Postface: The Limits of Berkeley's Natural Philosophy (English version) Stephen H. Daniel The essays of this volume are avowedly concerned with Berkeley's scientific thought and the epistemological presuppositions that inform it. Such discussions are not uncommon, for scientific enquiries often raise epistemological questions, just as epistemological questions raise metaphysical issues, and they in turn have theological or moral implications. In Berkeley studies in particular, questions about microscopic observation, minima sensibilia, or the role of geometry in mechanics generate enquiries about how such topics define the possibility for science itself. Discussions about how Berkeley resolves issues regarding the heterogeneity of visual and tangible ideas turn into discussions about the experience of their regular association. This in turn raises questions about causality and will and ultimately about the divine guarantor of the connections of our ideas. In this collection, however, something more seems to be at stake. Here mathematical and scientific issues and concepts seem always to be conditioned by epistemological, metaphysical, and theological considerations. Why that should be the case reveals something about Berkeley that we often overlook, namely that his various doctrines are linked to one another in much more structurally integrated ways than are typically acknowledged. My remarks are intended to indicate why Berkeley's doctrines in mathematics, optics, and physics-and for that matter, epistemology and metaphysics-exhibit such structural integration. I propose that this can be done by shifting the discussion of his doctrines away from an account in which objects are understood first as isolated entities (e.g., simple ideas, corpuscles of matter) to an account in which ideas are always already related in systems of signs. For Berkeley, to think of any thing-whether it be a geometrical figure or a visible or tangible object-is to think of it in terms of other things like it: as he remarks in New Theory of Vision, a thing "must not be entirely new, but have something in it old and already perceived by me" (NTV 128). We cannot assume, as do Locke and Boyle, that things in our experience can be dissociated from the semiotic contexts that identify them in the first place, for to think of a thing apart from its place in a network of sign relations is to abstract it from the very environment that makes it intelligible. It is no wonder that, as essays in this collection demonstrate, Berkeley shifts away from a Lockean framework to one in which comparisons with Malebranche and Leibniz make more sense. Indeed, the story of this shift can be told using these essays. For example, according to Locke we know reality insofar as our ideas represent primary qualities in ontologically distinct substances. But as George Pappas notes, Berkeley rejects Locke's attempt to ground the existence of such independent substances on an abstraction (viz., extension). This does not mean that Berkeley denies the existence of real things; rather, according to Atis Zakatistovs, he redefines them in terms of regularities in our experience guided by practical concerns. For Berkeley the real is not revealed microscopically but (as Margaret Atherton points out) as the 2 regularity of the connection of ideas. Philippe Hamou identifies such regularity in terms of networks of signs. Those semiotic networks are comprised of terms (e.g., visible or tangible ideas) that are ordered along lines that guide scientific inferences and everyday decisions but are not true by definition or necessarily guaranteed by God's uniform operation. In Berkeley's instrumentalist way of thinking, Dominque Berlioz observes, a science (e.g., geometry) substitutes a system of signs for a schema that purports to relate objects to one another. Such substitutions do not reveal any speculative truth about the way things are related in themselves, and they do not claim to describe an ontology of relations or the limits of science or metaphysics. Rather, as Jean-Michel Vienne suggests, by appealing to "notions" they simply show or provide a display of how ideas are intelligible in terms of either (a) the "useful fictions" of science that organize phenomena (e.g., force, attraction, gravity) or (b) the metaphysical concepts (e.g., grace, mind, will, God) that account for (and thus transcend) the things we perceive. David Raynor shows how notions of the former type provide the minimal limits of experience, as in the case of optics or mechanics where the minimum sensibile is considered the limit that makes experience determinate. Sébastien Charles and José Antonio Roblés indicate how notions of the latter type mark the maximal boundaries between science, on the one hand, and metaphysics and natural theology, on the other, by alluding to the causes of experience and Creation in terms that exceed (and thus specify) the limits of what can be known. By recognizing Berkeley's use of such limit-concepts, we are able to appreciate why doctrines in his natural philosophy inevitably raise seemingly non-scientific issues, for those issues are already implicit in the ways in which those areas of scientific enquiry or mathematical or scientific objects are differentiated. For example, in the New Theory of Vision (1709) Berkeley indicates that the discussion of