definition of parsimony

[Axel Rossberg <Axel@Rossberg.net>]

Dear List Members,

I am looking for a formal definition of parsimony for fundamental
scientific theories.  From the tiny bit I understood of category
theory, I had the impression it might provide the right framework for
such a definition.

The problem of motivating and defining parsimony is being discussed in
analytic philosophy.  An overview over the discussion can be found at
http://plato.stanford.edu/entries/simplicity/ , which starts off with
the sentences

  Most philosophers believe that, other things being equal, simpler
  theories are better. But what exactly does theoretical simplicity
  amount to? Syntactic simplicity, or elegance, measures the number
  and conciseness of the theories basic principles. Ontological
  simplicity, or parsimony, measures the number of kinds of entities
  postulated by the theory. One issue concerns how these two forms of
  simplicity relate to one another.

I am interested in the "ontological simplicity, or
parsimony". However, if one understands modern physics as describing
essentially only one thing, the wave-function of the universe, then
even the idea of defining parsimony in terms of numbers of kinds of
things seems to be a bit odd.

Yet, I think the idea is intuitively clear.  The minimum requirement
for a formal definition of parsimony is perhaps that it should
identify theories such as the dynamics of Newtonian point-particles or
the current "standard model" of particle physics as parsimonious, while
the same theories with some oddities added, which do not themselves
affect the "real" physics, should be identifiable as non-parsimonious.

Beyond this, such a definition should presuppose as little as possible
about the nature of the theories it applies to.

Does somebody know about applications of category theory to this
problem, or have an idea for who to do it?

Cheers,

Axel Rossberg
---
Evolution and Ecology Program
International Institute for Applied Systems Analysis
Schlossplatz 1
A-2361 Laxenburg
AUSTRIA
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