3 ideas
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 19405 | Substances are in harmony, because they each express the one reality in themselves [Leibniz] |
| Full Idea: Every substance expresses the whole sequence of the universe in accordance with its own viewpoint or relationship to the rest, so that all are in perfect correspondence with one another. | |
| From: Gottfried Leibniz (Identity in Substances and True Propositions [1686], p.98) | |
| A reaction: Thus 'expression' (something like mapping what is exterior) is the mechanism through which God achieves harmony in the universe. Instants of time are said to be successive moments of perfect harmony. |
| 8825 | It seems impossible to logically deduce physical knowledge from indubitable sense data [Kim] |
| Full Idea: It is agreed on all hands that the classical epistemological project, conceived as one of deductively validating physical knowledge from indubitable sensory data, cannot succeed. | |
| From: Jaegwon Kim (What is 'naturalized epistemology'? [1988], p.304) | |
| A reaction: This is the 'Enlightenment Project', which had a parallel in morality. Kim refers to the difficulty as 'The Humean Predicament'. Hume also hoped that induction might be deductive. One obvious move is to expand from 'deduction' to 'reason'. |