500 Paul Thompson
- Explanation consists in demonstrating that the dynamics of the model cor-
respond to dynamics of the empirical system in need of explanation. - Prediction consists in exploring the dynamics of the model and asserting a
future state of the empirical system.
In order to dispel a potential misunderstanding, I think it important to empha-
size one crucial similarity between the syntactic and semantic conceptions, namely,
they are both conceptions of the formal structure of theories. In addition, both
conceive of theories as deductive systems and both require fundamental principles
(axioms) in the formulation of the dynamics of a system. Hence, there is no refuge
to be found in the semantic conception for those philosophers who dispute the
appropriateness, and usefulness of formalisation in one or all branches of science.
Those of us who espouse the semantic conception are, like those who espouse
the syntactic conception, committed to the value of formalisation in science and
philosophy of science.
1.3 The Galilean Conception of Scientific Theories
Patrick Suppes encapsulates his view of the formalisation of scientific theories as
follows:
The sense of formalization I shall use in the subsequent discussion
is just that of a standard set-theoretical formulation. I do not want
to mean by formalization the stricter conception of a first-order the-
ory that assumes only elementary logic. Such stricter formalization
is appropriate for the intensive study of many elementary domains of
mathematics, but in almost all areas of science a rich mathematical
apparatus is needed. We can properly appeal to that apparatus within
a set-theoretical framework [Suppes, 1968, p.653].As the state-space version of the semantic view demonstrates, we can properly
appeal to that apparatus with a topological framework as well. Indeed, confining
the “rich mathematical apparatus” to set theory or topology is unnecessarily re-
strictive and does not accord with scientific theorising in many domains. Opening
up the domain of mathematics that can be drawn upon is a natural extension of
the semantic view.
As indicated above, by dubbing an extension of the semantic conception, the
Galilean conception, I am explicitly connecting it to Galileo’s famous claim (1623):
Philosophy is written in this grand book, the universe, which stands
continually open to our gaze. But the book cannot be understood
unless one first learns to comprehend the language and read the letters
in which it is composed. It is written in the language of mathematics,
and its characters are triangles, circles, and other geometric figures
without which it is humanly impossible to understand a single word of
it; without these, one wanders about in a dark labyrinth.