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The philosophical literature is heavy with discussions of the logical structure of various proposed schema of functional explanation (most of which are modifications of Hempel's schema [7]) but it is very light on detailed analysis of the way in which these schema actually work or the way in which they apply to the instances in which functional explanations are used by scientists. These papers use statements by scientists ascribing particular functions to particular traits, along with intuitions about the way in which ‘function’ is used in ordinary language, to ascertain the referents of the term and thus to determine the class of uses against which any schema should be tested; but such examples only show whether the schema under discussion refer to the same things as those the scientists’ refer to; they do not show whether the logical structure of the schema really captures the logical structure underlying the scientists’ use.

The rarity of Malthusian overexploitation has long puzzled naturalists. Nicholson has given an important proximate explanation of how population size is limited, but his discussion of density governing traits does not tackle the ultimate question of how populations acquired these traits which prevent overexploitation. This paper shows that Darwinian theory can explain the evolution of density governing limitation mechanisms which prevent overexploitation; they are a predictable by-product of selection for adaptation to the early growth phase of a population with recurrent population crashes. In this situation Darwinian selection, instead of maximizing the number of offspring of the ultimately favored allele, maximizes the number of its descendants in the comparable portion of the next growth cycle.

Since parts of future biomathematics which involve further development along directions already predominant can be extrapolated from the other papers in the volume, the purpose of this paper is to investigate less obvious, and therefore more speculative, directions. In particular, I intend to show reason to suspect that the laws of biology are of a different mathematical form than the laws of physics and that, therefore, the mathematical models of the future in biology will be radically different from the models used in physics. I will primarily concentrate on casting doubt on the ultimate usefulness of many differential equations models by examining the extent to which the mathematical assumptions underlying these models reflect biological reality. Since these mathematical assumptions seem to be seriously discordant with important parts of biological reality, this type of mathematical model should ultimately be replaced by essentially different types of mathematical models.

In what are almost asides Ghiselin (1974, 1981), Hull (1976), Holsinger (1984), and Williams (1985) have all claimed not only that species are individuals but that populations are individuals. This larger claim has been lost in the glare of dispute over whether species are individuals. Part of the reason for this neglect is that the term ‘population’, although central to population biology, is considerably more amorphous than the term ‘species’ and it is thus considerably more difficult to dispute any claims about it. But if the individuality of species is important because of what it tells us about the way they function in biological laws (as Hull (1976, 1981, 1987) assserts), then the individuality of populations should also be understood so that we can understand how they function in biological laws.

Professionally unemployed Ph.D.'s who wish to maintain active ties to the academic community should be encouraged to apply for an appointment as Adjunct Professor to an educational institution in the city in which they live. Adjunct Professor would be an unsalaried position with library privileges but no departmental duties. Since it is important that the Adjunct Professor be accepted as the professional equal of his departmental colleagues (rather than as a second class citizen)* his application should contain the same supporting information as an application for a regular positioni and it should be rejected unless he appears to be of professional caliber equal to present members of the department. (It should not* however, be judged on the basis of whether he would be offered a job in that department in the present competitive situation. Thus the department would have made no commitment as to his suitability for any job that might open up in the department.) Adjunct appointments should be for a period of 3 to 5 years and should be renewed if the Adjunct Professor has maintained his standing as a research scholar.

It is clear from the above discussion that if I had wished to do so I could have truthfully presented every paper as either testing a prediction, presenting evidence needed in the test of a prediction, or presentin a D-N explanation. (I would not have been able to do this if I had not been sufficiently familiar with the evolutionary literature to recognize what hypotheses were at stake in several of the papers; even when the authors mention the hypotheses they frequently do so only in enough detail to put their paper in context for the knowledgeable biologist.) Since these biologists are working in a period of normal science under the paradigm of the modern synthetic theory of evolution, none of these papers is presented as a test of the modern synthetic theory; but since this theory was used in the derivation of each prediction, each one is a test of it as well as of the hypothesis mentioned. Thus, once we learn to recognize the predictions beneath their cloaks of invisibility, we discover that prediction testing is not, as philosophers have claimed, at best peripheral to evolutionary biology; it is central to evolutionary biology.

This paper shows that the theory of natural selection is not tautologous and that the belief that it is stems from formulations of the theory which attempt to defy logical impossibility by defining all the words used in the theory. The correct method is to treat some of them as primitives characterized by axioms. The axiomatization used to resolve this controversy also resolves controversies about the units of evolution and the target of selection. The concatenation of the axiomatization, revealing the fundamental structure of the theory, and the controversies arising in the preaxiomatic theory gives insight into the structure underlying controversies about other preaxiomatic theories.

This is a collection of essays written by Levins and Lewontin over the years for a variety of audiences. Their purpose in collecting these essays is to provide an alternative view of the nature of knowledge to those biologists who have become uneasy with the mechanistic reductionistic view which is inherent in Western science. They wish to show the biologist "another active and productive intellectual tradition, the dialectical . . ." (p. vi). About a third of the book consists of general essays on evolution; the great majority of this portion was written for an Italian encyclopedia. About a third consists of Marxist analyses of the influence of society on science and of science on society. The final third contains serious discussions of insights derived from deep understanding of the mathematical form of particular analyses plus an attempt at a serious presentation of dialectics. Only three of the 14 essays were originally published in scholarly journals. These essays range from one giving a superb, insightful analysis of IQ and heredity to encyclopedia articles giving generally elementary discussions. They were not written for a single audience, nor for a single purpose; this review will focus on their significance for the readers of Evolution with respect to the purpose of convincing the reader that dialectics offers a potentially useful alternative to their present modes of thought. Intuitively speaking, the authors' strongest argument is their claim that their important books (Levins, 1968; Lewontin, 1974) were written from a consciously dialectical perspective. But, from the fact that both Levins and Lewontin are Marxists and have made important scientific contributions, one cannot conclude that their Marxism was a cause of their scientific contributions. It is a significant flaw in this book that the authors make no attempt to trace in detail the relationship between Marxist dialectics and any particular scientific contribution. Instead, Levins and Lewontin discuss (repeatedly, though not in great depth) the different sets of biases engendered by Marxism and Cartesianism. The Cartesian biases (reductionism, independent variables, etc.) are common among Western scientists because of the Western Cartesian world view. Marxism leads to a different set of biases (holism, interdependent variables, etc.). This does indeed make Marxism look promising; many problems of evolutionary biology are intractable because the phenomena cannot be reduced to a simple set of interactions among elements at a