490 Paul Thompson
and employed the logical empiricist view of theories. Among philosophers, opinion
on the applicability of this conception to biology was divided. Morton Beckner
[1959] proved to be prescient in his account of biological theories as a family of
models. He did not embrace the logical empiricist account assuming that its ap-
plication to biology was at best limited. Thomas Goudge [1961] was quite clear,
whatever applicability the conception might have in physics, it did not capture
important features of biological theories and explanation. Two philosophers who,
during the 1970’s and 1980’s stood squarely behind the applicability of this concep-
tion to biology are Alexander Rosenberg [1985a] and Michael Ruse [1973]. Others
with varying degrees of qualification and subtlety have argued in favour of this
conception’s relevance to biological theorising (e.g., David Hull [1974])
The account that Ruse provides of a biological theory that can be given a syn-
tactic conception formalisation focuses on population genetics [Ruse, 1973, pp.
32–37]. The axioms of population genetics are Mendel’s Laws: the law of segre-
gation and the law of independent assortment. The thrust of Ruse’s argument
is that the Hardy–Weinberg Equilibrium, a fundamental principle of population
genetics, can be derived from Mendel’s second law (the law of independent assort-
ment). What Ruse provides is a sketch of an axiomatic-deductive framework. He
does not cast Mendel’s laws as formulae in first-order predicate logic. He does not
include other required axioms: the axiom of differential reproduction, the axiom
of linkage, to mention only two key ones. One derivation is a little light. But per-
haps the most telling feature of Ruse’s argument is that his structure for Mendel’s
second law and the deductive machinery he employs is not first-order predicate
logic but that of matrix algebra — albeit a very elementary application of matrix
algebra. Hence, his account seems more like an instance of what I later in this
paper introduce as the Galilean conception of scientific theories.
The account that Alexander Rosenberg [1985a] provides builds heavily on an
axiomatisation of selection theory constructed by Mary Williams [1970]. Williams’
axiomatisation of selection theory is a superb and sophisticated example of the ap-
plication of an axiomatic method in biology. It is not surprising, therefore, that
Rosenberg makes it the centrepiece of his argument in favour of the logical empiri-
cist conception. Although Williams uses “evolution” in the title of the paper, the
axiomatisation is, in fact, of selection theory. The axiomatisation makes scant ref-
erence to genetics. Rosenberg attempts to mitigate this difficulty by arguing that
evolutionary theoryisselection theory — genetics (heredity) is just a background
condition.^11 I have argued elsewhere why this move fails to rescue this axioma-
tisation from the problem of its isolation from evolutionary theory as a whole
[Thompson, 1983]. In Part II below, I argue that evolutionary theory is a com-
posite of selection theory, genetics, ecology and a host of other domains. Within
this conception of evolutionary theory, Williams’ axiomatisation is powerful and
(^11) This stands in stark contrast to Ronald A. Fisher’s opening sentence in the Preface to his
classic workThe Genetical Theory of Natural Selection[1930]. Fisher writes, “Natural Selection
is not evolution.”