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Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.

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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 than only by means of this theory itself. This inaccessibility does not refer to what can be further linked to such objects in nature (the existence of such a link would be assumed in physics, or at various levels in other natural sciences) or in mind (a link customarily assumed in philosophy), or in other domains, such as society, politics, or culture, which a given theory would consider. Upon what happens at these levels as such, or how it can possibly be seen by other theories, nonclassical theory does not make any claim, including the claim that it is inaccessible, unknowable, unrepresentable, inconceivable, untheorizable, undefinable, and so forth. Accordingly, from the nonclassical perspective, the ultimate or, as it were, the ultimate ultimate objects of nonclassical theories are inaccessible even as inaccessible, unknowable even as unknowable, unrepresentable even as unrepresentable, inconceivable even as inconceivable, untheorizable even as untheorizable, and so forth. In other words, such un-objects may not correspond in any way to the objects of a given nonclassical theory, even though and because this theory conceives of its objects as unavailable to description or conception in terms of the theory or indeed in any terms (such as objects). This latter view, too, must be seen as a (possibly ultimately inadequate) form of idealization, in the way it would be, for example, in Bohrs interpretation of quantum mechanics (this is in part why it is an interpretation). This idealization is, moreover, not an approximation (of the kind classical theories often pursue), but instead a kind of irreducible rupture from whatever may physically exist. In all rigor, following and radicalizing Immanuel Kant, we may not even be able to speak in terms of the existence in space and time, or in terms of any specific form of materiality we can conceive of, since they may not be applicable, even in the sense of the remotest analogy. From this perspective, nonclassical theories entail two irreducible ruptures or discontinuities (hence there is no causality, which is, conceptually, a form of continuity). The first rupture is that between the knowable effects and their unknowable efficacity, for which the ultimate objects of a given theory are responsible. The second is that between these objects, qua objects of the theory, and thatthose un-objectsto which these objects can possibly be linked in nature, as in physics, or elsewhere. The second rupture, obviously, adds new complexity to the concept of the nonclassical. This complexity may appear excessive, and, indeed, one need not engage with it for most practical workings and applications of nonclassical theories, and even for many epistemological arguments concerning them vis-a-vis classical theories. As will be seen, however, at certain points this part of the nonclassical conceptual and epistemological architecture becomes crucial and, in fact, irreducible, for example, in considering the question of interpretation in quantum (or, for that matter, classical) physics. It is of course also necessary for a fully rigorous specification and understanding of the nature of nonclassical theories as they are defined by this study.
There may, again, be a link between such un-objects and the objects of a given nonclassical theory, and indeed what happens at these more remote levels may be and usually is ultimately responsible for, or is the ultimate efficacity of, everything at stake in the theory in question. For example, this type of link and this type of ultimate efficacity enter quantum theory through the experimental data of quantum physics, for which certain un-objects, as just defined, are responsible and through which an interpretation of quantum mechanics may conceive of quantum objects nonclassically, as irreducibly inconceivable, in the way Bohrs complementarity does. In terms to be developed in the next chapter, this view is part of Bohrs model and (this distinction will be properly established in the next chapter as well) interpretation of quantum mechanics, rather than necessarily a view of what ultimately happens in nature at the level of its ultimate constituents. Strictly speaking one should put quotation marks around nature, ultimate, constituents, or, when used, quantum. Complementarity does not claim the ultimate validity of this idealization for anything in nature, beyond its role in the argument for the completeness (an exhaustive account for the data) and consistency of quantum mechanics (thus interpreted) within its proper scope. It would be tempting to say in these circumstances (and one finds such claims sometimes) that, at the ultimate level of the quantum constitution of nature, there are no particles, no atoms, and so forth, rather than only that we cannot see the objects of quantum mechanics in these terms from the perspective of a particular interpretation, such as complementarity. It appears, however, more prudent to adopt the present, more cautious, view, which, in addition, suffices for the purposes of my argument. As will be seen, Bohr argues that there is no quantum world in the present sense. Or, at least, this statement and complementarity in general may be interpreted or adjusted in accordance with this view, since Bohr, on occasion, appears to make or to be inclined to make somewhat stronger claims.
