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.
Gist of Idea
Points can be 'dense' by unending division, but must meet a tougher criterion to be 'continuous'
Source
Harré,R./Madden,E.H. (Causal Powers [1975], 6.IV)
Book Reference
Harré,R/Madden,E.H.: 'Causal Powers: A Theory of Natural Necessity' [Blackwell 1975], p.111
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.
Related Idea
Idea 15274 Points are 'continuous' if any 'cut' point participates in both halves of the cut [Harré/Madden]