3 ideas
7529 | All philosophy should begin with an analysis of propositions [Russell] |
Full Idea: That all sound philosophy should begin with an analysis of propositions is a truth too evident, perhaps, to demand a proof. | |
From: Bertrand Russell (The Philosophy of Leibniz [1900], p.8), quoted by Ray Monk - Bertrand Russell: Spirit of Solitude | |
A reaction: Compare Idea 483. The obvious response to Russell is that it must actually begin with a decision about which propositions are worth analysing - and that ain't easy. I like analysis, but philosophy is also a vision of truth. |
10190 | From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki] |
Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures. | |
From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79 | |
A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s. |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |