Laws and selectionist explanation

Here we come across the rather entangled philosophical topic of scientific laws. Physicists state laws of nature. However interpreted, those laws of nature are general statements formulated in the modality of necessity. The usual puzzle in philosophy of science is to find a criterion distinguishing accidental generalities and laws (Ayer 1956). As an answer, Dretske (1977) claimed that laws have to be conceived as relationships between universals. But in any case, laws should support counterfactuals: this means that if some variables are changed within

5 Critique is made in Rosenberg (1982); other recent critiques led to the precision of the propensity definitions (Sober 2001; Ariew 2004).

6 I leave apart here the difference between empirical and a priori laws.

them, the results should be affected in a regular way. This implies that lawlike generalizations can be used in explanations, whereas accidental generalizations seem not to allow such a use and even less a predictive use.7 The positivistic account of science viewed explanation as a deductive argument whose conclusion is the explanans, and whose premise sets some laws of nature with some particular statements of facts [the so-called DN account of science: Hempel (1965)].

In a provocative chapter of his Philosophy of Scientific Realism, Smart claimed that there are no biological laws, since any law has to be reliable for any individual, e.g., has to be stated in the form "for any X, P(X).'' But in evolutionary theory, we only have statements concerning limited sets of entities, like teleost fishes, or more generally, birds in America, or Equus. People can forge seemingly law-like general assertions on the basis of such generalizations, like Dollo's law concerning irreversibility in evolution, or Cope's law concerning the increasing of size in populations; but they are nevertheless still spatio-temporally situated general statements lacking any nomothetic necessity. Necessity is supposed to hold for any individual of a given kind with no specification of space and time. These regularities fail to explain but merely describe; they are not predictive since they always find exceptions.8 For Smart, such biological regularities are like the schemata of engineers and are in the same way embedded in laws of physics. Even the universality of genetic code is a generalization on our planet, due to the contingent reason of common ascendance (contingent regarding the code itself), since the same correspondence laws between nucleotides and amino acids are not to be expected on any planet. For Beatty (1997), this contingency of generalized propositions affects the whole of the supposed law-like statements in biology. So the DN account fails to represent evolutionary theory.

The only evolutionary statement that could be a law is, thus, the one enunciating the process of natural selection since it specifies no particular entity. Philosophers debate about the nomothetic status of this principle of natural selection (PNS) (Bock and Von Wahlert 1963; Sober 1984, 1997; Brandon 1996, 1997; Rosenberg 1985,1994,2001). Rosenberg argues that the PNS is the only law of biology and relies on Williams' (1970) axiomatization of the theory, which conceives fitness as an undefined primitive term, e.g., a term which in some definitions, in some contexts, can be given only outside evolutionary theory, in

7 Taking a famous example from Goodman, what predictions could I infer from "all the men in this room are third sons'' (unless I have some additive information on those men, like: "they are all attending a third sons' meeting'', etc.)?

8 Rosenberg (1994) also denies that biology has laws in the sense of physical laws since it supervenes on all the physical laws and hence can only pick out disjunctions of laws applied in limited contexts.

another theory. But, even if by convention we say that it is a law, we still face the question of its differences from the other kinds of law.9 In effect, unlike physical laws, the PNS does not state any natural kind of property such as mass, electric charge, etc. The only property involved in its formulation is fitness, which is a mere supervenient property.

So the PNS becomes the equivalent of a physical law—stated in probabilistic language, of course—only as soon as some physical characters of the properties contributing to fitness are specified, a specification which is always context dependent.10 For instance, the "optimal shift towards viviparity'' described by Williams (1966) in some marine fishes results from a kind of law, since he stated the parameters ruling the selection pressures (density of predators, physiological cost of reproduction); parameters which in turn determine a range of relevant physical properties for selection. Hence, in this case the schema becomes predictive, and we can test it by building experiments in which the values of the variables concerned vary. This idea, however, does not exhaust all biological regularities, principally the aforementioned ones found in paleontology. Thus, recalling the two claims of evolutionary theory concerning both the Pattern and the Process of evolution, this way of constructing law-like sentences through the PNS is mainly relevant to the Process of evolution, whereas the Pattern is most likely to show nonexplanatory regularities.

So, if evolutionary theory is not, as Smart contended, a nomothetic science, neither is it a class of empirical generalizations combined with some mathematical tools. Moreover, in addition to the PNS, there is surely a set of genuine laws in evolutionary theory, since its core, population genetics, provides some models, such as the Hardy-Weinberg equilibrium, which prescribes a nomological necessity to any pool of genes in an infinite population. However, those kinds of propositions are not so much empirical laws as mathematical laws. They define a sort of mathematics of genes. Such models are in no case a description of any actual population, for in order to be applied to populations they have to integrate empirical content, i.e., by fixing the fitness coefficients of alleles. But this is not the same thing as fixing the parameters (mass, charge, etc.) in any standard

9 By changing the definition of what counts as law, and, more precisely, weakening the DN requisites on laws of nature, one can imagine that there is a continuum of kinds of laws instead of a sharp boundary between accidental and nomological generalization. For example, relying on the supporting counterfactual requisite, Woodward (2001) defines laws as statements invariant through a sort of change in the explanandum. This enables him to count several laws, like Mendel's laws, in biology, and then account for the predictive and explanatory role of an accidentally general statement such as the universality of the genetic code. My point is that characterizing the status of the principle of natural selection within such a continuum is still at stake.

10 A similar position is upheld in Brandon (1996) and Michod (1981).

physical case, because fitness can only be locally defined, its relevant parameters being determined by the environment considered.11 And, even worse, those parameters are likely to change without change of environment since many cases of selection are frequency dependent. Admittedly, over three decades, after Maynard-Smith (1982), we have developed a powerful mathematical tool to build models in cases in which selection is frequency dependent, e.g., the value of a trait in an individual depends on what other individuals are and do: this is evolutionary game theory, which can provide models in which ordinary population genetics fails because it treats fitness as a property of individuals and hence cannot forge models when fitness depends on frequency. The status of those models, however, is the same as that of the classical models of population genetics. Maynard-Smith (1982) insisted on the fact that one has to investigate the strategy set before applying any game theoretical model to empirical cases, which means that by itself, game theoretical theorems and proofs, no matter how illuminating, do not have empirical content. So, in a way, evolution contains both statements stronger than physical laws (since they are purely mathematical models) and statements nomothetically weaker such as those derived from the PNS by its empirical instantiation. Rather than a law, the PNS in the end proves to be an explanatory schema, providing ways of explaining and building models through its more or less empirical instantiations. The least empirically instantiated are models of population genetics; at the most empirically instantiated level, we have law-like generalizations, such as paleontological ones. In a way, it is a matter of convention whether or not to call them "laws": the point is just to determine their epistemo-logical nature.

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