replace a reproduction of it if that faded. But what, then, is it that you love? |
| 23215 | Even the poorest have a life to lead, and so should consent to who governs them [-] |
| Full Idea: For really I think that the poorest hee that is in England hath a life to live, as the greatest hee; …and every Man that is to live under a Government ought first by his own Consent to put himself under that Government. | |
| From: - (The Putney Debates [1647]) | |
| A reaction: [remark made by Thomas Rainsborough] This is the social contract idea which is explicit in Hobbes. I'm sure we can at least trace it back to John Lilburne in the 1630s. |