The Problem of Nomological Impossibility for Epistemic Structural Realism

ion, however, idealization involves more than simply excluding factors potentially relevant to the behavior of the physical system being studied: idealization also “[incorporates] factors that cannot exist as represented given the actual properties and relations involved” (Chakravartty 2007, 191). vii In other words, idealization employs certain nomologically impossible assumptions in order to simplify the model being constructed (where this simplification can be motivated by the pragmatic constraints mentioned above). 106 The Problem of Nomological Impossibility The Hilltop Review, Spring 2015 As an example of abstraction and idealization in a scientific model, consider that of a simple pendulum (Chakravartty 2007, 191). Such a model is usually presented as consisting of a weight attached to a pivot point by means of rod. Factors such as the air resistance affecting the motion of the weight or the friction of the rotating pivot are usually excluded from the model, in accordance with the abstraction process. Notice, however, that there is no principled reason why such a model that ignores these factors could not be physically realized. A closed physical system containing no air resistance and no friction is nomologically possible: i.e., it could be physically realized without violating the actual laws of nature. Other elements of the model are simplified beyond what is physically realizable in any such system, however. Examples are the rod’s total lack of mass in the model, as well as the representation of the weight as a point-mass: an object whose total mass is concentrated at a single extension-less point. These types of simplifications (idealizations) could not in principle be physically realized by any system: a rod pivoting around a point with a weight attached must have some non-zero mass in any physical system; likewise, the mass of this weight could not be completely condensed down to a single dimensionless point in any physical system conforming to the actual laws of nature. Both abstraction and idealization are often used simultaneously in scientific practice for the construction of models (Chakravartty 2007, 191). Nevertheless, the distinction concerning nomological possibility mentioned above will prove to have significant implications for the epistemic attitudes of the Structural Realist towards the formal structures of scientific theories. VI. Limiting Cases as Idealizations Recall the notion of structural continuity that is at the heart of the Epistemic Structural Realist’s version of the “No Miracles” Argument. The Epistemic Structural Realist will argue that there is substantial (even if incomplete) structural continuity between successive mature scientific theories, which means the formal structures of earlier theories will be viewed as approximately accurate from the point of view of later (mature) theories. This claim of approximate structural accuracy, in turn, will be the only acceptable explanation of the empirical success enjoyed by each of the successive theories and so should be accepted. Again, the notion of incomplete preservation of structure between successive theories is understood in terms of limiting cases. Consider the successive theories of classical thermodynamics and statistical mechanics, for example. viii Both theories seem to meet the criterion of maturity (in Worrall’s sense), since both have enjoyed novel predictive success. Moreover, the two theories exemplify the limiting case relation with which the Epistemic Structural Realist explains partial structural continuity. The formal structure of thermodynamics can be derived from the formal structure of statistical mechanics by taking the “thermodynamic limit” in the latter: assuming the relevant physical system contains an infinite number of particles (Batterman 2005, 227). By allowing the number of particles in the system to tend to infinity, the formal structure of thermodynamics can be recovered from the formal structure of statistical mechanics. Notice, however, that this “thermodynamic limit” is an idealization: no system with an infinite number of particles could be physically realized ix . It follows that the limiting case relation between thermodynamics and statistical mechanics can only be instantiated by making use of an idealization (viz., the “thermodynamic limit” assumption). But this means that the formal structure of the theory of thermodynamics can only be recovered from the formal structure of statistical mechanics through the use of an assumption that is not merely (strictly) false, but physically impossible. In other words, the partial retention of formal structure between these two mature theories in terms of the limiting case relation employs a nomologically impossible assumption. Patrick Manzanares 107 The Hilltop Review, Spring 2015 VII. Problems with Employing Idealizations This use of idealization in the derivation of limiting cases can be found among many other mature successive scientific theories. x It poses a problem, however, for the Epistemic Structural Realist’s claim about the approximate structural accuracy of scientific theories. Suppose, for the sake of argument, that there is partial structural continuity between two mature successive theories such as thermodynamics and statistical mechanics. The presence of this partial structural continuity will imply that the two theories exemplify the limiting case relation, since the partial structural continuity is understood in terms of this limiting case relation for the Epistemic Structural Realist. So thermodynamics will constitute a limiting case of statistical mechanics. This, in turn, means that the derivation of the thermodynamic formal structure from the statistical mechanical formal structure will involve an idealization. The theory of thermodynamics will thus constitute an idealization of the relevant physical system by virtue of the role the “thermodynamic limit” (discussed above) plays in deriving the formal structure of thermodynamics from the formal structure of statistical mechanics. But if this is the case, then the formal structure of thermodynamics will be rendered not just inaccurate, strictly speaking; it will constitute a nomologically impossible structure, by virtue of the use of the “thermodynamic limit” idealization. Given that the structure of thermodynamics cannot be physically realized, then, in what sense can it be said to be an approximately accurate representation of the physical structure of the world? To what degree could a nomologically impossible structure approximate a (the) nomological structure that actually obtains? Notice that the Epistemic Structural Realist cannot fall back on an appeal to approximate, as opposed to strict, accuracy of structure here (as was done in response to Pincock’s objection above). The problem for the Epistemic Structural Realist is not just that the formal structure of the thermodynamic theory is strictly false, and therefore disconnected from reality to some extent. xi The problem is deeper than this: the formal structure of thermodynamics could not possibly be realized by the structure of the physical system that actually obtains in our world. The notion of its approximate accuracy in representing the physical structure of the world is thus rendered a complete mystery. As a result, the Epistemic Structural Realist is left without a reason to believe in the approximate structural accuracy of thermodynamics. The nomological impossibility of the thermodynamic theory’s formal structure thus undermines the motivation for believing in its approximate truth. But if belief in the approximate accuracy of the thermodynamic structure can no longer be justified, then the Epistemic Structural Realist is left without an explanation for the empirical success of science. Without a reason to believe in the approximate accuracy of the thermodynamic formal structure, the structural continuity obtaining between thermodynamics and statistical mechanics is no longer enough to mount a structural version of the “No Miracles” argument. This appears to undermine the entire Epistemic Structural Realist position. VIII. Potential ESR Reponses and Replies (1) Appeal to Empirical Success At this point, the Epistemic Structural Realist might appeal to the empirical success of thermodynamics in order to argue that the use of idealization assumptions does not undermine the reasons for believing in the approximate structural accuracy of the theory. Of course, the mere empirical success of thermodynamics is not enough to ground the realism of the Epistemic Structural Realist: the latter must give an explanation of this empirical success. The problem, it seems, is that this explanation will have to take the form of another “No Miracles” argument: the reason thermodynamics proved so empirically successful is the fact that its formal structure is an approximately accurate representation of the physical structure 108 The Problem of Nomological Impossibility The Hilltop Review, Spring 2015 in the world (Worrall 2007, 143). But it is precisely the approximate structural accuracy of the theory that is being questioned. So an appeal to empirical success will either not be enough by itself (since this will not be enough to grant the Epistemic Structural Realist a “Realist” status), or will presuppose the approximate structural accuracy of the theory that is at issue. Other types of explanation seem to be off-limits to the Epistemic Structural Realist precisely because of the epistemic commitment to structures only. Worrall (2007) notes that the way in which the formal structure of a theory can successfully represent the physical structure of the world “cannot be further specified—to suppose that it can would be to suppose that we can somehow have access to the universe that is not theory-mediated and thus can directly compare what our theories say with reality”, this last claim being “untenable” (Worrall 2007, 143). In