5 ideas
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 14596 | Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr] |
| Full Idea: Just as there are no numbers or properties, there are no relations (like 'being heavier than' or 'betweenness'), or sets. I will provisionally use 'nominalism' for the conjunction of these four claims. | |
| From: Cian Dorr (There Are No Abstract Objects [2008], 1) | |
| A reaction: If you are going to be a nominalist, do it properly! My starting point in metaphysics is strong sympathy with this view. Right now [Tues 22nd Nov 2011, 10:57 am GMT] I think it is correct. |
| 14597 | Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr] |
| Full Idea: Natural Class Nominalists take as primitive the notion of a 'natural' class - a class of things that all resemble one another in some one respect and resemble nothing else in that respect. | |
| From: Cian Dorr (There Are No Abstract Objects [2008], 4) | |
| A reaction: Dorr rejects this view because he doesn't believe in 'classes'. How committed to classes do you have to be before you are permitted to talk about them? All vocabulary (such as 'resemble') seems metaphysically tainted in this area. |
| 14598 | Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr] |
| Full Idea: If there are abstract objects, there are necessary truths about these things that cannot be reduced to truths of logic. So only the nominalist, who denies that there are any such things, can adequately respect the idea that there are no brute necessities. | |
| From: Cian Dorr (There Are No Abstract Objects [2008], 4) | |
| A reaction: This is where two plates of my personal philosophy grind horribly against one another. I love nominalism, and I love natural necessities. They meet like a ring-species in evolution. I'll just call it a 'paradox', and move on (swiftly). |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |