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. |
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'). |
7073 | I am a creative nothing, out of which I myself create everything [Stirner] |
Full Idea: I am not nothing in the sense of emptiness, but I am the creative nothing, the nothing out of which I myself as creator create everything. | |
From: Max Stirner (The Ego and Its Own [1844]), quoted by Simon Critchley - Continental Philosophy - V. Short Intro Ch.2 | |
A reaction: This appears to be the germ of the entire existentialist view, which gives a helpful gloss on the concept of 'nothing' - as the motivation for human creation, the vacuum in the mind that has to be filled. Call it 'creative boredom'. |