Formalisations of Evolutionary Biology 4931.2 The Semantic Conception of Scientific Theories
The semantic conception is so called because scientific theories are formalized in
terms of models (semantic structures) and, hence, an adequate formal approach to
the structure of scientific theories consists in the direct specification of models and
not in the specification of a first-order predicate logic formulation (a syntax). On
the “received view” version of the syntactic conception, the semantics of a theory
are provided by correspondence rules. As indicated above, one could provide the
semantics, following Tarski, model-theoretically.
Briefly stated, with a more detailed exposition to follow, on a semantic con-
ception, the semantics of a theory are provided directly by defining a class of
models. For Patrick Suppes, the class of models is directly defined by specifying
a set-theoretical predicate. For Bas van Fraassen and Frederick Suppe, the class
of models is defined in terms of a phase space or state space (i.e., topologically).
One point of difference between van Fraassen and Suppe is that van Fraassen
identifies theories with state spaces whereas Suppe understands state spaces as
“canonical iconic models of theories” [Suppe, 1972a, p. 161, note 18] or “canonical
mathematical replicas of theories” [Suppe, 1977, pp. 227–228, note 565].
A broad outline of the points of agreement and the points of difference between
the Received View and the semantic is easily provided. The three major com-
ponents of a formalisation of a scientific theory on the Received View are: (1)
the mathematical domain used to provide the syntax for the theory is first-order
predicate logic, (2) a formalised theory is an axiomatisation and (3) the semantics
of the theory are provided by correspondence rules. The semantic conception re-
jects the stricture of (1), accepts (2) if “axiom” is understood broadly enough to
allow fundamental theorems of the theory to be classed as axioms when expressed
in mathematical domains such as topology, set theory, and so on, and rejects (3)
entirely.
Frederick Suppe has traced the origin of the semantic view of theories to John
von Neumann in the 1940’s [Suppe, 1989].^15 ) Two other early initiators and ad-
vocates were Evert Beth [1948; 1949; see also 1961] and Patrick Suppes [1957] in
hisIntroduction to Logic. Suppes further develops his account in several pub-
lications [Suppes, 1962; 1967; 1968]. Beth, and following him Bas van Fraassen
[1970; 1972; 1980; 1981], advanced a state space approach while Suppes advanced
a set-theoretical predicate approach. Fred Suppe has also been a developer and
champion of the state space approach [1967; 1972; 1977; 1989]. As I will show be-
low, Mendelian genetics can be formulated quite naturally on either approach.^16
In 1957, Suppes suggested that scientific theories are more appropriately for-
malised as set-theoretical predicates. Shortly thereafter, in 1961, Robert Stoll in
hisSet Theory and Logic [Stoll, 1961] made a similar claim about the formaliza-
(^15) Suppe [1989] provides an excellent history of the development of the semantic conception,
and a defence of scientific realism within this conception.
(^16) A set-theoretical version of the formulation of Mendelian genetics is as follows:
T: A systemβ−=〈P, A, f, g〉is a Mendelian breeding system if and only if the following axioms
are satisfied: