Chris, (01)
The point I have been emphasizing even more than the
lattice of all possible theories is the need for a
*registry* of actually specified and tested theories. (02)
Among the relationships to be recorded in the registry
are implication/entailment, analogy (or whatever you
want to call it), and many, many others, including
who defined them, used them, tested them, etc. (03)
We should also agree on some standard terminology
for the relations of theories: (04)
1. I have never liked the word "subsumption" -- partly
for the reason that it can be interpreted in many
ways (as you did in your note). I'd rather just
call it implication or entailment. (05)
2. That's an excellent reason for getting rid of the
word "subsumption": "... ZF subsumes Peano Arithmetic".
By using Goedel numbering, you could also say that
arithmetic subsumes all sorts of theories. That may
be theoretically interesting, but hopelessly confusing
for any serious discussion of practical problems. (06)
3. Relative interpretability is a big mouthful to say
or type, and it's hard to explain without getting
into lots of technical issues. I use analogy because
that's what Bohr did when he renamed the sun and earth
the proton and electron for his model of the H atom. (07)
Just one other point: (08)
CM> Is not subset the arc relation in the lattice under that
> understanding? (09)
It is true that if theory T1 implies T2, then T2 is a subset
of T1 and vice versa. However, that can be confusing, since
(a) the directions of the two relations are opposite, and
(b) implication is a logical relation (which is the main point)
and subset is a secondary issue that distracts attention. (010)
John (011)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/uos-convene/
To Post: mailto:uos-convene@xxxxxxxxxxxxxxxx
Community Portal: http://ontolog.cim3.net/
Shared Files: http://ontolog.cim3.net/file/work/UpperOntologySummit/uos-convene/
Community Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UpperOntologySummit (012)
|