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between causes and effects, it is longstanding in the philosophy of science
concerning the structure of scientific theories. Hempel ( 1966 ), for instance, when
discussing the distinction between observables and unobservables, suggests that in
an attempt to explain the performance of a black box which “responds to different
kinds of input by specific and complex output” (p. 81), the internal structure of the
black box is in principle observable, or can be directly inspected, as long as
appropriate instruments are available. Hence “any line drawn to divide them into
actual physical objects and fictitious entities would be quite arbitrary” (Hempel
1966 , p. 82). Similarly, Hanson ( 1963 ) illustrates that, as science progresses, our
understanding of phenomena switches from the stage of “black box” to that of “grey
box” and finally reaches the stage of “glass box” whence the theory and the
phenomena are of the same structure and the equations of the theory can actually
“mirror” the processes of the nature (Hanson 1963 , p. 38). Hanson's account is
shared by the mechanists. MDC, for instance, regard the schemata as essential
heuristic devices for discovering mechanisms. By reasoning with a schema,
scientists are guided to choose known and proper entities or activities to fill the
gap. Afterward, when a schema is instantiated, it provides a mechanistic explana-
tion of the phenomena that the mechanism produces (Machamer et al. 2000 , p. 29).
It is thus natural to relate mechanism sketches and schemata to scientific models;
both serve inferential and representational devices to understanding science. Recent
study (e.g., Morgan and Morrison 1999 ) emphasizes that models are independent of
theory and the world and thus have autonomous power for representing each of
them. Literature also shows that the distinction between models of theories and
models of data that was earlier made by Patrick Suppes in his influential article
“Models of Data” (Suppes 1962 ) has proven useful for characterizing scientific
modeling processes. Following Suppes and the discussion of empirical models in
science and philosophy, Ruey-Lin Chen argues in his chapter that scientific discov-
ery in biology can be explained and instantiated through the models of experimental
data. In contrast, Till Gr¨ne-Yanoff's chapter in this volume deals with the issue of
representing mechanisms at a theoretical level. He examines evolutionary game
theory (EGT), arguing that EGT models employed in biology and economics have
different interpretations concerning what causal factors and relations they repre-
sent, interpretations that are captured by informal mechanism descriptions rather
than by the EGT formalism. An abstract model is qualified as MDC's mecha-
nism sketch; it requires an interpretation of the model to represent a specific
mechanism in biology or in economics. In other words, biological or economic
mechanism descriptions are of a particular kind: They do not describe the compos-
ite parts of a system, but they describe in abstract form the stages through which the
mechanism runs. Because it does so in a highly abstract way, many different
mechanisms can be subsumed under these descriptions, making them general
schemata useful for many scientific purposes.
Hoover's and Steel's chapters demonstrate that representational devices such
as models can sometimes play a more active role. They both use directed
acyclic diagrams (DAGs) to represent causal relations, which has been a popular
representational tool employed by philosophers of causality. Hoover points out that
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