Chemistry Reference
In-Depth Information
Where first order logic is too weak, we can replace it with any formal system that is strong
enough to do what we need it to do. The bifurcation of the vocabulary plays no role at all.
(Dizadji-Bahmani et al.
2010
, p. 403)
Usually, the Nagelian requirements are read as requirements of a first-order
logic. On this basis, emendations of Nagel
s scheme have been proposed by
Schaffner (
1967
) and Sklar (
1967
). Causey (
1977
) argued that reduction postulates
must necessarily be
identities
. However, the detailed investigation of
actual
cases
of reduction
4
has highlighted that reductions based on identities and derivation
which fit this particular logical straitjacket are the exception rather than the rule.
The condition of derivability is formulated in terms of
three
formal requirements
for reduction. The three conditions that Nagel mentions in the formal section of the
chapter on reduction are that (1) the theories involved can be explicitly stated,
(2) the meanings used in the terms are fixed by common convention or by the
respective theories, and (3) the statements of the reduced theory are logical conse-
quences of the reducing theory and the reduction postulates.
In combination, the derivability conditions establish the unit of reduction as a
scientific
theory
which can be appropriately
paraphrased
(through linguistic for-
mulation in some formal language followed by axiomatisation) so that the right sort
of
formal connections
(i.e. logical consequence) can be established.
These conditions do not specify connectibility. To introduce connectibility,
Nagel introduces, in addition to the formal requirements, the notion of
coordinating
definitions
(which, for clarity, we will call
'
in the remainder of
this paper) as an additional assumption. The reduction postulates stipulate a sort of
translation manual through
[
reduction postulates
'
'
and traits represented by the
theoretical terms already present in the primary science (Nagel
1961
, pp. 353-354)
The reduction postulates themselves, however, are far from simple.
5
They allow
the language of the theory to be reduced to be connected to the language of the
...
] suitable relations between whatever is signified by
A
'
'
4
See for instance Kuipers (
1990
) for an example of reductions from many sciences, most of which
are not based on strict identities.
5
For instance, Nagel (
1961
) discussed three kinds of linkages postulated by reduction postulates
1. The links are logical connections, such that the meaning of
'
A
'
as
'
fixed by the rules or habits
of usage
'
is explicable in terms of the established meanings of the theoretical primitives in the
primary discipline.
2. The links are conventions or coordinating definitions, created by
deliberate fiat
, which
'
'
in terms of the primary science, subject to a criterion of
consistency with other assignments.
3. The links are factual or material, or physical hypotheses, and assert that existence of a state
'
assigns a meaning to the term
A
'
'
B in the primary science is sufficient (or necessary and sufficient) condition for the state of
affairs designated by
A
. In this scenario, the meanings of
A
and
B
are not related
'
'
'
'
'
'
analytically.
