5 ideas
17750 | The first clear proof of the consistency of the first order predicate logic was in 1928 [Hilbert/Ackermann, by Walicki] |
Full Idea: The first clear proof of the consistency of the first order predicate logic is found in the 1928 book of Hilbert and Ackermann. | |
From: report of Hilbert,D/Ackermann,W (Principles of Theoretical Logic [1928]) by Michal Walicki - Introduction to Mathematical Logic History E.2.1 |
9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
Full Idea: Logic is part of a normative theory of thinking, not a substitute for thinking. | |
From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.13) | |
A reaction: There is some sort of logicians' dream, going back to Leibniz, of a reasoning engine, which accepts propositions and outputs inferences. I agree with this idea. People who excel at logic are often, it seems to me, modest at philosophy. |
9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt] |
Full Idea: Vagueness in respect of membership is consistency with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of a concept. | |
From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.5) | |
A reaction: I find this view of sets much more appealing than the one that identifies a set with its members. The empty set is less of a problem, as well as non-existents. Logicians prefer the extensional view because it is tidy. |
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. |