Leibniz’s Theory of Bodies: Monadic Aggregates, Phenomena, or Both?

Leibniz’s conception of bodies seems to be a puzzling theory. Bodies are seen as aggregates of monads and as wellfounded phenomena. This has initiated controversy and unending discussions. The paper attempts to resolve the apparent inconsistencies by a new and formally spirited reconstruction of Leibniz’s theory of monads and perception, on the one hand, and a (re-)formulation and precisation of his concept of preestablished harmony, on the other hand. Preestablished harmony is modelled basically as a covariation between the monadic and the ideal realm. Palavras-chave Leibniz, corpos, metafísica, mônada, harmonia pré-estabelecida * Ludwig-Maximillian-Universität München KRITERION, Belo Horizonte, no 104, Dez/2001, p.33-48 02.pmd 28/9/2011, 16:49 1 2 Christina Schneider Leibniz’ theory of bodies gave rise to remarkable interpretational puzzles and controversies. On the one hand, Leibniz claims that bodies are aggregates of monads and, on the other hand, he asserts that bodies are wellfounded phenomena. The two conceptions of bodies are sometimes dubbed as “flatly inconsistent’’1. There have been several proposals to reconcile the two approaches. This paper is a new attempt to come to grips with Leibniz’ twofold conception of bodies. The resolution of the puzzle is rooted in a reconstruction of Leibniz’ theory of monads which give rise to an associated “theory of wellfounded phenomena’’. It makes use of mathematical methods and claims to be a twenty-century making sense of Leibniz’ metaphysical positions. It is somewhat like Strawson’s2 attempt to reformulate the position of a “hypothetical Leibniz’’, but, in contrast to Strawson, it is not on behalf of formulating a contrasting theory, but to present a Leibnizian portion of metaphysics worth of being thought about today. The article is organized as follows: it starts with some general remarks about the leading intuitions. Since there is no hope for a consistent story without making precise Leibniz’s conception of wellfounded phenomena and his theory of monads, section 2 is devoted to the theory of (simple) monads. Section 3 is about ideas. Based on the results of section 2 and section 3, section 4 will propose a resolution of the apparent tension between the two concepts of bodies. The upshot will be that the two “conceptions’’ are two sides of a single coin. The last section summarizes some reflections about whether a Leibnizian position can be endorsed. 1. Some general remarks The puzzle’s solution to be proposed is based on several assumptions and intuitions which should be kept in mind and are listed in what follows. First, whatever a body may be otherwise, it is a phenomenon. This assumption is rooted in Leibniz’s claim that all that which is (sensually) experienced, either in common life or in the frame of “experimental’’ science, is a phenomenon. So, for him even space and time, cause and effect are phenomena. Second, phenomena can be chimerical or wellfounded. That means they may be “true’’ or “false’’. Therefore, in the present context, they are attributed only to entities with intellectual capacities, in Leibniz’s terms: they are attributed to apperceiving monads only. 1 Adams 1983, p. 218. 2 See Strawson 1959. 02.pmd 28/9/2011, 16:49 2 3 LEIBNIZ’S THEORY OF BODIES: MONADIC AGGREGATES, PHENOMENA, OR BOTH? “True’’ or “false’’, chimerical or wellfounded, hints to some connection to the monadic realm. Therefore, thirdly, if a phenomena can be chimerical or wellfounded only if “thought about’’, reflected or apperceived, and if “thinking’’, “reflecting’’, “apperceiving’’ deal with ideas, the connection of ideas to the “monadic realm’’ has to be exploited, too. The clue to the solution is Leibniz’s claim that space and time, being phenomenal, are also ideal entities, from which “the real things can not escape,’’ as Leibniz puts it3. The coordination of space and time to the monadic realm is taken as a paradigm for the coordination of other ideas to space and time. The solution of the puzzle of bodies as wellfounded phenomena and as monadic aggregates relies on the explication of phenomena, wellfoundedness and apperception. The explication combines the two great metaphysical realms Leibniz deals with: the monadic world and the ideas in God’s mind, as well as idées innées and reflected ideas. The solution hinges crucially on the insight that for Leibniz an idea contemplated by God is strictly both: an intelligible content in God’s mind and a constituent of the best of all possible worlds. Virtually, the same holds for idées innées and ideas contemplated by finite beings. Therefore, the “relationship’’ between ideas and the monadic realm must be explained. The explanation will be a reinterpretation of Leibniz’s principle of preestablished harmony, which will make use of the “modern concept’’ of covariation. To sum up: If phenomena, wellfoundedness and apperception are explained, the solution of the problem ensues immediately. The explanation of the three topics is embedded in a reconstruction of the connection of the monadic world and the ideal realm. 