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Aggregate, composed, and evolved systems: Reductionistic heuristics as means to more holistic theories

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Abstract

Richard Levins’ distinction between aggregate, composed and evolved systems acquires new significance as we recognize the importance of mechanistic explanation. Criteria for aggregativity provide limiting cases for absence of organization, so through their failure, can provide rich detectors for organizational properties. I explore the use of failures of aggregativity for the analysis of mechanistic systems in diverse contexts. Aggregativity appears theoretically desireable, but we are easily fooled. It may be exaggerated through approximation, conditions of derivation, and extrapolating from some conditions of decomposition illegtimately to others. Evolved systems particularly may require analyses under alternative complementary decompositions. Exploring these conditions helps us to better understand the strengths and limits of reductionistic methods.

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Notes

  1. Kauffman arrived at Chicago as an assistant professor of theoretical biology in Fall 1969, when we both attended Levins’ weekly seminar course on Complexity. This is described with other events of that period in my appreciation of Levins (Wimsatt 2001).

  2. To biologists, a naturalist is one who studies whole organisms in the wild.

  3. This vision led Russell to speak of theoretical terms as nothing but “logical fictions” or objects as analyzable into “collections of actual and possible sense-data”, or led Quine to espouse his preference for a “desert ontology.” Eliminativist reductionists like Patricia and Paul Churchland have interacted with and clearly been influenced by scientists like Francis Crick.

  4. I question the assumed meaning and justification of such “in principle” claims in 1976b.

  5. John Maynard Smith told me (personal conversation Fall 1970) that he spent much of his war years as an aeronautical engineer picking up parts of crashed German aircraft to try to determine whether differences in where they located components or their detailed design were irrelevant contingencies or design advantages.

  6. This perspective is implicit in Herbert Simon’s writings on heuristics (1962, 1996) but is made explicit in Tversky and Kahnman (1974), and in my work on heuristics (1980b, 1985, 2007).

  7. I date this from the Complexity seminar that met weekly evenings at the Levins house in the fall of 1969, and led naturally to the philosophy of biology evenings that invigorated Conceptual Foundations of Science in the early years. For 37 years of friendship and inspiration, I thank you Dick. For your commitment and Rosario’s to social concerns and political involvement, humane example, polymorphic aphorisms, wry humor, and lovely insights, we must all thank you. For an appreciation of Levins from this period, see Wimsatt (2001).

  8. Wimsatt (1976a, b, 1979). See also Sarkar (1992), Waters (1990) and Bechtel and Richardson (1992). Some characterized by Waters as anti-reductionists are better viewed as opposing the standard philosophical analysis of reduction (I don’t cede ownership of the term to philosophers). What most scientists in the “compositional” sciences view as reductionism is a species of explanatory mechanistic materialism that may not require laws or theories as those terms are understood by philosophers (see “particularistic mechanism” in Wimsatt 1992). Glennan (1996) provides a complementary account of the relation between causation and mechanistic explanation.

  9. This proposal—by Stuart Glennan—is worth more elaboration than it will find here.

  10. There is a curious mis-match here: such philosophers also talk about “supervenience”—a relation between a system property and lower-level realizations of that property in which there is a many–one relationship from micro-states to that higher level property, using micro-state variables that are solely intra-systemic. Now called “narrow supervenience”, this is contrasted with “wide” supervenience (Haugeland 1999) where the many–one mappings depend also on the context of the system (e.g. Rosenberg (1978) on fitness). Philosophers of mind often see “wide supervenience” as irrelevant to their problems. This is a mistake. Reductionistic biases (Wimsatt 1980b) often lead us to think that narrow supervenience will do when “wide supervenience” is required. Thus we slip into regarding fitness as a property of organisms (or even of genes), rather than as a relation between organism and environment. Moss (1992) catalogues ways in which we attribute properties to genes that are properly regarded as characteristics of the cellular milieu or larger entities. McClamrock (1995) argues that our Cartesian heritage has mislead us—seeing consciousness as an organismally or computationally “inner” property, rather than a fundamentally relational set of properties of a developed, socialized, embodied brain (Wimsatt 1976a gives an early statement of this view). But there are problems with supervenience (as defined) in science: Levin’s heuristic analogue, the “sufficient parameter” better fits all claimed cases, is more operationally usable, and better fits with actual scientific practice than supervenience (Wimsatt 1981a, 1994).

