Notes

Instituto de Investigaciones Filosoficas, CU, UNAM, rgwinther@gmail.com

None of the biologists I explore had or have any deep training or expertise in social science. I will therefore remain vague about which theories of which exact social sciences (e.g., economics, anthropology, sociology, etc.) these biologists were attempting to unify with biology. This vagueness does not, however, affect my general argument that there are radically different manners of bringing together biology and social sciences.

I thank one of the reviewers and the editor for challenging me on the very desirability of any kind of biological social science.

He does, however, say: 'My study is a continuation of Kant's project of explaining how objectivity is possible' (Hacking 2002, 181).

The categories 'relativist' and 'rationalist' may not be particularly informative here, however.

On the trade-offs present in modeling, see Levins 1966; 1968.

Greg Mitman, a historian of biology, published a thought-provoking book on the history of the University of Chicago ecologists, which includes extensive analysis of the liberal and social-democratic political proclivities of this group. Mitman paints a detailed historical and sociological context, but provides little by way of conceptual or philosophical analysis (Mitman 1992). While I have learned much from Mitman's book, my project is different.

This definition is found in a paper presented at an important symposium gathering Allee, Emerson, Thomas Park, and the famous sociologist Robert Park, among others (Redfield 1942a). See footnote 13 below.

An epiorganism is a society of organisms (Gerard 1940, 340)

That is, aggregativity = 'the whole is equal to the sum of its parts', whereas non-aggregativity = 'the whole is greater (or less?) than the sum of its parts'. See Wimsatt 1986.

That is, units at lower levels Ni–2, Ni–3, … Ni–n do not have any effect on the whole (org) at level Ni. Here Ni denotes the focal level, and levels are individuated, from lowest to highest, as N0 (i.e., Ni–n), N1, N2, etc. Gerard (1940, 342) suggests this presentation.

And it was for this latter wish that Simpson (1941) and Novikoff (1945) accused him of being a totalitarian.

In their classic definitions: individual development and species evolutionary change, respectively.

These are: '(1) A definite structure and composition is constant for any moment of time, but fluctuates with age. (2) The population is ontogenetic. It exhibits (as does an organism) growth, differentiation and division of labor, maintenance, senescence, and death. (3) The population has a heredity. (4) The population is integrated by both genetic and ecologic factors that operate as interdependent mechanisms. (5) Like the organism, the population is a unit that meets the impact of its environment. This is a reciprocal phenomenon, since the population is altered as a consequence of this impact, and, in time, it alters its effective environment' (Allee et al. 1949, 264). They did, admittedly, point to some 'dissimilarities' between organisms and populations immediately after presenting this list.

Compare the claims about mathematical theory as the link among many disciplines (Boyd & Richerson 1985), and as the frame of thought for generating explanations (Cavalli-Sforza & Feldman 1981). In these radically different ways of viewing unification, we can also see the strong contrast between formal and compositional styles.

For a list of which author had the key responsibility for which chapter, see p. viii, where Allee is also thanked by the 'junior authors' for his 'leadership'. Some of Allee's key books and papers are Allee 1931; 1940; 1942; 1943; Allee & Park 1939.

Which, in Gerard's language, would be unit and org benefits. Individual/unit and group/org are recursive categories.

E.g., Michael Wade was Thomas Park's student and, upon finishing his dissertation, himself became a member of the University of Chicago faculty; Charles Goodnight was Wade's student; see Wade 1992; Wade & Goodnight 1998; Lloyd 2000.

On the important difference between "units" and "levels" of selection, see Brandon 1982; Lloyd 1988, 2000; Laubichler 2003.

It is interesting to note that Emerson cites Fisher, perhaps the most mathematically gifted of the three founders of neo-Darwinian evolutionary genetics (Fisher, Sewall Wright, and J.B.S. Haldane). There is a general point to be made here. Even though the authors of Allee et al. 1949 availed themselves of evolutionary theory, the text and most of their own work (except for Park, see below) was clearly done within a compositional style framework and relied relatively little, if at all, on formal methods. They approached their work through the compositional, rather than the formal, style.

See also: society 'as a unit', p. 848; 'individual atoms', p. 867; 'community as individuals' versus 'community as a whole', p. 956.

