6 ideas
| 3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
| Full Idea: Dedekind and Peano define the number series as the series of successors to the number zero, according to five postulates. | |
| From: report of Giuseppe Peano (works [1890]) by Simon Blackburn - Oxford Dictionary of Philosophy p.279 |
| 5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
| Full Idea: 1) 0 is a number; 2) The successor of any number is a number; 3) No two numbers have the same successor; 4) 0 is not the successor of any number; 5) If P is true of 0, and if P is true of any number n and of its successor, P is true of every number. | |
| From: report of Giuseppe Peano (works [1890]) by Antony Flew - Pan Dictionary of Philosophy 'Peano' | |
| A reaction: Devised by Dedekind and proposed by Peano, these postulates were intended to avoid references to intuition in specifying the natural numbers. I wonder if they could define 'successor' without reference to 'number'. |
| 20076 | An intending is a judgement that the action is desirable [Davidson] |
| Full Idea: We can identify an intentional action ...with an all-out conditional judgement that the action is desirable. ...In the case of pure intending, I now suggest that the intention simply is an all-out judgement. | |
| From: Donald Davidson (Intending [1978], p.99), quoted by Rowland Stout - Action 8 'Davidson's' | |
| A reaction: 'Pure' intending seems to be what Stout calls 'prior' intending, which is clearer. This still strikes me as obviously false. I judge that it is desirable that I make a cup of coffee, but secretly I'm hoping someone else will make it for me. |
| 20024 | Davidson gave up reductive accounts of intention, and said it was a primitive [Davidson, by Wilson/Schpall] |
| Full Idea: Later Davidson dropped his reductive treatment of intentions (in terms of 'pro-attitudes' and other beliefs), and accepted that intentions are irreducible, and distinct from pro-attitudes. | |
| From: report of Donald Davidson (Intending [1978]) by Wilson,G/Schpall,S - Action 2 | |
| A reaction: Only a philosopher would say that intentions cannot be reduced to something else. Since I have a very physicalist view of the mind, I incline to reduce them to powers and dispositions of physical matter. |
| 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. |