Accordingly, the unknowable of my title are the unknowable objects of nonclassical theories, coupled to the unknowable (or the unknowable unknowable) unobjects, as just explained. While, however, knowledge or, conversely, the unknowable appear to be almost maximally capacious terms to be deployed in this context and often indeed subsume other denominations deployed by this study, such as (in)accessible, (un)representable, (un)conceptualizable, and so forth, it does not appear possible to fully contain this situation, even negatively, by any single term. Indeed, as will be seen, this impossibility is itself a rigorous consequence of the nonclassical view and is correlative to the nonclassical character of the unknowable in question.
The view just outlined, thus, accommodates the possibility that other theories may define the un-objects of nonclassical theories differently and may differently relate to or idealize them as their objects, for example, along more classical and specifically realist lines. The ultimate viability of such alternative approaches is a different question and may become a subject of criticism or assessment, for example, vis-a-vis the nonclassical view. On the other hand, given that our physical theories are manifestly incomplete, moving beyond the scope of the standard (nonrelativistic) quantum mechanics, to which Bohrs complementarity rigorously applies, may change the way we need to idealize quantum objects. For the moment, however, nonclassical epistemology appears to hold, at least in terms of an interpretation, for most available quantum theories and even for relativity, or their extensions, such as higher-level field theories, quantum gravity, or string theory. The same type of argument would apply to nonclassical theories elsewhere, and outside mathematics and science the space of possibilities is perhaps even more ambiguous and uncertain. Perhaps! There is plenty of epistemological ambiguity in mathematics and science as well.
In quantum theory, in Bohrs complementarity and related nonclassical interpretations, we cannot ascribe conventional properties (such as position and momentum of classical mechanics) or any physical properties describing their spatial-temporal behavior to quantum objects qua quantum objects, such as elementary particles, which we now see as the ultimate constituents of matter. Or, again, in accordance with the qualifications just given, such interpretations see such objects as an idealization of the ultimate constitution of matter as unknowable. Being a particle or, conversely, a wave would of course itself be defined by a set of such properties, and, accordingly, as Bohr stressed already in his introduction of complementarity, the terms particle and wave cannot be applied to quantum objects otherwise than provisionally (PWNB 1:5657). Nor, at the nonclassical limit, can the terms quantum or objects be applied, or, ultimately, any conceivable term or concept. Some of these complexities transpire already in Einsteins so-called special relativity of 1905, which deals with the propagation of light in a vacuum. According to this theory, this speed (in a vacuum) is always constant, the famous c, regardless of the state of motion of the source, which cannot be accelerated so as to change the emitted lights speed relative to it. It follows from the latter fact that in the case of light itself such classical properties as time dilation cannot apply. Were it possible (it is not) to install a clock on a photon, according to relativity the time shown by this clock would stand still. Relativity may, however, be seen as a classical theory in other respects, specifically causality. Remarkably, quantum theory can predict, primarily in statistical terms, the outcome of the experiments involved as well as classical statistical physics, which enables its extraordinarily successful functioning as a physical theory. Classical or classical-like theories failed to do this, or at least they failed to do so when quantum mechanics was introduced. (As will be seen, the question whether such a classical-like account is in principle possible is under debate.) Classical physics may be statistical, too, but not quite in so radical a way as quantum physics appears to be. From this perspective Einsteins famous pronouncement God does not play dice may well be true, but only in the sense that, as Bohr observes on several occasions, it is not clear in what sense one can even speak of dice (ultimately a classical statistical game) when confronting the statistical game of quantum mechanics. (The concept of game, too, may no more be applicable here than any other.) Eventually (in 1953, one year before he died) Einstein came to accept this point, even though he would still, apparently for this very reason, clearly prefer Gods playing dice rather than the games of quantum physics and its predictions, effective as they may be in practice, which Einstein had always acknowledged.