  11. As urged by Sarkar (1996) this corrects earlier analyses (1976a, b), where I called an account reductionistic if there were a mechanism at any level or combination of them which explained the phenomena—even if it included mechanisms at a higher level or external to the system in question. In drawing the distinction, I would now require explicitly relativising an account to two (or more) reference levels: (1) a bottom level—the lowest level at which specific parts of a mechanism must be invoked to explain the phenomena (so an explanation of “position effect” requires characterizing an operon as a genetic control structure and how it works, but not the atomic physics accounting for the relevant electron orbitals which yield the binding which occurs.) (2) a top level—drawing the system boundaries broadly enough so that all relevant parts of the mechanisms involved are included. [Still broader things may sometimes be required, but taken for granted, as features of solar and planetary dynamics may be crucial to evolutionary processes on a variety of different time scales.] This “multi-level reductionistic analysis” picks out the appropriate levels for objects, processes, and phenomena, and articulates and explicates their relations to complete the explanatory task with no further mystery. It is to be distinguished from apocalyptic reductionism both through the recognition of relevant dynamics at multiple levels and at the same time the robustness associated with phenomena at levels that renders lots of lower-level detail unnecessary and irrelevant. Wagner’s new (2005) is full of richly described biological examples of these kinds of multi-level cross-cutting relationships.

  12. These are relevant and important criteria, but may not be completely independent, and thus fail to be separately necessary (in all combinations). They seem sufficient, but I'd welcome sensible additions: each gives new handles on tough cases or special circumstances. This pragmatism, first urged upon me by Dick Levins, makes sense—classification of a property as aggregative often emerges as highly conditional and qualified, with little or no foundational or architectonic significance. But it may have lots of practical import: by choosing decompositions of the system to maximize their fit, these criteria can help us choose good boundaries around objects and parts of objects, acting as a tool of discovery in theory formulation and construction. See below.

  13. Some philosophers distinguish synthetic identities from realizations or instanciations. It makes no difference here, but see my 1994, note 30, pp. 228–229.

  14. Addition, multiplication and other operations (e.g., logical disjunction) could be appropriate in different contexts. The context of the parts properties, the system property, the question being asked, the purposes of the investigation, and the relevant applicable theories can all play important roles in such judgements.

  15. Sergio Martinez (1992) points out that in the 17th century something very much like aggregativity was used, together with robustness, as a criterion for natural kinds.

  16. These approximations are endemic in the formal sciences, and in virtually all attempts to build mathematical models of phenomena. Ramsey (1990) and Sarkar (1998) both have nice discussions of the role of approximations in theory construction and justification.

  17. But Levin’s “fine grained” adaptive function—unlike expected utility—is what would be called the utility of a mixture (of environments). Expected utility is glossed as the utility of a lottery among (exclusive) alternatives with given probabilities, but the above definitions of fitness (and of mean Darwinian fitness) are the utilities of mixed ensembles of sub-environments in proportions given by the probabilities. [Similarly for the mixed populations of different genotypes in th common definitions of mean Darwinian fitness.] As von Neumann and Morgenstern (1947, p. 18, note 1) suggest, it is like comparing the utility of a lottery in which you get coffee or cream with probabilities p and 1−p, to the utility of getting (for sure) a mixture of coffee and cream in proportions p and 1−p. These are not the same. Thus Levins’ “adaptive function” is an empirical hypothesis about how to model certain biological situations, whereas the definition of expected utility is an analytical (though useful) exercise in probability theory.

  18. Were the p i’s integers rather than probabilities, this would be the multiplicative law.

  19. This last qualifier, and similar phrases are dead giveaways that approximations are being used—commonly to treat non-linear relationships as linear. They are warning flags that all bets are off regarding the aggregativity of described relationships. The models are aggregative all right, but the phenomena aren’t.

  20. Actually, the derivations of both functions implicitly assume that the order of the sub-environments doesn't matter, but it is clearer for the coarse-grained adaptive function. See Strobeck, (1975).

  21. In length, though not in volume. The actual relationships of heat transfer are more complicated than might be suggested by the simplicity of the length relations here. For example, the fly moves far faster than its smaller size would suggest, perhaps a tenth as fast as the buffalo, and it, but not the buffalo, would carry a significant boundary layer with it, unless the buffalo wetted itself. And the complications go on

  22. See discussions of perceptual grain in predation and “contest” vs. “scramble” competition in Wimsatt 1980a.

  23. Deviation from multiplicative proportions in multi-locus systems is called “linkage disequilibrium” (See Crow and Kimura 1970, or any population genetics text.) “Linkage equilibrium” values are equilibrial because they are a state of highest entropy—a maximally mixed state. “Linkage disequilibrium” is misnamed because it is a product of both linkage and gametic packaging. In 1981b, I discuss this and similar cases (pp. 152–164), which provide the basis for higher level “segregation analogues” defining higher levels of genetic organization. Systems capable of linkage disequilibrium have more complicated dynamics than one always in linkage equilibrium. Here, as elsewhere, a system which behaves aggregatively is simpler. Complexities involved in going from relative locations of genes along the chromosome to their “linkage distance”—which further qualify the remarks here—are discussed in Wimsatt 1992.