As one reviewer pointed out to me, Talcott Parsons also employed the compositional style in his sociology. I know significantly less about Parsons and I understand that many of his functionalist views are problematic in a number of respects, including the social oppression that they can be interpreted as endorsing (as sociologist Elihu Gerson has informed me, Parsons' views can be summarized as 'a place for everyone and everyone in their place'). Here I simply point to a context that could be further developed in light of this paper.

And the two are not distinct. Levins has developed mathematical methods to assess qualitative properties, as also described in Levins and Lewontin 1985.

i There are clearly many ways of mathematizing and formalizing (i.e., formal methodology). In my work on formal biology, I have focused on the formalization of evolutionary genetics (e.g., Winther 2003; 2006c). The mathematics present in evolutionary genetics involves classic techniques from algebra and calculus. Increasingly, simulations of various sorts have also become important. And statistical techniques are crucial for the evaluation of theory in light of the data. Given this diversity of mathematical methods even within formal biology, we now seem to arrive at a problem regarding the clarity of the formal/compositional biology distinction. Undoubtedly, a philosophical investigation of other areas, even of those that are 'compositional', such as evolutionary developmental biology, will show both 1st that many different mathematical (formal) techniques are used in biology and 2nd that the compositional style can, on occasion, employ methods from the formal style. See, for example, mathematical work on gene regulation and morphological development by a variety of authors interested in evolutionary developmental biology (Arnone & Davidson 1997; Davidson 2001; Goodwin 1989, 1994; Kauffman 1993; Salazar-Ciudad et al. 2001; Salazar-Ciudad & Jernvall 2004). But, in light of this, let me bolster my distinction between formal and compositional biology by noting, in response to (2), that many compositional biological sciences rely primarily on non-mathematical techniques and representations. On this point, the philosopher of biology Kenneth Schaffner insightfully states: 'In addition to the extensive variation, which defeats simple axiomatization of biomedical theories, the axiomatizations that are formulated are usually in qualitative biological (e.g., cell) and chemical (e.g., DNA) terms and thus do not facilitate deductive mathematical elaboration' (Schaffner 1993, 117; see also Schaffner 1980). Furthermore, in response to (1), there certainly is a vertiginously large variety of mathematical methods used in biology, but formal biology focuses on those which most resemble the kind of gold-standard we have inherited from theoretical physics: closed form analytical equations. Many of the simple and classic equations of evolutionary genetics are of this form. Theoretical structure in formal biology is organized around analytical equations. Many of the other formal presentations of knowledge in other domains of biology (including the 'compositional' domain) lack this compactness and, perhaps more importantly, breadth of scope of application (one form of universality). Another area in which compositional studies employ formal methods is formal mereology (e.g., Simons 1987; Smith 1982; 1996; see also Simon 1996). Mereology is the study of part-whole relations. Formal logic has recently been applied, in creative ways, by these and other authors, to elucidate part-whole relations. But these investigations stem much more from the point of view of philosophy and formal computer science, rather than of either theoretical or experimental work in biology. Furthermore, this work has focused primarily on spatio-temporal properties of the part-whole relation and is not particularly close to biological practice. On the other hand, a set of philosophical analyses significantly closer to the actual practice of compositional biology revolve around the organization, dispositions and functions of parts (e.g., Kauffman 1971; Wimsatt 1974; 1986; 1994; 1997; Cummins 1975; 1983; Levins & Lewontin 1975; see also Haugeland 1978; 1998) and around the concept of mechanism (e.g., Wimsatt 1976, Bechtel & Richardson 1993; Glennan 1996; 2002; Machamer et al. 2000; Craver 2001; Winther 2006a; see also Schaffner 1980; 1993). It is in this literature that I believe we will be able to get to the theoretical core of compositional biology. Here is a sketch of that core. The fundamental concern in compositional biology is articulating the various properties, relations and processes of biological parts and wholes using whichever methodology may be available or useful. Mathematical methods and derivations, which are a kind of deductive or subsumptive method, can indeed be used. Another form of deductive (-like) explanation - reduction - can also be employed when the theories/theoretical perspectives applying to the parts and wholes are distinct (e.g., Schaffner 1993; Sarkar 1998). But even in the case of reduction (and certainly in the case where we stay within the same theory/theoretical perspective), we ultimately desire to characterize a compositional relation (which could, but need not, include material causal relations), and not, in particular, abstraction or formal relations (or hierarchies). We seek to understand, for example, what kind of function a particular organization of parts has within a particular whole. So although a variety of explanatory strategies are consistent with that characterization (including, on occasion, but relatively rarely in compositional biology, mathematical methods), presenting the compositional relation is, in the final analysis, the aim. And, at any rate, biologists tend to adopt properties, concepts, and strategies close to that relation, such as mechanisms and part-dispositions, which themselves can themselves be rather abstract (but almost never mathematical) claims. Theoretical structure in compositional biology is organized around the part-whole relation and its various aspects. As the philosopher of biology, John Beattty, put it to me colorfully: in compositional biology, the goal is to draw (causal) arrows rather than write equal signs. This is itself a heuristic rule and should not be taken too literally. While distinguishing these two styles from each other (and from other styles, such as narrative biology) is very much work in progress, I do believe that the formal/compositional biology distinction stands up to a fair amount of scrutiny even if there are areas of intertwinement and even if the distinction is difficult to articulate precisely (see also Winther 2003; 2006a, b). I thank one of the reviewers for asking me to be much clearer about both the formal/compositional distinction and 'formal methods.'

