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5. The Theory of the Instrument
So far, I have argued that the mere fact that there was an experimental mechanism that, in combination with the semi-conservative scheme, explained the banding pattern provided grounds for holding the latter to be true, even though some possible alternative interpretations of the data had not (yet) been ruled out, that is, even though there were lots of untested auxiliary assumptions. But this is not quite the full story yet. Clearly, the evidence is only as good as the correlation between the density of the DNA and the position of the bands. As we have seen, it was crucially important that the band of intermediate density was lying exactly between the heavy and light bands. But how good was Meselson’s and Stahl’s analytic technique to resolve molecules according to their density? Obviously, a good calibration of the instrument was of the essence for this experiment. For this reason, I want to briefly examine how this was done.
The theory of ultracentrifugation had been worked out to a large extent by Theodor Svedberg in the 1920s. In his PhD thesis, Matthew Meselson extended the work of Svedberg to experiments with solutions of very high density, such as the CsCl-gradients that they were using. Meselson investigated in particular the conditions under which such a gradient and the macromolecules that float in would reach a point of equilibrium. At equilibrium, the centrifugal force and the buoyant force would balance each other, tending to keep the DNA at that point where its buoyant density equals that of the solution. But there is another force that tends to displace the DNA from this equilibrium: namely molecular diffusion or Brownian motion. Meselson was able to show theoretically that, at equilibrium, these opposing forces would generate a Gaussian distribution of the molecules.
Here is the relationship that Meselson derived:
This equation describes the concentration of a charged polymer such as DNA in a linear density gradient. This is a Gaussian distribution with standard deviation . Meselson also obtained the following expression for the standard deviation:
partial specific volume of the polymer PXn
slope of the density gradient
r distance from rotation axis
The width of the distribution therefore allowed the biologists to calculate the molecular weight of the bands. The physical reason for this is that lighter molecules diffuse more rapidly, therefore they will smear more strongly when they form a band.
Meselson and Stahl checked these theoretical results against their experimental data, using DNA from bacteriophage T4 as a marker. The agreement was quite remarkable11:
This clean result may be viewed as a test that the measuring device worked properly and that the gradient was almost perfectly linear over a certain range. Thus, distances from the center of rotation translates directly into buoyant density. This linear CsCl gradient was an important part of what I have called the experimental mechanism, which is the centerpiece of my IBE-based reconstruction of the experiment. I would like to call the theory of how centrifugation produces a linear gradient from which the density of molecules that float in it can be read off directly the theory of the instrument. The final question to be discussed in this section is how this theory of the instrument was confirmed.
My proposed answer to this last question is that the theory of the instrument was also supported by an IBE-type argument, and that explanation is best understood in the mechanistic sense. Here, the relevant experimental mechanism contains the DNA molecules, the cesium and chloride ions, as well as the water molecules. These entities interact by electrostatic forces and weak chemical bonds (hydrogen bonds). Further, this experimental mechanism involves the centrifuge itself with its rotor and the cell containing the DNA / CsCl solution. Together with physical laws12 (Newton’s laws, Coulomb’s law, and the laws of thermodynamics), this mechanism explains why, under suitable conditions, DNA molecules will reach a sedimentation equilibrium, in which they are distributed in accordance with a Gauss curve where the mean is a linear function of density and the width an inversely linear function of molecular weight, which is what was actually observed. It is this explanatory relation that provided grounds for thinking that the analytic ultracentrifuge is a reliable instrument for determining the density of certain biopolymers. In other words, it’s IBE-turtles all the way down.
