4 ideas
18256 | Quantity is inconceivable without the idea of addition [Frege] |
Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former. | |
From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit' | |
A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree. |
9831 | Geometry appeals to intuition as the source of its axioms [Frege] |
Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms. | |
From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics | |
A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged. |
8628 | I hold that algebra and number are developments of logic [Jevons] |
Full Idea: I hold that algebra is a highly developed logic, and number but logical discrimination. | |
From: William S. Jevons (The Principles of Science [1879], p.156), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §15 | |
A reaction: Thus Frege shows that logicism was an idea that was in the air before he started writing. Riemann's geometry and Boole's logic presumably had some influence here. |
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'). |