visual ideas must be framed in the context of tangible objects, because only another kind of sensible object could serve as a limit-concept for visual objects. In the Principles (1710) and Dialogues (1713), he shows how an independent material world could not serve as the limit-concept of ideas, for the existence of an independent, "external" world in no way helps us understand how ideas constitute a domain. But our recognition of the domain of ideas as a domain requires that there be a limit in terms of which ideas are "com-prehended" as ideas. Such a limit could not itself be an idea, for that would beg the question of its own selfidentification. There must be something else, then, that "comprehends" ideas as ideas-and thus serves as the limit (or "limiting concept") of ideas; and that, of course, is mind. We need not stop here, however, for as De Motu (1721) demonstrates, the defining practices and limit-concepts of science and epistemology themselves are properly the concern of metaphysics, theology, and morality. And in Alciphron (1732), in the passages on "notions" added to the revised editions of the Principles and Dialogues (1734), and in Siris (1744), he proposes strategies for conducting those discussions. At each step in this process, Berkeley insists that the topic with which he is concerned can be understood only by recognizing its features in terms of what it presupposes. In this regard, the De Motu is particularly helpful for understanding the place of his scientific work. There Berkeley notes that the principles, objects, and abstract geometrical strategies adopted in experimental philosophy apply only to what we experience. 3 For example, he argues, mechanics or physics is properly concerned with the study of the regularity of motion. But we cannot explain why motion in the physical universe should behave in a rule-governed fashion without appealing to a metaphysical cause. Even to imagine the motion of physical objects requires that we consider the cause or principle of such motion, because the concept of a cause of motion is already implicit in stipulating the limits of the proper domain of physics. So the stipulation includes acknowledging a limit to the domain that itself is not included in the domain. As Berkeley puts it in De Motu, metaphysical principles and real efficient causes of the motion and existence of bodies or corporeal attributes in no way belong to mechanics or experiment, nor throw light on them, except in so far as by being known beforehand they may serve to define the limits of physics, and in that way to remove imported difficulties and problems. (DM 41) As in the case of other disciplines, the limits of physics are not part of physics even though they indicate which kinds of problems are appropriate for it. By knowing these limits we know that the proper concerns of physics are the motion and existence of bodies. But we also know that the principles and causes of motion and existence are intrinsically related to bodies as their principles and causes. This means that physics cannot be fully explained without invoking concepts (e.g., mind) that go beyond what is properly the domain of physics. To invoke such concepts, however, threatens the intelligibility of terms in a science by dissolving the bounds that differentiate and relate the sciences to one another. Faced with that prospect, Berkeley recommends that we respect the differentiation of the sciences by acknowledging their limits. But if anyone were to extend natural philosophy beyond the limits of experiments and mechanics, so as to cover a knowledge of incorporeal and unextended things, that broader interpretation of the term permits a discussion of soul, mind, or vital principle. But it will be more convenient to follow the usage which is fairly well accepted, and so to distinguish between the sciences as to confine each to its own bounds. (DM 42) Admittedly, the motions or existence of bodies can be explained physically by using notions such as force or attraction. But to think of souls, minds, or vital principles as the determinate causes of bodily motion is to risk ignoring how mind serves as the limit-concept of physical objects. In a sense, mind-ultimately the divine mind-is the "real efficient cause" of ideas. But mind is not an object of physical enquiry and cannot be associated with bodies other than as the metaphysical principle in terms of which bodies are identified as scientific objects. To extend natural philosophy beyond experience to include mind or God would apply the notion of physical cause illegitimately. But Berkeley is careful not to treat minds as if they were things in the world, for mind as a limit-concept cannot be described as a cause in the same sense as causes in the physical world. Instead, mind serves as the principle for the experience of things in the physical world. No doubt, we can still give a metaphysical account of the motion and existence of bodies, but in such an account the cause of motion must be understood as nothing more than the limitconcept for physics or mechanics in terms of which all regularity of motion becomes intelligible. The key, then, for understanding the structural integrity of Berkeley's thought lies in 4 seeing how he uses these boundary or limit-concepts to differentiate and relate different components of his philosophy. Because these