display all the ideas for this combination of philosophers
4 ideas
| 15273 | Points can be 'dense' by unending division, but must meet a tougher criterion to be 'continuous' [Harré/Madden] |
| Full Idea: Points can be 'dense' by indefinitely prolonged division. To be 'continuous' is more stringent; the points must be cut into two sets, and meet the condition laid down by Boscovich and Dedekind. | |
| From: Harré,R./Madden,E.H. (Causal Powers [1975], 6.IV) | |
| A reaction: This idea goes with Idea 15274, which lays down the specification of the Dedekind Cut, which is the criterion for the real (and continuous) numbers. Harré and Madden are interested in whether time can support continuity of objects. |
| 15274 | Points are 'continuous' if any 'cut' point participates in both halves of the cut [Harré/Madden] |
| Full Idea: Divide points into left and right set. They're 'continuous' if that point is either last member of left set, and greatest lower bound of right (so no least member), or least upper bound of left set (so no last member) and first member of right set. | |
| From: Harré,R./Madden,E.H. (Causal Powers [1975], 6.IV) | |
| A reaction: The best attempt I have yet encountered to explain a Dedekind Cut for the layperson. I gather modern mathematicians no longer rely on this way of defining the real numbers. |
| 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. |
| 15211 | There is not an exclusive dichotomy between the formal and the logical [Harré/Madden] |
| Full Idea: The assumption that there is an exclusive dichotomy between the formal and the psychological is, in our view, an error of enormous consequence. | |
| From: Harré,R./Madden,E.H. (Causal Powers [1975], 1.I.A) | |
| A reaction: I agree entirely with this, and am opposed to the Fregean view of the matter. The psychology is the bridge between the physical world and the logic. Frege had to be a platonist, so that the formalism could latch onto something. |