As will be seen, in Bohrs interpretation, this possibility of quantum-mechanical predictions is seen as enabled by the interactions between quantum objects and measuring instruments. The instruments themselves, or more accurately, those parts of them through which we register outcomes of measurements, are described (idealized) in terms of classical physics and classical epistemology. As a result, in this interpretation, the role of technology becomes constitutive and irreducible in quantum mechanics (and, by implication, giving the term technology its broader meaning, in nonclassical theories elsewhere), while it may be seen as merely auxiliary and ultimately dispensable in classical physics. Indeed, one could also define nonclassical theories through the irreducible role of technology in them and, conversely, classical theories by the auxiliary and ultimately dispensable functioning of technology there.
It follows that in this interpretation quantum mechanics does not describe, either through its mathematical formalism (as classical mechanics often does) or otherwise, even in principle and as an idealization, the actual properties and behavior of its objects in the way classical mechanics describes the behavior of its objects. Indeed, as I said, it is the latter view that becomes the idealization of nature at the quantum level according to complementarity. By the same token, it is neither causal nor, more crucially, realist in any sense hitherto available. Nor, in the view here adopted, are other nonclassical theories.
Obviously, classical theories, too, involve things that are, at least at certain moments, unknowable and inconceivable to them, while nonclassical theories enable new knowledge, indeed often knowledge that would be impossible without the intervention of nonclassical theories. Nonclassical theories change the nature of the unknowable and of the relationships between the knowable and the unknowable, as against classical theories, and, consequently it is what we can know and conceive of that are different in nonclassical theories. The ultimate knowledge concerning the objects of nonclassical theories becomes no longer possible, while the existence of these unknowable objects or what they idealize and their impact upon what we can know is indispensable. Ultimate, however, is, in turn, a crucial qualifier here and throughout this study, where it features prominently (and it is of course subject to the same ultimate inapplicability at the ultimate level of description). For, in the first place, classical theories or ways of thinking in general are often extraordinarily effective and sometimes indispensable across a broad spectrum of theoretical thinking and other human endeavors, or indeed in everyday life. Second, indeed as a corollary of the definitions given here, they are equally indispensable in nonclassical theories, since they serve as a pathway, indeed the only pathway, to establishing the existence of and the connections to the unknowable. Or, more accurately, classical theories allow us to handle the classically manifest effects of the unknowable in question in nonclassical theories, which unknowable cannot be inferred or treated otherwise. By the same token, some among such knowable effects, specifically certain configurations of such effects, or, it follows, the emergence (efficacity) of each of these effects cannot be properly explained by means of classical theories and require nonclassical theories. The latter are able to use them, while leaving the ultimate nature of the efficacity of these effects unknowable and inconceivable even at the level of idealization. The models at stake in such theories and the way they construct their objects require this irreducible unknowability in order to account for the effects in question. Indeed, even is not altogether appropriate here, since, as I explained above, this (irreducibly unknowable) character of any such efficacity is itself now seen as an idealization, a nonclassical idealization, and, in the case of Bohrs complementarity, part of the model it considers. Nonclassically, one does not make even (now even is necessary) this claim concerning the ultimate inaccessibility of anything, any more than any other claims, as regards more remote levels, such as that of the ultimate constitution of nature qua nature (again, to the degree this term applies) in quantum physics. The unknowable ultimate constituents of nature as quantum objects and quantum processes (or any forms of efficacity they entail) are idealizations of quantum mechanics as comple-mentarityare part of its model. These idealizations are, however, argued to be consistent with available data and prediction that the theory makes by using its mathematical formalism. These remote levels may be seen as part of, or indeed as, the ultimate efficacity of everything to which a given nonclassical theory relates. For example, as I said, the data in question in quantum mechanics may be seen or, again, may be idealized as linked to such efficacities, while the efficacities themselves are seen or idealized as irreducibly unknowable according to a nonclassical view without making any ultimate claim of unknowability upon them. It follows that the term efficacity or effects is as provisional as any term here deployed (for example, elementary particles of quantum physics) at the level of the nonclassical unknowable.
