<div>This book investigates the relationships between modern mathematics and science (in particular, quantum mechanics) and the mode of theorizing that Arkady Plotnitsky defines as "nonclassical" and identifies in the work of Bohr, Heisenberg, Lacan, and Derrida. Plotinsky argues that their scientific and philosophical works radically redefined the nature and scope of our knowledge. Building upon their ideas, the book finds a new, nonclassical character in the "dream of great interconnections" Bohr described, thereby engaging with recent debates about the "two cultures" (the humanities and the sciences).<br></div><div>Plotnitsky highlights those points at which the known gives way to the unknown (and unknowable). These points are significant, he argues, because they push the boundaries of thought and challenge the boundaries of disciplinarity. One of the book's most interesting observations is that key figures in science, in order to push toward a framing of the unknown, actually retreated into a conservative disciplinarity. Plotnitsky's informed, interdisciplinary approach is more productive than the disparaging attacks on postmodernism or scientism that have hitherto characterized this discourse.<br></div><div>Arkady Plotnitsky is Professor of English and Director, Theory and Cultural Studies Program, Purdue University. Trained in both mathematics and literary theory, he is author of several books, including <i>In the Shadow of Hegel: Complementarity, History and the Unconscious</i> and <i>Reconfigurations: Critical Theory and General Economy</i>.<br></div>

The Knowable and the Unknowable

Modern Science, Nonclassical Thought, and the "Two Cultures"By Arkady Plotnitsky

University of Michigan Press

Copyright © 2002 Arkady Plotnitsky
All right reserved.
ISBN: 0472097970
Chapter 1 - An Introduction to Nonclassical Thought
The Classical, the Nonclassical, and the Quantum
Throughout this study, classical theories will be understood as considering their principal objects available to conceptualization and, often, to direct representation in terms of particular properties of these objects, their behavior, and the relationships between them. Indeed, these features define such objects as objects of classical theories, since these objects may be idealized from some other objects, some of whose other properties, moreover, are disregarded by the theory, in the way, for example, classical physics abstracts certain key physical properties from other properties of material bodies it studies. Thus, classical mechanics, the part of classical physics that deals with the motion of individual physical objects or systems composed of such objects, is or (this qualification is crucial) may be interpreted as such a theory. It fully accounts, at least in principle, for its objects and their behavior on the basis of physical concepts and abstracted or idealized measurable quantities of material objects corresponding to them, such as the position and momentum of material bodies. Other possible properties of actual physical objects involved, say, planets moving around the sun, are disregarded by classical mechanics, which thus deals with idealized objects. The equations of classical mechanics allow us to know the past state (or to operate under the assumption of such knowledge) and to predict the future state of the system under investigation at any point once we know it at a given point. Other areas of classical physics, such as thermodynamics and statistical physics, chaos theory, and electromagnetism (a wave, rather than particle, theory), can be shown to be, or to be interpretable as, classical in the same sense. While, thus, in general an idealization, within its proper limits (short of relativity and quantum physics), classical physics offers an excellent approximation of the behavior of material bodies in nature and enables most of the technology currently in use, including that used in quantum measurement.
Classical physics is, thus, by definition, realist and usually causal. Or, again, it may be and usually is interpreted as such for most purposes of its analysis and use; that is, one can combine theory (specifically mathematical formalism) and experimental data so as to construct models, classical models, each comprising a set of idealized objects, whose causal behavior the theory describes. I shall consider the concepts of causality, which relates to the nature of the processes themselves in question, and determinism, which relates to our ability to predict the outcome of such causal processes, in detail in the next chapter. In general, classical theories, as here defined, need not entail causality. Classical physics, however, is virtually uniformly causal, although not always deterministic, while nonclassical theories are neither causal, nor deterministic, nor realist as concerns their ultimate objects. Within its proper scope, classical physics offers both excellent descriptions of the natural objects it considers (or ultimately constructs as such) and from which it idealizes the objects of physical theories, and excellent predictions of the outcome of experiments it performs upon natural objects. In Bohrs nonclassical interpretation, complementarity, quantum mechanics allows only for the latter, not for the former, and indeed rigorously disallows even the possibility of constructing a model of the classical type with respect to the ultimate objects it considers, since it only describes the effects of the interaction between these objects and measuring instruments. This stronger prohibition is crucial, since, in principle, classical models need not be seen as describing, even approximately, the behavior, let alone the ultimate nature, of actual physical objects (even though they can be and often are seen as so doing), but only as serving to predict outcomes of experiments. In other words, in question here is a rigorous impossibility of applying classical-like models, rather than merely abandoning such models. The key aspects of the classical situation in physics just outlined can be generalized to classical theories elsewhere. Reciprocally, classical physics may itself be seen as derived from classical theories elsewhere and also, in part correlatively, as a refinement of everyday experience and language (no longer applicable to physical objects at the quantum level), a point often made by both Bohr and Heisenberg. Thus, the classical and the knowable of my title are one and the same, denoting that which is available to knowledge, representation, conceptualization, theorization, and so forth. Indeed, according to this view, what is knowable is classical, and only what is classical is, in all rigor, knowable.
By contrast, the ultimate objects of nonclassical theories are irreducibly, in practice and (this defines the difference between classical and nonclassical thinking) in principle, inaccessible, unknowable, unrepresentable, inconceivable, untheorizable, undefinable, and so forth by any means that are or ever will be available to us, including, ultimately, as objects in any conceivable sense of the term. Hence, they cannot be assigned any conceivable attributes, such as those conceived by analogy with objects of classical theories. For example, it may not be, and in Bohrs interpretation is not, possible to assign the standard attributes of the objects and motions of classical physics to the ultimate objects of quantum physics. It may no longer even be possible to speak of objects or motions (such as particles or waves, for example), which, however, does not imply that nothing exists or everything stands still. The latter, naturally, is itself a classical physical attribute, a refinement of everyday experience. But then, how else can we even conceive of such attributes, given the present understanding of classical theories? For, in this understanding, only classical theories or, more generally, thinking could allow us such an attribution. Thus, the ultimate objects of nonclassical theories are not their objects insofar as one means by the latter anything that can actually be described by such a theory. The impact of such objects on what the theory can account for is crucial, however, and this impact cannot be described classically, which is what makes a nonclassical description necessary in such cases.
This statement requires the following further qualification in view of the fact that the situation is subtler than just presented as concerns the ultimate efficacity of the impact of the unknowable objects in question upon what we can knowof the effects of the nonclassical upon the classical. Here and throughout this study, I use the term efficacity in its dictionary sense of power or agency producing effects but, in this case, without the possibility of ascribing this agency causality, which point is especially significant in quantum theory and in Bohrs work. The nonclassical inaccessibility, as here understood, must be seen as referring to the objects, or the efficacious processes leading to the effects in question, as they are defined by a given nonclassical theory, even though ultimately we may not be able to access such objects by any conceivable means, rather...