488 Paul Thompson
these conceptions in more detail and explore the relationship of each to biological
theorising.
1.1 The First-order Predicate Logic (Syntactic) Conception of The-
ories
This conception is a syntactic conception. That is, a scientific theory is formalised
in terms of well-formed-formulae (wff’s) of the syntax of first-order predicate logic
with identity.^7 It is also an axiomatic-deductive structure. Some sets of wwf’s
capture those claims of the theory which cannot be deduced from other claims
and from which all the other claims within the scope of theory can be deduced.
This set constitutes the axioms of the theory. All other wff’s of the theory are
deducible from the axioms. Hence, for obvious reasons, this conception has also
been called the axiomatic-deductive conception.^8 However, although it is indeed
anaxiomatic-deductive conception, this characterisation does not distinguish it
from the conception of theories put forward by Patrick Suppes. On his conception
of theories, which we will explore later, theories are formalised in set theory, and
the axioms of a theory are specified in terms of a set-theoretical predicate. All
other claims of the theory are expressed in set-theoretical terms and are a logical
consequence of the axioms. Therefore, characterising a conception as axiomatic-
deductive does not provide a unique descriptor. On the other hand, characterising
a conception as syntactic does distinguish it from the other conceptions that have
been advanced. Hence, “syntactic” is a more useful characterisation of the view set
out in this section. This view held such sway in the first half of the 20th-century
that Hilary Putnam in 1962 dubbed it “The Received View.”
The syntactic account arose within the school of philosophy known as logi-
cal positivism and in the wake of the publication of Bertrand Russell and Alfred
North Whitehead’sPrincipia Mathematica.Principia Mathematicacodified math-
ematical logic and made possible the symbolic representation of ordinary language
statements; those statements being rendered as well-formed-formulae in first-order
predicate logic with identity. It also made possible the exploration of the logical
(deductive) relationships among those formulae and, hence, among the linguistic
statements they represent. The syntactic account’s most influential and impor-
tant formulation was worked out by the logical empiricists,^9 Rudolf Carnap, Carl
Hempel, Ernest Nagel and Richard Braithwaite (see [Suppe, 1977] for an excellent
exposition and historical account of this conception).
(^7) First-order logics are those logics whose entities are individuals. In the case of first-order
predicate logic, the objects are individual things. Subjects and predicates are symbolically rep-
resented and the quantifiers “all” and “some” are employed. Second-order logics are those logics
whose entities are sets of individuals.
(^8) Alfred Tarski provides a clear and influential account of the deductive method and its appli-
cation in constructing mathematical theories in Tarski [1946].
(^9) Logical empiricism is a descendent of logical positivism (see Giere and Richardson [1996],
and Misak [1995]). Carnap proposed changing the name to reflect both its empiricist stance and
the softening of some of the positions found in logical positivism.