"Register of theories" should go on the issue list for tomorrow. (01)
DS (02)
At 3/13/2006 04:08 PM, you wrote:
>Chris,
>
>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.
>
>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.
>
>We should also agree on some standard terminology
>for the relations of theories:
>
> 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.
>
> 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.
>
> 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.
>
>Just one other point:
>
>CM> Is not subset the arc relation in the lattice under that
> > understanding?
>
>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.
>
>John
>
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Dagobert Soergel
College of Information Studies
University of Maryland
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