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introduced in this model can take on the role
of beliefs in a belief revision scheme. This situation reflects actual scientific practice
in the (trivial) sense that approximations and idealisations to a complex theory can
be seen as various additional beliefs that play a role in the overall scheme.
It is interesting to note that from this point of view we consider the entire
reduction
schema
as a key element of the activity of scientific reduction, as opposed
to individual
theories
featuring as elements in an abstract reduction scheme which
is largely removed from actual scientific practice.
The
idealisations and assumptions
'
'
2.3 Structures and Beliefs: Reduction for a Dappled World
In this section, I will consider reduction in the context of a structuralist approach to
belief revision based on conceptual spaces. In general, adaptive logics such as belief
revision adapt themselves to the situation at the moment of inference. In this, they
represent the dynamics of reasoning - a Reichenbachian
-in
which, to save overall consistency, some beliefs are dropped from the overall
scheme. I will first briefly characterise the structuralist approach to theories before
proceeding with my proposal.
context of discovery
'
'
2.3.1 Structuralism Characterised
The structuralist theory approach to scientific theories originates in the work of
Suppes (
1957
) and was given most of its present form in the work of Sneed (
1971
).
It was discussed in detail in Balzer et al. (
1987
). The key elements of the structur-
alist theory are summarised in Table
2.1
. In the structuralist approach, a scientific
theory is characterised as a structure
where
K
is a structure that characterises
the theory
'
core
'
at both the theoretical and non-theoretical level in terms of its
(potential) models and partial potential models.
In the structuralist approach, reduction is characterised as a (structural) similar-
ity between structures.
A (specialisation) theory net is a set of structures that are connected through the
specialisation relation
h
K
,
I
i
.
7
The specialisation relation connects a (general) theory to
a specialised instance of that theory, which is applicable to a particular situation
through the introduction of a special set of limiting constraints. Technically, the
specialisation relation can be reconstructed as a constraint condition on the models.
It is interesting to note a strong relationship between the (partial) potential
models of a theory and the
conceptual space
of that theory. The (partial) potential
models specify the
σ
language
that is used in the theory, together with some rules for
'
'
7
See Balzer and Sneed (
1977
,
1978
) for an introduction of this relation and the corresponding
notion of a theory net.
