Crítica, Revista Hispanoamericana de Filosofía, Volume 13, number 38, August 1981
Aproximaciones admisibles dentro de teorías empíricas
[Admissible Approximations in Empirical Theories]
Ignacio Jané
Universidad Autónoma Metropolitana
C. Ulises Moulines
Instituto de Investigaciones Filosóficas
Universidad Nacional Autónoma de México
Abstract: In some previous writings (listed in the bibliography) the authors
have dealt with the concept of approximation in empirical science
by using a formal approach that departs from the standard one: It does
not consider the relation of approximation as a relation between statements,
but as a relation between certain kinds of structures (potential
models of a theory). Within this same approach, the question is
raised now: Which approximations are (empirically) admissible
and why? The authors try to give a general account of the conditions
that make an approximation between models admissible. The
discussion is illustrated by means of examples taken from planetary
astronomy; for example, the question : When are we going to say
that two descriptions of a planetary orbit approximate each other
within an admissible degree of approximation? And what does this
mean precisely?
In the first part of the article, it is shown that different aspects or’
factors must be taken account of when trying to give a complete answer
to the preceding questions. Some of them are of a qualitative, some
are of a quantitative kind, but all must be somehow “integrated” into
a “global” approximative relationship. The explication of such factors
can only partially be carried in formal terms. The main concepts
that are involved in this explication are those of “(relative) importance”
of different objects within the domain of the models; “very
similar descriptions of objects”, and “quasibijective correspondence
of models”. It is clear that the first two notions cannot be explicated
in purely formal or’ quantitative terms. This does not mean that we
cannot try to make them reasonably clear.
The second part of the article is devoted to the question of whether
the notion of a maximum degree of admissible approximation makes
sense and can be made precise. It is argued that each kind of application
of a theory must have a supremum of admissible approximations
and that this supremum is univoquely determined.
Finally, all the aspects considered in the discussion are summarized
in a set of necessary conditions for approximation within an empirical
theory.
[C. Ulises Moulines]
Keywords:
 PDF en Spanish (269 Kb)
