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. |
| 21382 | Things get smaller without end [Anaxagoras] |
| Full Idea: Of the small there is no smallest, but always a smaller. | |
| From: Anaxagoras (fragments/reports [c.460 BCE], B03), quoted by Gregory Vlastos - The Physical Theory of Anaxagoras II | |
| A reaction: Anaxagoras seems to be speaking of the physical world (and probably writing prior to the emergence of atomism, which could have been a rebellion against he current idea). |
| 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. |