  24. This complexity arises only for multi-locus genotypes, and is the single largest difference between single and multi-locus theory. Moreover, under special circumstances linkage can sometimes be ignored, and multi-locus problems can be treated as an aggregate of single-locus problems (at or near linkage equilibrium, and when selection forces, migration rates, or other things which could displace the population significantly are kept small). This illustrates again situations of conditional and approximate aggregativity, or “quasi-independence” (Lewontin 1978).

  25. We should use two different locutions for the effects of sufficiently close location in the same chromosome (0 > r > 0.5) and chromosomal association in the gametes. I propose chromosomal and gametic linkage, though the latter term misleadingly suggests that the association is solely a product of gametic packaging. It is a product of this packaging in the context of a haploid gamete/diploid genotype/two-sex system. If for example, there were n sexes each contributing a monoploid gamete to make an n-ploid genotype, with arbitrary recombination and independent assortment among the n homologous chromosomes of each type, then (0 > r > (n − 1)/n)), and the asymptotic equilibrium value, now (n − 1)/n), would be approached successively faster for larger n. It would behave more like the 1-generation equilibration of the single locus case as n became large enough for the individual n-adic genotype to be potentially a good sample of the chromosomal and gametic variability in the population.

  26. Signs in the four squares indicate where recombination contributes to (+) or retards (−) approach to equilibrium, if starting with AABB and aabb homozygous genotypes. Starting with double heterozygotes AaBb would reverse the signs. These two pairs of squares are always opposite in sign, except at equilibrium.

  27. In the more general quantitative version of this diagram, for arbitrary gametic and recombination frequencies, gametic frequencies p, q, s, and t (of gametes A- -B, A- - b, a- -B, and a- -b) are entered along row and column margins, and cross-multiplied to give zygotic frequencies. Then r of those in the squares along the diagonal undergo recombination.)

  28. It is not clear whether the squares that produce heterozygotes or those that produce homozygotes should be the analogous ones. (Both occur in equal frequency.) The segregants—homozygotes—are the new combinations produced in a cross among heterozygotes, and thus analogous to the new combinations one can find along the reverse diagonal in the two locus case. But it is the heterozygotes which involve dissimilar combinations and (thus) occur along the reverse diagonal. The structural differences between alternative alleles and alternative loci prevent formulation of an exactly analogous case.

  29. Mike Wade suggested the happy contrast pair, endogenetics and exogenetics, for what I had been calling internal- and external- genetics, reflecting what are normally called genetics and population structure. The first involves structural features affecting what kinds of gametes and gametic combinations are produced by matings of given individual genotypes, while the second involves structural factors (including geographical, physical, biological and behavioral) that affect what array of matings are produced from a specified distribution of organisms. Exogenetics and endogenetics can play equally powerful roles in producing the genotypes resulting as zygotes in the next generation, and both are manipulable by evolutionary forces. It is an open question which aspects of either are stabler or more malleable.

  30. This is the story emerging from classical genetics. Molecular genetics complicates it with new levels of modularity—intron, exon, and transposon—in between base pair and codon and the whole gene, and mechanisms which explain deletion, insertion, inversion, duplication, and transposition. These don’t seriously change the picture, but further demonstrate that various design processes exist for increasing the apparent aggregativity in meiosis. The design of mitosis and meiosis for reliable transmission and assortment of hereditary factors is one of the most elegant adaptations in the history of evolution, and their functional analyses through the work of Roux, Weismann, Boveri (1902), Sutton, and others is a high point in the history of biology. The editing and rearrangement of the genome in somatic lineages to mediate gene expression in development make this point in yet another way: the properties of the genome are not an aggregate of the properties of its parts. The arrangement of the genes in the genome DO matter for development. (See Shapiro 1992, for more details.)

  31. Figure 3 used 2-strand models of recombination to emphasize the parallels between recombination and independent assortment in preserving larger structures. More realistic models from classical cytogenetics (ca. 1928–1934), use 4-strand models of mechanisms (and failures) of normal recombination to explain the kinds of chromosomal rearrangements taken as givens by population geneticists in describing species differences and giving cytological explanations of inversions, some cases of meiotic drive, and other mutations of large fitness effect.

  32. All other known aggregative properties are fundamental physical properties that are conserved. It is tempting to refer violation of conservation (in this case of mass) to QS or CI, but it fits neither. CI presupposes mass conservation, but doesn’t address the issue. QS envisions adding or subtracting, say mass, and having the quantity scaled up or down appropriately, not ignoring (or refusing to ignore) some of the products of a transformation. Part of the problem here is that though invariance under transformations are required for some of the criteria, the analysis is not addressed directly towards evaluating whether processes or changes are aggregative. This could suggest the need for another criterion, or alternatively, as Paul Humphreys (2006) does, adopting a different kind of analysis for temporal emergence such as some have sought for evolution.