ii I discuss this book explicitly and in detail because it is the main (and only) product the Chicago Ecology Group wrote as a unit. It is important to mention in this context that the Redfield (ed.) volume was also, in part, a product of the Group. However, this volume consists of papers by individual authors. Robert Redfield was, at the time, professor of Anthropology and Dean of the Division of Social Sciences at the University of Chicago (Redfield 1942a, cover page; Mitman 1992, 151). It is worthwhile citing extensively some passages from his introduction to the volume in order to provide an idea of the explicit compositional biological social science synthesis that was attempted (relevant page indicated in brackets): 'This symposium had a double origin. Representatives of the Division of the Social Sciences planned a program of papers having to do with some of the more comprehensive and underlying aspects of society. The program was to emphasize three borderland fields of recent research interest - borderland from the point of view of the student of human society. In the first place there was the disposition in recent years for students of primitive society on the one hand and of modern society on the other to study their subjects in common terms: the significant event here was the rapprochement of anthropology and sociology. In the second place recent investigations of the social behavior of monkeys and apes had made a fresh contribution to the understanding of the origins of human society. In the third place the rapidly developing work of students of mammalian and bird societies had aroused the interests of sociologists and anthropologists. …The essential idea was to present human society as an example within a class, societies, and to have a look at some of the resemblances and differences among examples of the class. [1] [2] In the meantime biologists at the University were making ready a program of papers concerned with the ways in which parts are organized into wholes in life forms. Here again there was a wish to represent new frontiers of research, and to consider special problems in wider contexts. …There was… a disposition to recognize that the integration of parts into wholes within an organism, and the integration of parts into wholes within a population or social aggregation, were not entirely separate problems, but that they could be considered in relation to each other, and together. … The social scientists then accepted with enthusiasm a suggestion from the biologists that the two programs be consolidated into a single symposium with the present title. [2] [5] …What these papers seem to be saying, in most general terms, is this: The organism and the society are not merely analogues; they are varieties of something more general: the disposition, in many places in the history of life, for entities to undergo such modification of function and such adjustment to other similar entities as result in the development and persistence of larger entities inclusive of the smaller [5]' (Redfield 1942b).

iii It is important to note that their famous sociology textbook (Park & Burgess 1921, 1st edition) appeared nearly three decades before Allee et al. 1949. Furthermore, while these scholars were all at Chicago, and while R.E. Park contributed to the 1942 Redfield volume, it is not clear how strong the link between Chicago Sociology and Ecology actually was (e.g., Mitman 1992 barely mentions R.E. Park; in one of two places where he is discussed, Mitman, p. 92, notes that 'despite Park's ecological interests and his close proximity to the zoology faculty [physical or causal?], he rarely cited Allee's work' – Park did, however, cite Child's work, also at Chicago, but at least a generation older than many in the Chicago Ecology Group and not a member of the Group). Thus, this link, for which I do not have particularly strong evidence, has to be investigated further. While a causal and historical link remains to be clearly established, a link in terms of the similarity of the content of the ideas is clearly present. As we shall see, there are some extremely insightful passages on compositionality to be found in the Park and Burgess book. I ask the reader to peruse the current section of my paper more for the ideas themselves than for a clearly integrated historical narrative linking Chicago Sociology and Ecology. I thank one reviewer and the editor for pointing out this problem to me.