Mechanisms and Laws: Clarifying the Debate - Mechanism and Causality in Biology and Economics - page 128

why certain facts can be extrapolated and others cannot. Nor does he tell us how to
discern which features of a system can be extrapolated from those that cannot.
Rather, by invoking the idea of a p-law, he merely asserts that there is a distinction
between knowledge that can be extrapolated and knowledge that cannot be
extrapolated. But the bald statement that there is a difference between the
predicates that project and those that do not, conditions that project and those that
do not, and times when the consequent really ought to obtain and times when it
should not is not a victory for p-laws but simply an assertion that a central problem
for any theory of p-laws has a solution.
Let's push a bit deeper. For a defender of strict laws, which by definition apply
always, without exception, and without limitation of scope, it is reasonably clear
how knowledge of the laws would warrant extrapolation. For a defender of a robust
metaphysical notion of a law, where a law is part of the structure of the world that
explains (rather than merely describes) the p-regularities we observe, then knowl-
edge of the laws would presumably warrant extrapolation. But Leuridan weakens
the notion of a law so that p-laws are mere regularities and p-law statements are
descriptions of these regularities; further, such descriptions are nonuniversal, have
exceptions, and apply only in restricted regions of space-time. In effect, he turns
p-laws into imperfect regularities with no robust metaphysical backing. Whether
such a weakened p-law warrants extrapolation outside of the laboratory depends
upon whether one in fact finds that the regularity continues to hold outside of the
laboratory, whether the necessary background conditions hold, whether the target
instance under consideration is one of the exceptions, or whether it is not. p-laws, as
Leuridan understands them, might not warrant extrapolation. The laws might hold
only in Morgan's laboratory, after all. At the very least, if one believes that p-laws
offer a solution to the problem of extrapolation, then one owes a further story about
how one knows when the conditions for extrapolating the regularity have been met.
Leuridan offers no such story.
Bechtel and Abrahamsen ( 2005 ), whom Leuridan picks out for particular criti-
cism on this matter, argue on independent grounds that it is philosophically
unfruitful to think about the problem of generalization (or extrapolation, in
Leuridan's vocabulary) 4 in terms of laws. In a section of their paper called
“Generalizing without Laws,” they criticize law-based views of generalization
and develop an alternative, prototype-based account. Because Leuridan does not
mention these arguments, we repeat them here. They argue that if one thinks of
biologists as attempting to build law statements, paradigmatically represented in
terms of material conditionals, then it is difficult to understand the prototypical
structure of biological theories. One is tempted to think of biologists as
constructing, for example, a law statement of heredity (such as Mendel's laws).
When one encounters variation in that mechanism (as Morgan did), one is tempted
4 One might distinguish generalization (i.e., expanding the scope of the schema within a species/
class) from extrapolation (i.e., expanding the scope of the schema beyond the species/class). Given
that the parties to this dispute do not draw this distinction, we treat them as synonymous.