On Jan 11, 2009, at 11:03 PM, John F. Sowa wrote: (01)
> Pat and Pat,
> I think that this discussion has converged on something useful,
> for which there is already well established terminology. But
> the word 'primitive' is not one of the terms.
> PC> Those various temporal theories can all be expressed in terms
>> of three concepts: time-point, time-interval and duration.
> PH> but they also use various different relations, such as the
>> and subinterval orderings and the various relations between points
> All these relations can be expressed with the real number system
> together with units of measurement, such as 'second' and 'meter'. (02)
No, they can't. Some of the temporal ontologies (notably, the most
complicated one) are incompatible with the reals. The real line is not
in fact a very good model for the intuitive time line. But this is an
aside from your main point about the importance of units, with which I
> The relations among the numbers lead us to other useful terms, such
> as 'multiply' and 'divide', which can be combined with 'meter' and
> 'second' to give us 'meter per second' and 'meter per second per
> Any foundational ontology suitable for science and engineering must
> include all those units of measurement, plus many others, such as
> ampere, volt, ohm, coulomb, joule, etc.
> If you want to talk about financial systems, there will be units
> such as dollars, euros, yen, etc.
> In any case, there is no question that all these terms belong
> in any foundation ontology, but the term 'unit of measurement'
> is better than 'primitive'.
> And the number of theories that relate those units is vastly
> greater than the number of units.
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