While the ideas of Bohr and several other thinkers, such as Nietzsche and Derrida are significant here, the conception just outlined is especially indebted to the work of Georges Bataille, who had a powerful influence on most other nonclassical authors considered here, and to his concept of unknowledge (nonsavoir). According to Bataille, it would be impossible to speak of unknowledge [ultimately even as unknowledge] as such, while we can speak of its effects. Reciprocally, it would not be possible to seriously speak of unknowledge independently of its effects.
The conjunction of both propositions equally defines Batailles and Bohrs complementary epistemology, as well as a number of other nonclassical or near nonclassical conceptions, such as Derridas differance or Foucaults power (both in turn indebted to Bataille). To cite Bohrs statement, with which I began this study, in quantum mechanics [as complementarity], we are not dealing with an arbitrary renunciation of a more detailed analysis of atomic phenomena, but with a recognition that such an analysis is in principle excluded (PWNB 2:62; Bohrs emphasis). (The term phenomena in this statement should be given Bohrs special sense, necessitated by his nonclassical view, the sense to be explained in chapter 2.) This impossibility, however, does not preclude, but instead enables, a rigorous analysis of the effects of this unknowable efficacity. Bohr, especially in his later writings, often, and at crucial junctures, spoke in terms of effects typical quantum effects, the peculiar individuality of quantum effects, and so forthusing them very much in the present sense. In particular, non-classically we cannot speak of the quantum world itself (for example, as the quantum world) but only of the effects of the interaction between quantum objects and measuring instruments, which interaction initiates the efficacity of these effects. This interaction is itself quantum (and thus depends on the quantum aspects of the constitution of the measuring instruments) and hence is unavailable to classical or, again, any treatment, even though the effects of this interaction are available to classical physical and epistemological treatment. The character of the (knowable) effects in question irreducibly precludes the knowledge or conception, specifically on any model of what is knowable, of their ultimate efficacity or, at least, the ultimate nature of their efficacity. In other words, the (irreducibly) unknowable itself in question is no more available to nonclassical theories than to classical theories. Nonclassical theories, however, allow us rigorously to infer the existence of this unknowable (rather than merely imagine its existence) on the basis of the phenomena that they consider, and explain its significance for what we can know, and utilize the (manifest) effects of this interaction, while this cannot be done by means of classical theories. Accordingly, nonclassical theories are defined by the interaction between what is knowable (the previous list of related terms is presupposed) by, it follows, classical means and what is unknowable (the same parentheses apply) by any means, classical or nonclassical.
It is worth noting (since misunderstanding can occur on this point) that nonclassical epistemology, as here understood, does not refer to a kind of temporary state of affairs whereby something (such as the efficacity of certain effects in question in quantum mechanics) that is not known, accessible, or conceivable now could eventually become conceivable, accessible, or known. This possibility would make this unknowable into something that could in principle become known and, hence, classical in the present sense. By contrast, as I have stated at the outset, the nonclassical unknowable refers to something that cannot be known or conceived not only by any means that is now available but also by any means that could ever be available. Such a conception, to return to Bohrs locution, is in principle excluded. The nonclassical view of knowledge is not defeatist or nihilistic, as Nietzsche, arguably the first thinker of the ultimate limits of both the nonclassical and nihilism (but, importantly, not a nihilist himself), was first to understand. Bohr makes this point clear as well in relation to quantum theory, when he points out that his argumentation does of course not imply that, in atomic [quantum] physics, we have no more to learn as regards experimental evidence and the mathematical [or other theoretical] tools appropriate for its comprehension. Indeed, Bohr adds it seems likely that the introduction of still further abstractions into the formalism will be required to account for the novel features revealed by the exploration of atomic processes of very high energy (PWNB 3:6). The history of quantum physics has demonstrated and continues to demonstrate just that, as all of its experimental and theoretical findings so far appear to be consistent with Bohrs epistemology. In other words, new knowledge at the level of the effects of the unknowable is generated all the time. The unknowable itself, however, remains irreducible under nonclassical conditions. This irreducibility of the unknowable is one of the (permanent) effects of the nonclassical efficacities.