2. Monads and perceptions Whereas it seems much easier to understand what an aggregate of monads (as a body) could mean, the understanding of phenomena, especially wellfounded phenomena, is much more complicated. Since wellfoundedness indicates a certain rooting in the monadic realm, a reconstruction of monads, perceptions, and the monadic realm will be given. The reconstruction will be rather informal and sketchy here. It presents the minimal assumptions needed to understand wellfounded phenomena.4 3 Gerhardt 1965a, IV, p. 569. 4 A detailed account can be found in Schneider 1998 and 1999. 02.pmd 28/9/2011, 16:49 3 4 Christina Schneider 2.1 The monadic realm The Monadology starts with characterizing monads as simple and partless, and, therefore, enduring entities. These partless entities nevertheless have qualités. Moreover, without these qualités they would not even be entities. The qualités are called perceptions and in virtue of these perceptions each monad “mirrors’’ the “world’’ from their respective situs. “The world’’, in turn, is not anything over and above the monads, their perceptions and their appetites. The task of any reconstruction is, therefore, to make explicit the strong entanglement between monads, perceptions and “the world’’. There is no monad without world and no world without monads. This means: “World’’ cannot be conceived of as being made up by collecting a heap of ready-made monads, since in that case, before being collected, monads would not have anything to perceive and would not be entities at all. But similarly, “world’’ cannot be conceived of as a certain sort of preexisting entity in which some monads are placed to perceive it (among other monads), since in that case there had to be some further structure “of the world’’ to be perceived at all. The main idea of the reconstruction basical for this article is: Monads should turn out to be welldefined substructures of the world, and the world, in turn, should be defineable uniquely by coordinated families of structures, i.e., monads. Further, starting the exposition with monads should come to the same structure, the perceptional-monadic world, as starting with reconstructing the perceptional-monadic world and then working out those substructures which are monads, their perceptions, and their situsses. Instead of going into details, some guiding and some refused paradigms in making sense of “monads’’ and “perceptions’’ will be addressed. Instead of fromal definitions an example, better a “picture’’, of the monadic world will be given. First, “monads’’ are not modelled as structureless tiny billard balls or geometrical points. They are structured entities, encompassing in some sense other entities of the same kind. Second, perceptions are not seen, even not remotedly, under the paradigm of sensual experience, faint as it may be. What could be called “sensual experience’’ belongs to the “phenomenal realm’’ and is coordinated to special higher monads as are “souls’’ or “spirits’’ only. 2.2 Monads, perceptions and appetite The structures that fit the above mentioned entanglement are special families of filters, topological spaces and their neighborhood-filters. Therefore, the monadic world, monads and their perceptions are conceptualized as topological spaces and topological (neighborhood) filters are used: Monads 02.pmd 28/9/2011, 16:49 4 5 LEIBNIZ’S THEORY OF BODIES: MONADIC AGGREGATES, PHENOMENA, OR BOTH? are special filters, the elements of the filters being the respective perceptions. The filters in turn define uniquely the respective situs and, taken together, define uniquely a topological Hausdorff space — the perceptual-monadic world. This topological space has, in turn, the defining filters as its neighborhood filters. Conversely, starting with a topological Hausdorff space, the monadic