limit-concepts identify the objects proper to a science, they cannot themselves be understood in terms of the strategies adopted, for example, by geometry, optics, or mechanics. Nor are they comparable to the things they constitute. Rather, they designate those things as interrelated components of sign systems and thus provide the basis for the claim that those components are connected in more than simply accidental ways. As Berkeley remarks in the Dialogues, this assumption is the key that guarantees that our knowledge is grounded in the nature of things, for "the more a man knows of the connexion of ideas, the more he is said to know of the nature of things" (D 245). That is, to know the nature of things is to understand them in terms of their connections, for it is by means of their connections that they are identifiable and intelligible in the first place. Such understanding is most evident when a science describes its objects as inherently related by a concept that differentiates (and thus associates) objects. What makes an idea "like nothing but an idea" (PHK 8) is the fact that it, like all ideas, is differentiated from what is not an idea by its limit-concept. As I have suggested, in the epistemology of ideas, the limit-concept is mind. In geometry, the limit-concept is a point; in optics, the minimum visibile; in mechanics, the minimum tangibile. Each science has limit-concepts that define the proper objects and boundaries of the science but which themselves cannot be described in terms of the science. A point is not a geometrical object (e.g., an infinitely short line) but the limit of geometrical objects, and minima sensibilia are not objects of scientific enquiry but the limits of such enquiry. Minima sensibilia are not simply very small perceptions, they are all but insensible, almost not even objects of sensation. But that does not mean that they are not sensed. Indeed, they are sensed precisely as the limits that give the objects they constitute their identities. Because such limits inscribe the bounds for which objects can be sensed, they themselves cannot be described other than by invoking a vocabulary that is not formally part of the area of discourse they inscribe. That means that in order to speak about the limits of one science, we have to appeal to another in terms of which the limit-concepts of the first are intelligible. That, in turn, opens the way for showing how the different vocabularies are integrally related. This structuralist approach to knowledge reveals how, for Berkeley, everything is a component in a network of signs, and each network is validated to the extent that it can be used as a substitute for another. Geometrical figures or drawings can be signs of physical objects, microscopic observations can be signs of naked-eye observations, and visible ideas can be signs of tangible ideas, all because heterogeneous things can be imagined in relations that are structurally substitutable. Of course, it is possible to imagine something apart from its relations (PHK 89), that is, apart from its being a sign. But to think of such an idea (e.g., the redness of an apple) would be to remove it from lived experience and thus to treat it as an abstraction. Unlike Malebranche, who argues that the world we know is the world as structured by God, Berkeley thus suggests that practical human interests generate different systems of signs or instrumental structures that can be used to describe reality. In fact, it is because of the inherently semiotic character of mathematical and scientific ideas that they can be substituted for one 5 another. They can serve as the basis for a knowledge of nature, however, only if nature itself is a divinely regulated network of signs in which things are understood as related to one another. As Berkeley remarks about mathematical signs in his third edition (1752) addition to Alciphron: The signs, indeed, do in their use imply relations or proportions of things; but these relations are not abstract general ideas, being founded in particular things, and not making of themselves distinct ideas to the mind, exclusive of the particular ideas and the signs. (Alciphron VII.12; Works III: 305) By understanding things in nature in terms of their relations or connections, we understand them as signs of one another. In this way our knowledge of "the nature of things" depends on our thinking of them in terms of semiotic structures that are defined by limit-concepts and notions of science that organize our otherwise fragmented ideas. But to speak about these limiting and organizing principles, we have to invoke topics beyond the purview of science (e.g., mind, freedom) precisely because they legitimate enquiry into the transcendental conditions of experience. Along with highlighting how Berkeley insists on not transgressing those limits, the essays in this collection thematize his doctrines on the inherently semiotic character of ideas and his treatments of mathematics and science as substitutable codes. Such a shift in focus is crucial if we expect to appreciate how, for Berkeley, the immediate objects of sensation are not fragmented, simple ideas but rather ordered, interconnected experiences. In this way we are invited to think of Berkeley's scientific and mathematical contributions less in terms of Locke and more in terms of Malebranche and Leibniz.