  33. Sober's widely advertised objections to the additivity criterion(1981, 1985) have never been compelling. (1) He does not address how the criterion is actually used by scientists—who do so in ways not subject to his criticisms (Griesemer and Wade 1988). (2) He has also seriously botched the criticisms—e.g., offering as a “counterexample” a case which only tries to meet one of two necessary conditions (see discussion on pp. 147–152 of Wimsatt 1981b), and fails to try his “counterexamples” on his own analysis, which (as Lloyd 1989, 1994 points out) fails in exactly the same cases! I don’t actually think his analysis is wrong-headed, though the “additivity” approach captures central features of the theory which his does not. His account provides correct intuitions about the level at which causes act if there is group selection, but—unlike the “additivity” account—gives no operational criteria for applying it. Brandon’s (1982) complaint is more interesting: if the units of selection debate is taken to be about individuating the relevant genetic units for selection or evolution, it neglects the fact that selection generally acts directly on phenotypes (or “interactors”) rather than genotypes (or “replicators”), except insofar as the material entities picked out as genotypes are also interactors (which sometimes occurs.) We saw that additive models didn’t make fitness an aggregative property of genic fitnesses. Those complexities are reflections of Brandon’s point. See also Sarkar (1994) for a more general and compelling critique of additivity—which still, however, does not vitiate the points of Griesemer and Wade (1988)—nor the usefulness of the additivity approach in most situations.

  34. I know of no close precedent for Lewontin’s table, thought there have been implicit recognitions of the relations between dimensionality and the combinatorial properties of genetics from the beginning. Awareness of dimensionality in the inheritance of traits properly goes back to Mendel in 1866, when he points out that (for two segregating factors per locus, and with simple dominance) the number of gametes should scale as 2n, the number of distinguishable phenotypes as 2n, and the number of genotypes (treating Aa and identical with aA) as 3n. In Sutton’s famous 1903 paper urging that Mendel’s factors are loced on chromosomes, he shows a table of how the number of possible haploid and diploid combinations increases with the numb, making it plausible that the combinatorial explosion of chromosomal combinations had the right kinds of properties to explain the enormous variety of organic life.

  35. My table differs from Lewontin’s in arrangement, in the inclusion of additional values, and in correction of a minor error. The conception of it is unchanged from the original, however.

  36. This does not of course imply that mating or attraction is a random affair, but only that there is no statistical correlation between who mates with who detectable at the genotypic level of description.

  37. In a parallel way, Taylor series expansion of a function at a point can “linearize” it in the immediate neighborhood, but one shouldn’t infer from that that all continuous and differentiable functions are linear! This is an analogous error—to mistake an approximation that is only “locally” valid for one that is globally sound.

  38. In 1976b, I discuss the purported meaning and testability of these in principle claims and show that in empirical science (as opposed to in mathematics) they are better seen as corollaries of identity (or localization) claims than as claims to knowledge we cannot have.

  39. The others: (1) heuristics don’t guarantee results, (2) are cost-effective, and (3) break down systematically—not at random, so one can predict when they will fail, or or recognize the “footprint” of their application. (4) Heuristics are purpose-relative—normally designed for a given purpose, which they can be expected to do well, and less well when applied in other contexts. (5) Heuristics tend to come in families of related tools specialized for slightly different applications. These conditions and their consequences are reviewed in Wimsatt 2007 (appendix).

  40. See Allen’s (1979) biography of Morgan, Mainschein’s (1991) study of Wilson, Conklin, Morgan, and Harrison, Darden (1992) on early theory construction in genetics, and Wimsatt (1987, 1992) on the early history of linkage mapping.

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Correspondence to William C. Wimsatt.

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The immediate stimulus for this analysis was Levins’ germinal essay “Complexity” (1973, from 1971 draft) and his distinction (1970) between aggregate, engineering, and evolved systems, which also influenced my 1974. The analysis of aggregativity began as class handouts in the Philosophy of Social Science and Philosophy of Biology courses that Levins and I co-taught at Chicago in the Winter and Fall quarters of 1971, later written up in my 1986b. I pointed Bechtel and Richardson to Levins’ work in the early 1970’s. They discuss this particular distinction on pages 25–26 of their superb and insufficiently appreciated (1992). Some properties of aggregativity are also noted by Nagel in his (1961) and classic, “Wholes, Sums and Organic Unities”—though we diverged in what we made of them. Stuart Glennan, Peter Taylor and Bill Bechtel gave especially useful comments on prior versions.

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Wimsatt, W.C. Aggregate, composed, and evolved systems: Reductionistic heuristics as means to more holistic theories. Biol Philos 21, 667–702 (2006). https://doi.org/10.1007/s10539-006-9059-1

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