6 ideas
19395 | Philosophy is sanctified, because it flows from God [Leibniz] |
Full Idea: Philosophy is sanctified by having its streams flow from the fountain of God's attributes. | |
From: Gottfried Leibniz (A General Principle to Explain Laws of Nature [1687], p.69) |
15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
A reaction: [Brouwer 1952:510-11] |
18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
19394 | Inequality can be brought infinitely close to equality [Leibniz] |
Full Idea: Equality may be considered as an infinitely small inequality, and we may make inequality approach equality as much as we wish. | |
From: Gottfried Leibniz (A General Principle to Explain Laws of Nature [1687], p.67) | |
A reaction: An interesting response to David Lewis's brusque dismissal of the problem of identity, as all-or-nothing...end of story. |
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. |