On Jan 8, 2009, at 4:00 PM, Patrick Cassidy wrote:
(6) [PC] >> At this point we seem to be getting redundant. I believe that these can all be described by a single set of primitives, and apparently PH doesn?t think so. It can?t be resolved here, and needs to be the subject of a proper experiment.
[PH] > I know
they cannot, and the 'experiment' is already done. Those various temporal theories can all
be expressed in terms of three concepts: time-point, time-interval and duration. Duration cannot be reduced to the other two (there's a model-thoeretic argument in the paper) and the other two can be reduced to oine in some, but not all, of the theories. That gets you down to two or at most three concepts, known to be irreducible to smaller sets. And still, there are many variations possible in the ontologies.
I am getting confused here. Your first sentence says the time theories *cannot* be expressed by a small set of primitives, and the seocnd sentence says they *can* be expressed by a set of three primitives. I am clearly misundersanding something you are saying ? we must be using words in different senses.
Well, I am not sure what you are meaning. My point was only that your claim that all these various temporal ontologies can be 'reduced' to a single small set of 'primitive' concepts is pretty much meaningless, since they only use a small set already, so there isn't any more 'reducing' possible. Yet they are not compatible, and not reducible to one another. The way I have understood your argument, this is already a clear counterexample to your claims for the hypothetical single basic FO. Unless, of course, it simply does not refer to time at all.
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