On this view, the question could only be whether or not the phenomena in question in quantum physics (either as coupled to a particular mathematical formalism or in themselves) or in analogous theories elsewhere in fact require epistemologically nonclassical interpretation and treatment, rather than whether such phenomena will eventually become better known so as to enable any further access to the ultimate objects of a given theory and the ultimate efficacity of these phenomena. (As will be explained later, these phenomena are constituted by knowable effects.) Nonclassically, the unknowable is to remain as irreducible in the future as it was at the initial stages of nonclassical theoriesunless, of course, we change our very conception of what it means to know or to conceive so as to leave space for the irreducibly unknowable. This argumentation would be consistent with the nonclassical view, such as Bohrs, in the case of quantum mechanics. Indeed, to some degree this change may be seen as in practice taking place in quantum physics, whether the practitioners themselves like it (or even recognize it) or not. It transpires, for example, when the results of experiments are being discussed directly in terms of those elements of the quantum-mechanical formalism that do not refer to space-time processes at the level of quantum objects (which reference is nonclassically impossible) but only to outcomes of experiments, already performed or possible.
One may hope, as did Einstein or Erwin Schrodinger and, following them, many others who also thought the epistemological cost exorbitant or even unacceptable, that such phenomena might at some point no longer require an appeal to nonclassical thought and theories. In other words, the hope here is that the unknowable aspects of the phenomena in question in quantum physics could be configured classically. The better thinking of that type, such as that of Einstein and Schrodinger, was far too complex and sophisticated to expect that the unknowable could be altogether eliminated in physics, only that its nonclassical character could be. Hence, Einstein and Schrodinger did not think that they could abandon the search for what they would (from a more classical perspective) see as a more complete and (which is in fact what greater completeness ultimately meant for them) epistemologically more palatable conception. Many still continue to resist or do not perceive, to begin with, this potential irreducibility of the nonclassical unknowable in quantum mechanics or elsewhere, and some question the necessity or superiority of the standard quantum mechanics itself as an inevitable or even valid account of the data it considers. Thus, most proponents of David Bohms so-called hidden-variables theories (there are several versions) belong to the latter group and, accordingly, see Bohms theory as an alternative to quantum mechanics. These theories lend themselves more naturally to a classical-like epistemology, albeit at the cost of their own problems, in particular their nonlocality.
Is then quantum mechanics itself, that is, the experimental data in question in it and the mathematical formalism that accounts for it, uncircumventably nonclassical, something that ultimately disallows classical-like interpretation? It may well be, and, while exercising caution, Bohr and others were and many are inclined to think so. Here, however, I only argue for the nonclassical nature of Bohrs complementarity, or, even more cautiously, for the nonclassical nature of the present interpretation of complementarity as an interpretation of quantum mechanics, since this interpretation may be challenged as well, just as, again, may be Bohrs claims (in whatever interpretation). I do not find currently available more classical-like readings of Bohr sufficiently compelling to be seen as having already offered such a challenge or alternative. In any event, the potential effectiveness (or ineffectiveness) of the present argumentation does not depend on the fact that it concerns and extends only a particular interpretation of quantum mechanics rather than the (ultimate) character of nature itself. As I have explained earlier, upon the latter, this interpretation, by definition, makes no claim in any event by virtue of its nonclassical character, ultimately, not even a claim that such claims are ultimately impossible. We do not ultimately know whether what is behind the nonclassical unknowable is ultimately knowable or unknowable. My contention is only that Bohrs interpretation is at least as consistent and comprehensive as any, indeed more so than most, even if not all (although the latter possibility is not inconceivable to the present author). My argument here, however, need not go that far. It is of course crucial that the nonclassical interpretations of quantum mechanics, or (with due qualifications) nonclassical theories and interpretations elsewhere, remain consistent (logically and with respect to the data specifically in question in a given theory or otherwise relevant to it) and complete, even by classical criteria. This requirement is, I argue, amply satisfied by Bohrs interpretation, arguably more so than by most other interpretations, but at least as much as by most opposing interpretations on the current scene. This view also assumes that quantum mechanics itself remains logically consistent and complete within its proper scope, that is, as Bohr puts it, that it employs a logically consistent mathematical formalism and that one cannot demonstrate that the consequences of this formalism exhibit the departure from experience or that the predictions based on this formalism do not exhaust the possibilities of observation (PWNB 2:57).
