5 ideas
17813 | Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP] |
Full Idea: The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers. | |
From: Nicholas P. White (What Numbers Are [1974], V) |
17812 | Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP] |
Full Idea: Statements involving finite cardinalities can be made without treating numbers as objects at all, simply by using quantification and identity to define numerically definite quantifiers in the manner of Frege. | |
From: Nicholas P. White (What Numbers Are [1974], IV) | |
A reaction: [He adds Quine 1960:268 as a reference] |
11911 | Some philosophers always want more from morality; for others, nature is enough [Blackburn] |
Full Idea: The history of moral theory is largely a history of battles between people who want more (truth, absolutes...) - Plato, Locke, Cudworth, Kant, Nagel - and people content with what we have (nature) - Aristotle, Epicurus, Hobbes, Hume, Stevenson. | |
From: Simon Blackburn (Précis of 'Ruling Passions' [2002], p.133) | |
A reaction: [Thanks to Neil Sinclair for this one] As a devotee of Aristotle, I like this. I'm always impressed, though, by people who go the extra mile in morality, because they are in the grips of purer and loftier ideals than I am. They also turn into monsters! |
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. |