6 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. |
| 12251 | Substantial forms are not understood, and explain nothing [Descartes] |
| Full Idea: Clearly no explanation can be given by these substantial forms for any natural action, since their defenders admit that they are occult and that they do not understand them themselves, ...so they explain nothing. | |
| From: René Descartes (Letters to Regius [1642], 1642.01), quoted by David S. Oderberg - Real Essentialism 267 n5 | |
| A reaction: [Oderberg gives refs for attack by Locke and Hume, p.66] Descartes' target is Aristotle's hylomorphism. The problem seems to be understanding what Aristotle meant, which is much more than mere 'shape'. More like 'controlling principle'. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |
| 16772 | An angelic mind would not experience pain, even when connected to a human body [Descartes, by Pasnau] |
| Full Idea: Descartes points out that an angelic mind, even if causally connected to a human body, would not experience the same sort of bodily sensations; it would, instead, simply observe flesh being torn, like a piece of paper. | |
| From: report of René Descartes (Letters to Regius [1642], III:493) by Robert Pasnau - Metaphysical Themes 1274-1671 25.6 | |
| A reaction: Does that mean that the angel could not have the experience even if it wanted to have it. So they can't pick up a cup either? So they can't make themselves known to us, even if they are desperate to? So the Annunciation never happened? |