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. |
| 6040 | There is no universal goal to human life [Aenesidemus, by Photius] |
| Full Idea: Aenesidemus does not allow either happiness or pleasure or prudence or any other goal held by anyone on the basis of philosophical doctrine as the goal of life; rather, he says that there just is no such thing as a goal which is recognised by all people. | |
| From: report of Aenesidemus (Pyrrhonian Arguments (frags) [c.60 BCE], Bk 8) by 'Photius Bibliotheca' - Aenesidimus (frags) 170b | |
| A reaction: This is probably the dominant modern (post-Darwinian, existentialist) view. Personally I am sympathetic to the Aristotelian view that (to some extent) appropriate goals for life can be inferred from a fairly stable human nature. |
| 19399 | Prime matter is nothing when it is at rest [Leibniz] |
| Full Idea: Primary matter is nothing if considered at rest. | |
| From: Gottfried Leibniz (Aristotle and Descartes on Matter [1671], p.90) | |
| A reaction: This goes with Leibniz's Idea 13393, that activity is the hallmark of existence. No one seems to have been able to make good sense of prime matter, and it plays little role in Aristotle's writings. |