display all the ideas for this combination of philosophers
2 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. |