5 ideas
| 17606 | Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline] |
| Full Idea: The axiomatic method ....revealed precisely what assumptions underlie each branch [of mathematics] and made possible the comparison and clarification of the relationships of various branches. | |
| From: Morris Kline (Mathematical Thought from Ancient to Modern Times [1972], p.1027), quoted by Penelope Maddy - Defending the Axioms 1.3 | |
| A reaction: I take this to be the 'fruitfulness' which marks out the discovery of the essence of something. |
| 2602 | What experience could prove 'If a=c and b=c then a=b'? [Descartes] |
| Full Idea: Please tell me what the corporeal motion is that is capable of forming some common notion to the effect that 'things which are equal to a third thing are equal to each other'. | |
| From: René Descartes (Comments on a Certain Broadsheet [1644], p.366) |
| 2600 | The mind's innate ideas are part of its capacity for thought [Descartes] |
| Full Idea: I have never written or taken the view that the mind requires innate ideas which are something distinct from its own faculty of thinking. | |
| From: René Descartes (Comments on a Certain Broadsheet [1644], p.365) |
| 2601 | Qualia must be innate, because physical motions do not contain them [Descartes] |
| Full Idea: The ideas of pains, colours, sounds etc. must be all the more innate if, on the occasion of certain corporeal motions, our mind is to be capable of representing them to itself, for there is no similarity between these ideas and the corporeal motions. | |
| From: René Descartes (Comments on a Certain Broadsheet [1644], p.365) | |
| A reaction: Simple and brilliant! We know perfectly well that there is no redness zooming through the air from a tomato (or the air would be pink!). Redness occurs when the light arrives, so we add the redness, so it is innate. |
| 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'). |