Pat H, Francis, Pat C, (01)
I agree with that point: (02)
PH> 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. (03)
A lattice (or hierarchy) of theories would certainly accommodate
mathematical structures other than just the usual number system. (04)
PH> But this is an aside from your main point about the importance
> of units, with which I agree. (05)
Yes, that is the main point I wanted to emphasize. (06)
FMcC> If there are no primitive symbols, then all you have a network
> of relationships. For that to be useful, there has to be a way of
> relating the network to the Real World™. One might imagine that it
> is straightforward to 'link' a symbol to a feature of the RW; but
> relating a sub-graph to a feature sounds more challenging. (07)
The question of how the symbols of any theory are linked to the
world is important, and that has always been a central issue of the
philosophy and practice of science, engineering, and everyday life. (08)
But there is no such thing as a single "way", and the variety
of ways is constantly increasing as new theories and technologies
are developed. I would never imagine or claim that all or even
most of the ways or links or are "straightforward". (09)
Primitives are in the eye of the beholder (or theorist), and
every generation of scientists reanalyzes and refines the
"primitives" of the preceding generation: the simple atoms
of one generation become little solar systems of the next;
then the particles of those systems are reanalyzed as
combinations of smaller particles, which may be further
reanalyzed as vibrating strings or whatever. (010)
As Pat H. noted, the real numbers, which have been the most
common "primitives" of most scientific theories, may be
replaced by more complex mathematical structures. In all
these refinements, the methods for relating the theoretical
symbols to the experimental procedures become more and more
complex. But that is the normal way science develops. (011)
PC> F=ma is only a *theory* of motion, and as I have mentioned
> in this thread, incompatible theories would have to be
> maintained in some extension(s) to the basic FO....
> Force can be directly perceived by the sense of touch, and
> things that make direct sensory impressions have, in my view,
> a privileged status as prime candidates for primitiveness. (012)
More precisely, the equation F=ma may belong to a large sublattice
of theories, and the complete lattice is infinite. Instead of
thinking of new theories as "extensions" to the old theories, it
is better to think of the known (or implemented) theories as a
tiny part of the infinite lattice of conceivable theories. (013)
PC> Sets of concepts that are mutually dependent on each other for
> their description would have to be located together – whether in
> the base FO or in some extension to it... Force can be directly
> perceived by the sense of touch, and things that make direct
> sensory impressions have, in my view, a privileged status as
> prime candidates for primitiveness. (014)
PH> Why would this notion of what one might call 'psychological'
> primitiveness have any relationship at all with your earlier
> notion of 'definitional' primitiveness? Science seems to have
> advanced by abandoning sensorially rooted concepts in favor of
> much more abstract notions such as symmetry preservation and
> conservation laws. (015)
I certainly agree. Each generation of scientists refines and
replaces the so-called "primitives" of the older generation.
Aristotle's physics was psychologically "natural" for two
thousand years. But for anyone who has been exposed to modern
science, it seems weird. (016)
PC> Deciding what is "primitive" may never be formally resolvable
> in a mathematical sense... (017)
Absolutely true! Nor can it be resolved in any psychological,
sociological, or linguistic sense. Young children have a very
animistic theory of the world, but with experience and education,
they grow out of it. We don't want to build animism into our
ontologies just because it's more "natural" for babies. (018)
PC> I think that a principle for construction of the FO should be
> to include everything that is desired by someone... (019)
PH> Stop right there. Let us agree on that. Whether it is logically
> consistent with the rest or not. Intransigent logical
> inconsistencies require divisions to be drawn between theories,
> hopefully in some reasonably principled way and hopefully
> documented. That is the best we can hope for, and we know we can
> do it and that it can be useful. Let us be content with that. (020)
I heartily agree. (021)
And the lattice of all possible theories provides a principled
framework for relating theories to theories. Since the complete
lattice is infinite, I suggest the term 'hierarchy of theories'
for the finite subset that have been documented in the registry. (022)
John (023)
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