6. Van Fraassen’s ‘bad lot’ Argument
In the previous section, I have shown that the IBE approach combined with a mechanistic account of explanation avoids Duhem’s first problem. But we still have Duhem’s second problem to cope with, which is that scientists can never have rational grounds for believing that the available hypotheses exhaust the space of possible hypotheses. There is a more recent version of this argument that pertains directly to IBE, namely Van Fraassen’s ‘bad lot’ objection (Van Fraassen 1989, 142ff.). According to this argument, IBE can perhaps rank a set of hypotheses with regard to their explanatory merits, but it cannot provide grounds for accepting one of them as true. For the best explanation could still be a very bad one; it affords no epistemic distinction to be the best of a bad lot.13
The best way of meeting this objection for the present case study is by focusing on the genesis of the three alternative hypotheses and trying to show that the process of hypothesis construction had a certain propensity to produce a set of alternatives that contain the true one. For this purpose, it is helpful to note that all three schemes of DNA replication had to incorporate some very stiff constraints. Most importantly, the schemes had to explain how DNA molecules with the same nucleotide sequence as an existing molecule could be synthesized. Thus, explanatory considerations were already involved in the construction of hypotheses. This fits nicely with Lipton’s two-stage process, according to which the generation of a number of “live options” of candidate hypotheses is followed by a stringent selection of the “loveliest” one and where explanatory considerations enter at all stages of the research process. The main difference to my account is that I propose to base these explanatory considerations on a mechanistic account of explanation.
This mechanism-based view puts very stringent constraints on what qualifies as a live option. Suitable candidate hypotheses must incorporate a considerable body of knowledge from organic chemistry and molecular biology. In my example, the double helix model was such a constraint. It incorporated a great body of knowledge from organic chemistry, the physical chemistry of colloids, and crystallography. Furthermore, it was already fairly clear at that time that the sequence of bases in DNA was biologically highly significant (see Crick 1958, who could already cite a considerable body of evidence that supported this idea). Therefore, the replication mechanism had to preserve the nucleotide sequence of DNA. The complementarity of base pairing provided a lovely explanation for how a mechanism of DNA synthesis could achieve this. Hence, it was set that either single or double-stranded DNA had to serve as a template for the (then still putative) DNA polymerase. Indeed, all the three major replication mechanisms that were considered as live options during the mid-1950s incorporated this template idea. The great open questions were whether the template was single- or double stranded, and the extent to which the template was conserved in the process. Thus, background knowledge imposed a set of mechanistic constraints on the space of possible solutions to the replication problem. Unless this background knowledge was rotten to the core, the plausible hypotheses that had been proposed were not a bad lot.
Of course, it is not possible to exclude with certainty that the background knowledge that constrained the live options was fundamentally mistaken. But such is the nature of inductive inference: It strongly relies on material assumptions about the domain of induction (Norton 2003) and it is only as reliable as these assumptions are.
I have argued that a mechanistic version of IBE permits a reconstruction of the Meselson-Stahl experiment according to which the latter provided decisive veridical evidence for the semi-conservative hypothesis, while the two alternatives remained without such support. This is pretty close to what crucial experiments were always supposed to do, except that that I am of course not claiming that such an experimental demonstration reaches the apodictic certainty of deduction (as Duhem required, see Section 2). We are in the world of uncertain, inductive inference. As I have already argued elsewhere (Weber 2005), two major accounts of scientific inference – Bayesianism and Mayo’s error-statistical approach – don’t do quite enough to illuminate hypothesis testing in experimental biology. What both accounts lack is a good justification for judgments about evidential likelihoods or error probabilities. In this paper, I have argued that IBE can provide this. In contrast to Lipton’s (2004) account of IBE, I have used a mechanistic account of explanation. An advantage of such an account is that it does justice to actual explanations in molecular biology. Another advantage is that it makes explanation an objective relation between explanans and explanandum14, which means that the evidential relation can also be objective.
I have introduced the notion of an experimental mechanism, which is like the physiological mechanisms discussed by philosophers of biology and neuroscience, except that it may include human manipulations and artificially created entities and activities. This notion allows IBE to be extended to infer hypotheses from experimental data such as the banding patterns observed in an analytic ultracentrifuge.15 Furthermore, IBE can also reconstruct the tests that the scientists did in order to make sure their measurement apparatus functions reliably.
