Models of Mechanisms: The Case of the Replicator Dynamics - Mechanism and Causality in Biology and Economics - page 81

On the other extreme, we have an ideally complete model. 'Such models include
all of the entities, properties, activities, and organizational features that are relevant
to every aspect of the phenomenon to be explained' (Craver 2006 , p. 360). Even if
completeness is relativised with respect to explanatory purpose, few, if any, such
complete models can be found. More relevant, thus, seems the notion of a mecha-
nism schema, which is a somewhat complete, but less than ideally complete,
mechanistic model.
For a given mechanism, a mechanism sketch thus represents less of its features
than a mechanism schema does. The sketch does so either by not at all specifying
some features that the schema specifies (this is easier with formal models: a set-
theoretic model, say, may stay silent about the colours of the objects it represents; a
computer model may successfully evade specifying the weight of the structure it
represents). Alternatively, sketches often specify certain features, but users of the
sketch might exclude these features from the representational function of the
sketch. That is, they declare these certain features to be idealisations . Scale models,
for example, have many features, like size and weight and materiality, that are
usually considered idealisations and hence not representations of the target object's
properties. By either way, a mechanistic sketch represents less features of a given
mechanism than a mechanism scheme does. Consequently, mechanism sketches are
more abstract than mechanism schemata.
Abstraction is often thought of in relation to generality. 1 A mechanism sketch,
then, is more abstract than a mechanism schema, because those properties described
in the sketch are a proper subset of those described in the schema. Different
mechanisms, described by different schemata, may therefore be described by one
and the same sketch.
Such a view of mechanistic models is particularly plausible when seen from
an 'exemplar' account of mechanisms. Such an account points out that mecha-
nistic models often represent a particular, exemplary mechanism (Bechtel and
Abrahamsen 2005 , p. 438). Such exemplars or prototypes are particular tokens of
causal structure in the world. A mechanistic model close to being ideally complete
might represent just a single such exemplar. A mechanism sketch, on the other
hand, might represent a large set of such exemplars. With increasing abstraction,
mechanistic models get more and more general.
Scientists use exemplars and prototypes, according to Bechtel and Abrahamsen,
in order to accommodate the subtle variations between related mechanisms. For
example, they model a mechanism in wild-type Drosophila and then extrapolate
from this prototype to mechanisms in other strains and species, all the while
acknowledging that these are not identical mechanisms. In this view, explaining
with a mechanistic model typically commences by explaining the phenomenon with
1 Take, for example, Nancy Cartwright's Aristotelian account of abstraction: ' A is a more abstract
object than B if the essential properties, those in the description of A , are the proper subset of the
essential properties of B ' (Cartwright 1989 , p. 214).