|From:||Pat Hayes <phayes@xxxxxxx>|
|Date:||Tue, 22 Jan 2008 13:04:35 -0600|
At 12:02 PM -0500 1/22/08, Ed Barkmeyer wrote:
John Sowa wrote:
All true and important. Nevertheless, it is also important to distinguish having points in ones ontology from claiming to be able to locate points numerically with absolute precision. These are not the same issue. One can embrace the former without claiming the latter. Indeed, one can show rigorously that under certain reasonable assumptions about intervals (basically, that they can satisfy a coherent notion of 'meeting' one another, or being adjacent without any gaps or overlapping), that point-like entities must exist. This is not to say that one can pin one of them down with a finite representation: but it does mean that would be foolish to deny that they are real things; and, moreover, it demonstrates that to assume that they exist will not produce any contradictions or difficulties. And such assumptions are extremely useful, to put it mildly. We say things like, see you at noon; we don't say, see you in the fuzzy interval 11:59-12:01.
I would also point out that very discussion about time-references being approximate itself presumes that there is a finer-grained "real" time available for the approximate times to fail to coincide in. If we were really at the universal discrete limit of Plank time, notions of approximation become paradoxical.
40 South Alcaniz St.
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