4 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 5064 | Rights are moral significance, or liberty, or right not to be restrained, or entitlement [Mawson] |
| Full Idea: A 'right' can mean 'x counts morally', or 'x is permitted to do this' (liberty), or 'x can't be stopped from doing this' (negative right), or 'someone should provide this for x'. | |
| From: Tim Mawson (Animal Rights talk [2003]), quoted by PG - lecture notes | |
| A reaction: A useful analysis. It is a useful preliminary to considering whether any of these are natural rights. Personally I am sympathetic to that concept. You cannot deny a person's right to self-defence, even when you are sitting on them. Persons have rights. |