This status of quantum mechanics is by and large accepted now. Most arguments against quantum mechanics and even Bohrs interpretation (although the latter continues to generate much discontent) now center on possible and, to those who are more classically minded, epistemologically more classical alternatives, such as along the lines of Bohms theories. While it has attracted some public attention, the latter is a small minority view in the physics community (for the reasons to be explained later). As will be seen, however, there many other (more) classically oriented approaches to quantum mechanics and its interpretation. How viable such interpretations are is, again, a separate question, which I shall not, and for my purposes need not, fully address here. I shall comment on some of these attempts later in this study, especially since meeting some of Einsteins challenges in fact requires an interpretation, and, as I shall argue, with Bohr, complementarity does meet them. The classical-like attempts at interpreting quantum mechanics or offering classical-like alternatives to it, such as Bohms, bear significantly on the discussions and controversies that have surrounded nonclassical epistemology throughout the twentieth century and have by now extended into the twenty-first.
Geneologies, Disciplinarities, and Interconnections
Nonclassical itself is a relatively new term, which, as here defined, may be related to and deployed alongside such terms as poststructuralist, deconstructive, and postmodernist used more prominently in similar contexts, mostly outside mathematics and science, in current discussions. On the other hand, classical is a capacious and widely used denomination, for example, in Michel Foucaults work, and relates to a wide and diverse set of practices, much wider than does nonclassical. It may be argued, however, that the view of the classical here adopted is sufficiently fundamental to relate to, if not to subsume, a large spectrum of such denominations, including Foucaults. It goes without saying that it is not a question of introducing yet another uniquely fundamental conceptual opposition that would fully master the field(s) in question and to which all other theoretical descriptions would be subordinate. At this point, largely thanks to nonclassical theories from Nietzsche to Derrida and beyond, it is difficult to sustain the assumption that this is possible or, again, ultimately possible. But, as Derrida has stressed from the outset of his deconstructive project (associated with the deconstruction of binary oppositions and with the impossibility of the kind of mastery just described) and as Heraclitus perhaps already knew, such oppositions may be inescapable. They become even more effective once we understand the more complex dynamics underlying their emergence and functioning, which we may need to do nonclassically. They are certainly crucial for Bohrs interpretation of quantum mechanics. There certain mutually exclusive (and hence never applicable simultaneously) or, in Bohrs terms, complementary features of physical description are both necessary for a comprehensive theoretical account and strictly correlative to the nonclassical nature of Bohrs interpretation, called complementarity in view of this correlation. In general, such oppositions may be more or less traditional, such as mind/nature, language/ thought, logic/intuition, and so forth, or more or less new, such as the classical and the nonclassical, as here defined, speaking for the moment of fundamental aspects of theorizing knowledge. They may be more descriptive, as, for example, are those used in quantum physics, say, between the wave and the particle descriptions. Besides, classical theories are themselves irreducible in nonclassical theorizing. Hence, the relationships between classical and nonclassical thought cannot be strictly oppositional or mutually exclusive, although the two types of epistemology thus designated are irreducibly different. They are not complementary, however, since they are not applicable to the same types of objects. For in Bohrs interpretation, nonclassical epistemology applies exclusively to quantum objects (to the degree the latter denomination itself applies), while classical epistemology applies to certain parts of measuring instruments. The role itself of measuring instruments in the constitution of the data of quantum mechanics and in the physical description it provides can never be neglected or idealized away so as to deal, even ideally, with objects themselves.