Finally, I have shown that the two predicaments that Duhem identified for crucial experiments (though on the assumption that all inferences would have to be deductive) as well as Van Fraassen’s well-known “bad lot”-objection to IBE can be dissolved in the IBE-based framework that I have used. As regards Duhem’s first problem, the mechanistic variant of IBE allows (fallible) inferences to hypotheses about mechanisms even if there are untested experimental assumptions. Even so, some experimental assumptions were actually tested in this case. Van Fraassen’s “bad lot” problem (which I take to be basically Duhem’s second problem as applied to ampliative instead of deductive inference) can be handled by showing how an extensive body of background knowledge provided a host of stringent material constraints on the candidate hypotheses. Mechanistic-explanatory considerations are involved in the construction of such candidates as well as in the selection of the best one by a crucial experimental test.
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1 See Weber (2005, Chapter 3) for a detailed account of the latter example. Another case, the closure of the oxidative phosphorylation controversy, is treated extensively in Chapters 4 and 5 and in Weber (2002a, b).
2 A similar point can be found in Laudan (1990), though he discusses not crucial experiments but underdetermination of theory by evidence in general.
3 Today, it is known that this is actually what happens. There is a whole class of enzymes called topoisomerases that control the coiling of the DNA molecule. These enzymes can catalyze extremely fast breaking and re-joining of the sugar-phosphate backbone of DNA. Some enzymes can even introduce rotational strain into the molecule under the expenditure of metabolic energy.
4 See Holmes (2001) for an extremely detailed account. As usual, this experiment was preceded by a long and painstaking series of failures and cul-de-sacs. Holmes, who had the complete lab records available and conducted extensive interviews with the two scientists, traces the progress of Meselson’s and Stahl’s work on a day-to-day bases.
5 See Lipton (2004) for a book-length philosophical study of IBE. Lipton uses a contrastive account of causal explanation, whereas I shall use a mechanistic account.
6 The term “mechanism” is sometimes used in a double sense in this literature, sometimes ontological and sometimes epistemic. The latter use is shorthand for “description of a mechanism” or “model of a mechanism” and the context should normally make it clear which of the two senses is relevant.
7 Experimental mechanisms are part of experimental systems in the sense of Rheinberger (1997). See my (2005, Chapter 5) for a critical assessment of the experimental systems approach.
8 Hanawalt (2004). Thanks to Beatrix Rubin for bringing this paper to my attention.
9 Meselson to Watson, 8 November 1957. Quoted from Holmes (2001, 327-328).
10 For similar reasons, I don’t think that an appeal to Bayesian confirmation theory is of much help here. However, as Lipton (2004, Chapter 7) nicely shows, Bayesianism and the IBE approach are not necessarily in conflict. Explanatory considerations could be one possible way of estimating likelihoods. As for the error-statistical approach, perhaps a similar reconciliation is possible. Of course, this could lead to diverging claims with respect to the evidential import of the experiment. At any rate, this is not an issue that I can pursue any further here.
11 This curve appeared only in Meselson’s Ph.D. thesis, not in the 1958 publication. By the way, the thesis committee contained Linus Pauling and Richard Feynman. This obviously means that, had there been a problem with the physics, this could not have gone unnoticed!
12 Some proponents of a mechanistic account of explanation have argued that laws are redundant; all the explanatory work they were once thought to do can be captured by activities (see also Cartwright 1989). In Weber (2005, Chapter 2), I criticize this view. So does Glennan (1996).
13 A penetrating critique of the argument can be found in Okasha (2000).
14 Daniel Sirtes (unpublished) argues that mechanism boundaries are sensitive to pragmatic contexts. If correct, this obviously would spell difficulties for the alleged objectivity of the explanatory and mutatis mutandis for the evidential relation. This problem will have to be treated elsewhere.
15 Existing accounts of IBE, in particular Lipton’s seem to have focused on phenomena rather than data as the explanandum in IBEs. I must take exception to Bogen’s and Woodward’s view that data cannot be predicted or systematically explained by theory (Bogen and Woodward 1988, 305-306). Experimental mechanisms, as I use the term, do provide causal explanations for data in the sense of directly observable patterns produced by some measurement device. In experimental biology, theories are typically descriptions of mechanisms.
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