4 ideas
10053 | Geometrical axioms imply the propositions, but the former may not be true [Russell] |
Full Idea: We must only assert of various geometries that the axioms imply the propositions, not that the axioms are true and therefore that the propositions are true. | |
From: Bertrand Russell (Foundations of Geometry [1897], Intro vii), quoted by Alan Musgrave - Logicism Revisited §4 | |
A reaction: Clearly the truth of the axioms can remain a separate issue from whether they actually imply the theorems. The truth of the axioms might be as much a metaphysical as an empirical question. Musgrave sees this as the birth of if-thenism. |
10052 | Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave] |
Full Idea: Russell sought what was common to Euclidean and non-Euclidean systems, found it in the axioms of projective geometry, and took a Kantian view of them. | |
From: report of Bertrand Russell (Foundations of Geometry [1897]) by Alan Musgrave - Logicism Revisited §4 | |
A reaction: Russell's work just preceded Hilbert's famous book. Tarski later produced some logical axioms for geometry. |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
7604 | Amos was the first prophet to emphasise justice and compassion [Amos, by Armstrong,K] |
Full Idea: Amos was the first prophet to emphasise social justice and compassion. | |
From: report of Amos (30: Book of Amos [c.740 BCE]) by Karen Armstrong - A History of God | |
A reaction: It increasingly strikes me that early religious thinkers were actually working out the rules for good community living, but seeing them through the distorting spectacles of religion as a means to post-life salvation. |