4 ideas
18832 | Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett] |
Full Idea: On an intuitionistic view, neither the truth-value of a statement nor any other mathematical entity can be given as the final result of an infinite process, since an infinite process is precisely one that does not have a final result. | |
From: Michael Dummett (Elements of Intuitionism (2nd ed) [2000], p.41), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.3 | |
A reaction: This is rather a persuasive reason to sympathise with intuitionism. Mathematical tricks about 'limits' have lured us into believing in completed infinities, but actually that idea is incoherent. |
9284 | Reasons are 'internal' if they give a person a motive to act, but 'external' otherwise [Williams,B] |
Full Idea: Someone has 'internal reasons' to act when the person has some motive which will be served or furthered by the action; if this turns out not to be so, the reason is false. Reasons are 'external' when there is no such condition. | |
From: Bernard Williams (Internal and External Reasons [1980], p.101) | |
A reaction: [compressed] An external example given is a family tradition of joining the army, if the person doesn't want to. Williams says (p.111) external reason statements are actually false, and a misapplication of the concept of a 'reason to act'. See Idea 8815. |
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. |