An axiomatic interpretation of the neo-darwinian theory of evolution.

Abstract

AN AXIOMATIC INTERPRETATION OF THE NEODARWINIAN THEORY OF EVOLUTION C. LEON HARRIS* It is often assumed that hypotheses are promoted to the status of theory or law only after being verified experimentally. Such a model of scientific progress overlooks the fact that many of the most fundamental statements of science have been not only unproved but untestable. Most readers are aware that Euclid's axioms and Newton's three laws are untestable, and I propose that the neo-Darwinian postulates of chance mutation and natural selection are also axiomatic in the same sense. In this paper I briefly review the historical role of axioms in science and explain why the neo-Darwinian theory is axiomatic. I shall restrict the discussion to axioms as classical or Kantian statements of seemingly intuitive truths. The motivation of this paper is not to argue for rejection of the neo-Darwinian theory or to propose alternatives. Nor does it provide support for the arguments of antievolutionists, since evolution is a fact regardless of whether the neo-Darwinian theory is correct, just as weight is a fact regardless of whether our theories of gravity are correct. Rather, my motivation is to correct what I view as an unhealthy state for the progress of science, a state in which the majority of biologists do not recognize the nature of one of our most important theories and, therefore , do not recognize the opportunity of creating new theories by changing the axioms. Axioms in Mathematics and Physics In science and in logic it is often necessary to make assumptions which appear intuitively obvious but which cannot be tested. These assumptions or axioms are usually untestable because they are universals and their proof would require the test of every case to which they apply; or because their proof would require some other logically unattainable condition or procedure; or because the axioms are tautological. Aristotle was apparently the first to direct attention to axioms [1], and *Department of Biological Sciences, State University College of Arts and Science, Plattsburgh, New York 12901. Perspectives in Biology and Medicine · Winter 1975 | 179 Euclid's Elements was apparently the first conscious use of axioms as the basis of mathematical proofs. Newton used axioms to deduce the theory of universal gravitation, but he also called the three axioms "laws," perhaps to satisfy rationalist contemporaries. Kant's Critique of Pure Reason later put rationalist minds at ease by arguing that axioms are intuitive truths. The first sign that axioms might not be true came in the late nineteenth century when non-Euclidean geometry was created by negating Euclid's fifth axiom to allow parallel lines to intersect. Because Euclidean and non-Euclidean geometry are indistinguishable at finite distances , there is no way to prove that Euclid's fifth axiom is true or false. Einstein [2, p. 41] cast further doubt on the truth of axioms with his special theory of relativity, which replaced Newton's three laws with the axioms that "the laws of thermodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good" and that "light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body." From this brief sketch it is apparent that axioms have been fruitful in mathematics and physics. One might wonder why the axioms of Euclid, Newton, and others were not smothered by a host of spurious axioms, since anyone can make an untestable assumption. The explanation is apparently that good axioms are immediately recognized by intuitive value judgments. I propose the following criteria as being among those by which good axioms are recognized: (I)A good axiom is canonical; that is, it does not directly contradict accepted facts. (2) A good axiom h productive; in conjunction with other axioms it produces testable theories. (3) A good axiom is neat; it does not require a multitude of ad hoc assumptions to support it, and it is not so restricted as to be trivial. These criteria apply only to axioms in the classical sense. In the twentieth century axioms have been used formally in mathematical logic in quite different ways. Woodger...