I call the thinking in question nonclassical rather than, say, postclassical (the term employed in similar contexts previously, including by this author) for the following reason. It is true that its most radical forms may be argued to be relatively recent. In science, we find them in quantum physics or modern biology and genetics and in certain areas of modern mathematics and mathematical logic. In the humanities, we encounter them beginning more or less with Nietzsche and then extending to the authors previously mentioned, many of whom, such as the authors discussed here, follow and develop Nietzsches ideas (the list of nonclassical thinkers is actually rather limited). Indeed, it may be argued that nothing like quantum mechanics appears to have been even remotely imaginable before it came onto the scene. It appears difficult to trace the quantum-mechanical epistemology, in its full measure, prior to the emergence of quantum theory, and, then, as will be seen, some of its nonclassical effects are strangers still in their quantum-mechanical specificity. In this sense the term postclassical is not out of place. Certain key elements of nonclassical thinking could, however, be traced throughout the earlier history of theoretical thinking in mathematics, science, and philosophy, which compels one to speak of nonclassical rather than postclassical thought.
In philosophical, if not physical, terms, the history of nonclassical thinking concerning causality extends at least to David Hume and Immanuel Kant or indeed to earlier critics of Sir Isaac Newton and (which is not quite the same) Newtonianism. Nietzsche (in general no friend of Kant) speaks of Kants tremendous question mark that he placed after the concept of causalitywithout, like Hume, doubting its legitimacy altogether. Rather, Kant began cautiously to delimit the realm within which this concept makes sense (and to this day we are not done with this fixing of limits) (emphasis added). This is not that far from Bohrs agenda, at least from the causality part of it (the realm within which this concept makes sense was delimited by him as that of classical physics); and Bohr might well have been aware of this aspect of Kants project, and, possibly, of Nietzsches assessment of it. On several occasions he speaks of complementarity as a rational generalization of the idea of causality (PWNB 2:41), an important point to which I shall return in chapter 2. One might also cite Ludwig Wittgensteins statement (intriguingly, in turn, immediately following an elaboration on Kant) in his Tractatus Logico-Philosophicus, published first in 1922 amid the turmoil of quantum theory prior to the invention of quantum mechanics, a statement that might have been known to Bohr at some point in his lifelong work on complementarity. Wittgenstein says: What can be described can happen too, and what the law of causality is supposed to exclude will not let itself to be described either (translation modified). Obviously, both causality and reality are at stake here and are mutually implicated. Bohrs, or Nietzsches, epistemological agenda may well be more radical and more (radically) nonclassical than Kants, especially in view of the questioning of the limits of the concept of reality it involves. Kants project, however, remains significant in this context as well, as Bohrs appeal to the concept of phenomenon would indicate, and may indeed require a rereading from this quantum-mechanical perspective. Ultimately, the history of nonclassical thought, at least of some of its key ingredients, can be traced as early as the pre-Socratic thought, as, to qualify with Blanchot, we reconstitute it now, for example, in the Heraclitean becoming or the Pythagoreans discovery of irrational magnitudes, which I shall discuss in chapter 3. Most modern nonclassical thinkers mentioned here, Bohr among them, credited the pre-Socratics with at least as much.




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Excerpted from The Knowable and the Unknowableby Arkady Plotnitsky Copyright © 2002 by Arkady Plotnitsky. Excerpted by permission.
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