RE: Processes and Causality
Chris,
I believe that we agree on the essentials. The axioms and
definitions concerning processes, time, causality, etc., are
in the numbered definitions and axioms of the paper:
http://www.bestweb.net/~sowa/ontology/causal.htm
The note that I circulated is an excerpt from the end of
Section 3 of that paper, and it presupposes Sections 1, 2, 3.
Following are some comments on your comments:
>>"In summary, time is the set of all possible measurements by a clock, and
>>space is the set of all possible measurements by a rigid ruler."
This is an informal interpretation of the formalism. Time is
introduced in Definition 2.1 as coordinate x4 of a four
dimensional space-time continuum. Then Axiom 3.4 introduces
clocks as discrete processes for measuring time, and the
definitions and axioms from 3.6 to 3.9 provide a way of
relating the discrete processes to the continuous processes.
They relate the measurements by a clock to the coordinates
of the continuum.
>.... It seems to me that the 'possible measurements by a clock'
>measure time - but are not time. Similarly for 'possible measurements by a
>rigid ruler'.
In physics, there is no other definition of time or space.
They are simply the coordinates that are measured by some
instruments -- the totality of all possible measurements.
>Surely it is the cement that keeps things and events regular and reliable -
>and an account of time should respect this intuition.
I agree. The term "cement of the universe" is a metaphor,
which highlights the importance of causality. I quoted it
to emphasize the importance of causality. I also agree with
the quote by Carnap that the concept of law is the best
approach toward understanding the meaning of causality.
The causal influences introduced in Definition 3.1 are
determined by the laws of physics (and everything built up
on top of them).
>Am I to interpret this as saying there is "a space-time continuum" and your
>clocks/rulers are meant to explain how we measure it?
Yes. That is the point of Definition 2.1 and Axiom 3.4.
The functions defined over that space-time continuum are
all the physical fields and entities that make up the universe
and all the stars, planets, people, dogs, and all the events
and interactions between them.
John