world, neighborhood filters, the monads and their perceptions, are uniquely defined. There is no topological space without its unique neighborhood filters and no families of a special family of filters without the uniquely associated topological space whose neighborhood filters they are.5 In the first place only monads at one instant of their respective histories are regarded; they are called “instanteneous monads’’. The appetite of monads will be addressed later. For the present purpose, it is sufficient to note that the monadic world is a topological Hausdorff space and the instantaneous monads are the neighborhood filters thereof. The points of the topological space are the (instantaneous) situsses of the monads. Instead of going into formal details, the intuition behind this conception may be visualized as follows: The best known topological Hausdorff space is, perhaps, the Euclidean plane, where the Euclidean distance defines the topology. It is a more specialized topology as needed here, but that does not matter for fixing ideas only. Take one point,x say, of the plane and regard all the circles around that point: { ( ) : { : | | } : , }, C x y x y r r r r = − < ∈R > 0 joining to these circles all sets, which enclose at least one of the circles C x r ( ) ; then, one gets the filter of neighborhoods of x. Such a filter can be conceived of as an instantaneous monad, the elements of the filter, i.e., the circles and the other sets can be regarded as perceptions. The x can be regarded as the situs of the respective instantaneous monad. To make sense of this identification, note that every neighborhood filter has the whole set, here the wohle Euclidean plane, as its element. This means, each monad perceives the whole world and with it all other monads (other neighborhood filters), but only confusedly. Circles with a smaller radius, or “smaller sets’’, are distincter perceptions than those with greater radius. The “smaller’’ circles intersect fewer other monads and distincter perceptions of them. The smaller circles, distincter perceptions, perceive only “neighboring’’ instantaneous monads, but of these monads, distincter perceptions. An instantaneous monad is “one’’ in the following sense: if one would leave out only one set of the filter, i.e., one perception, the remainder would not be a filter/instantaneous monad. 5 For detail, see Kelley 1955. 02.pmd 28/9/2011, 16:49 5 6 Christina Schneider The conception of instantaneous monads as neighborhood filters has also extrinsical virtues: It leads to a natural interpretation of Leibniz’s conception of space-time, it is the interpretational clue to his “principle of continuitiy’’ and, as will be shown soon, it gives rise to an interpretation of the wellfoundedness of phenomena. Keeping these intuitions in mind, one can write the monadic world as (W, T), where T is the topology and the u W ∈ are the situsses of the respective instantaneous monads Wu u W , . ∈ The elements u u ∈W are the perceptions of the respective instantaneous monad and may be, as the example with the circles in the Euclidean plane show, more or less confused. So far, appetite has not been considered. Without going into formal details, the monadic world, getting its structure from instantaneous monads or, if preferring the converse reading, having instantaneous monads as substructures, is not regarded as a “time-slice’’ where other “time-slices’’ are needed to complete the history of the monadic world. Instead, the special “series’’ of instantaneous monads are joined to monads in an ordered way. To be slightly more precise: A monad is an ordered family of intantaneous monads. This is similar to a series or sequence of instantaneous monads, with one important difference: whereas series have atmost countable members, a monad encompasses “as many instantaneous monads as are members in R “. This makes it possible to regard perceptual change as “continuous’’. Further, monads should not overlap. I.e., two different monads cannot share a perception. Mathematically, this comes to defining appetite by means of a “flow’’. As a consequence, each monad has its private history. It is rooted in Leibniz’ intuition that “time’’ (“global time’’) is not a monadic matter, but an ideal or phenomenal entity which has its foundation in the monadic reality, and that time, as physical entity, “presupposes’’ change, i.e., appetite.6 In its simplest version, a flow is a mapping Φ : R × → W withΦ( , ) 0 u u = and Φ Φ ( , ( , )) s t u =