3 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. |
| 604 | Knowledge is mind and knowing 'cohabiting' [Lycophron, by Aristotle] |
| Full Idea: Lycophron has it that knowledge is the 'cohabitation' (rather than participation or synthesis) of knowing and the soul. | |
| From: report of Lycophron (fragments/reports [c.375 BCE]) by Aristotle - Metaphysics 1045b | |
| A reaction: This sounds like a rather passive and inert relationship. Presumably knowing something implies the possibility of acting on it. |
| 17319 | There are 'conceptual' explanations, with their direction depending on complexity [Schnieder] |
| Full Idea: The direction of conceptual explanations seems to be owed to factors of conceptual complexity and primitiveness. | |
| From: Benjamin Schnieder (Truth-making without Truth-makers [2006], p.33), quoted by David Liggins - Truth-makers and dependence 10.2 | |
| A reaction: Schnieder proposes that there are just 'causal' and 'conceptual' explanations. Liggins objects that there are other types of dependence which offer explanations. |