Identity, Structure, and Causal Representation in Scientific Models - Mechanism and Causality in Biology and Economics - page 36

should understand causation generally. The roots of the approach advocated here
are found in my own work as a practitioner of economics and draw on sources, such
as the work of Herbert Simon, that were originally aimed at problems that arose in
economic and econometric analysis. The application is much broader than these
origins might suggest.
In part, this chapter reacts to Cartwright's ( 2007 ) “pluralistic” account of
causation. In stressing plurality, Cartwright fails to illuminate the close
relationships among a number of approaches to causality that are hidden in alterna-
tive schemes of representing causal relations. In part, the chapter reacts to James
Woodward's ( 2003 ) “manipulability” account of causation - an account which is
much criticized by Cartwright. Woodward's understanding of causation appears to
be driven by particular schemes of representing causes. A more effective scheme of
representation suggests different conclusions with respect to several important
issues. The account proposed here in no way fundamentally conflicts with the
general approach of modeling causal relationships graphically, developed espe-
cially by Judea Pearl ( 2000 ) and Peter Spirtes et al. ( 2000 ) and used by Woodward.
Rather it clarifies the relationship between graphical representations and systems of
equations in a manner that both enriches the graphical approach and demonstrates
the fundamental kinship of the two approaches.

2 Representing Causal Structure

2.1 Graphs and Equations

While many philosophers understand causal relations as holding fundamentally
among particular events, occurrences, or properties (i.e., among tokens ), Woodward
and most economists understand causal relations as holding among variables (i.e.,
among types ). Token-level relationships for Woodward and the economists are
causal to the degree that they instantiate a type-level relationship. In stochastic
cases, token-level relationships are seen as the realization of random processes.
Relations among variables are often expressible in the form of systems of
equations. Equality is a symmetrical relationship, and the most distinctive charac-
teristic of causal relations is their asymmetry: A causes B gives no ground for
holding that B causes A (although we must not rule out mutual causation without
further consideration). Woodward, in common with Pearl ( 2000 ), Spirtes et al.
( 2000 ), and other advocates of graph-theoretic or Bayes net methods of causal
inference, represents causal relations by graphs in conjunction with equations.
Figure 3.1 shows a typical causal graph (uppercase letters represent variables)
that corresponds to a system of equations:

A ¼ α A ; ð 3 : 1 Þ