Pat Hayes and Pat Cassidy,
These statements are only true for "Newtonian"
conceptualizations of time.
Relativistic models of "space-time" require the
specification of both spatial and
temporal locations. Relativistic temporal models
arise in astronomy, astrophysics,
high energy physics.
In a purely computer science context see the classic
paper by Leslie Lamport
on Time, Clocks, and the Ordering of Events in a
Communications of the
ACM, vol. 21, no. 7, p. 558-565, July 1978
On Jan 11, 2009, at 10:18 AM, Pat
you say “Those various temporal
theories can all be expressed in terms of three
concepts: time-point, time-interval and duration.” , what do you mean by
that? Is being “expressed in terms of” used only for necessary and
No, I mean only that each theory uses only those three
terms, or can be reformulated using only those (or in some cases only two
of them.) Of course, since the theories have different axioms, they assign
somewhat different meanings to them.
Thinking more, this isn't really accurate. They all use only these three
classes, but they also use various different relations, such as the
timepoint and subinterval orderings and the various relations between points and
intervals. So perhaps the typical number of concepts is more like six or seven
than two or three.