Philosophy of Biology

Formalisations of Evolutionary Biology 519

where:

L=

f 1 f 2 f 3 ... fω− 1 fω

P 1 00 ... 00

0 P 2 0 ... 00

00 P 2 ... 00

···... ··

···... ··

000 ... Pω− 1 0

The first row contains net fecundities, the diagonal ofPxs contains survival prob-
abilities. This is known as theLeslie matrixrecognizing its promoter in ecology,
P.H. Leslie, and is an age-classified model growth rate. If some other factor is
more important than age (e.g., size) a more complex matrix can be constructed.^48
The above provides an elementary glimpse at the rich mathematical apparatus
employed in formalising the dynamics of population ecology systems. There is
a wealth of literature on mathematical models in ecology. An excellent starting
place is John Maynard Smith’s little bookModels in Ecology[1974].

4 REVISITING MODELS AND THEORIES

As the title of Section I indicates (“The Path to a Galilean Conception of Scientific
Theories”), I consider scientific theories to be mathematical models of empirical
phenomena and I have touched on this issue in Section I.4 above. Not all philoso-
phers of science agree with equating theories with modelssimpliciter. For many
of these philosophers, mathematical models are seen as iconic representations of
the dynamics of phenomena. Theories, on the other hand, describe those repre-
sentations. That is, theories provide an account of the dynamics of phenomena
whereas modelsmerelyrepresent them. Hence, the syntactic account of theories,
by identifying nomically necessary regularities and the logical interrelationships
among them, purports to be providing anaccountof the dynamics; mathematical
models, on the other hand, merelyrepresentthem. There are two reasons to reject
this position and accept that models are theories.
First, representation in the case of mathematical models is an account of the
dynamics. The language of the account is mathematics; what is said in that
language (the content) embodies all of the concepts, interconnections, possible
causal relations, etc. that are required toaccountfor the phenomena. To hold that
a syntactic account of theories is a view that specifies what it is to actually account
for the dynamics, not merely represent them, is to privilege first-order predicate
logic among all the available mathematical frameworks. In effect, to declare that
that mathematical framework providesan accountand all others providemere
representations. This seems philosophically parochial and untenable. Sometimes

(^48) See, for example, Caswell [1989].