Answers to: definition of parsimony

Answers to: definition of parsimony

[Axel Rossberg]

Dear List Members,

two days ago I posted a message asking whether there is a formal
definition of parsimony for fundamental scientific theories, perhaps
using category theory.

Here is a short summary of answers I received:

Ralph Wojtowicz recommended to have a look at Part D in Volume II of
Johnstone's "Sketches of an Elephant", which as he wrote contains
discussions of constructions involving translations between formal
systems and their semantic categories.

As an example for parsimony in category theory, Eduardo Ochs suggested
the have a look at the relationships between set theory, local set
theories, and elementary toposes.

The paper by F. Wiedijk, "Is ZF a hack? Comparing the complexity of
some (formalist interpretations of) foundational systems for
mathematics", Journal of Applied Logic 4, 622-645, 2006 ps.gz pdf dvi
via http://www.cs.ru.nl/~freek/pubs/index.html also was recommended.

Many thanks to all respondents and also to Vaughan Pratt for his
refreshing critical remarks!

The answer to the question appears to be more difficult than I had
expected.  As often in philosophy, this may be to a good extent due to
difficulties in explaining what the question is.  One important point
which I failed to clarify is the difference between fundamental
mathematical theories and fundamental scientific theories.
Fundamental scientific theories may, I think, assume the fundamental
mathematical theory to be given.  They should not describe all
possible structures but, on the contrary, pick from the mathematically
given structures those that are physically realized.  This difference
might also put the problem of parsimony for scientific theories into a
different light.  But I'm not sure, of course.

So long,

Axel