FORMALISATIONS OF EVOLUTIONARY
BIOLOGY
Paul Thompson
...it is [mathematics] which reveals every genuine truth, for it knows
every hidden secret, and bears the key to every subtly of letters; who-
ever, then, has the effrontery to study physics while neglecting mathe-
matics, should know from the start that he will never make his entry
through the portals of wisdom
(Thomas BradwardineTractatus de Continuo,^1 circa1330s)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.
(Galileo Galilei,Il saggiatori,^2 1623)INTRODUCTIONA formalisation of a theory is an abstract representation of the theory expressed
in a formal deductive framework^3 for which there is a complete specification of:- what constitutes a well-formed-formula (wff), and
- all the permissible rules of inference.
(^1) As quoted by J.A. Weisheipl, “Galileo and his precursors,” in E. McMullin (ed.)Galileo:
Man of Science.
(^2) Commonly known in English asThe Assayer(Middle English “assay” assimilated to French
“essayer”). A superb translation by Stilman Drake can be found in: C.D. O’Malley and S. Drake
(eds.)Controversy on the Comets of 1618, Philadelphia, 1960.
(^3) This is a broader conception than that employed by logicians. The narrower concept con-
ceives of a formal system in terms of first-order predicate logic with identity.
General editors: Dov M. Gabbay,
©c2007 Elsevier B.V. All rights reserved.
Handbook of the Philosophy of Science. Philosophy of Biology
Volume editors:
Paul Thagard and John Woods
Mohan Matthen and Christopher Stephens