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Leibniz: Theory of Monads

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Introduction

Whether ultimately correct or not, Leibniz rejects both Cartesianism and atomism. What ought not be missed is that throughout his objections Leibniz's focus never strays far from the mereological issues of wholes, parts, their unity, etc. Indeed, the very nature of his arguments against the mechanist project clearly demonstrate Leibniz's underlying concern for the problem of the continuum, which seems never very far from his mind. (Thompson)

In rejecting Cartesianism, Leibniz's concern is with its inability to make sense of the whole, except at the expense of the reality of the parts. In rejecting atomism, his concern is with its inability to make sense of the parts, except at the expense of the unity of the whole. Neither can provide illumination sufficient to escape from the second labyrinth, and the entire mechanist project therefore finds itself impaled effectively on both horns of a dilemma. Since the problem of the continuum has so much relevance to the unity of substance, Leibniz considers mechanist philosophy inadequate. (Brown)

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Remaining entirely in character, it should not be surprising that Leibniz's own metaphysics is most fundamentally an attempt to reconcile the mechanistic philosophy to that of Aristotle. He attempts to take the best of each of these two systems and synthesize a new theory that manages to escape their individual defects. (Thompson)  Monads are the unit of substance which supposedly bridge the gap between the old and the new, and plug the holes in mechanist theories. Thus, it is with this in mind that his argument for the existence of monads must be examined, for it is the very heart of Leibniz's theory of substance.

At the core of Leibniz's metaphysics one finds monads, which are dimensionless and "windowless" centers of force, the true substances that comprise the created universe. Infinite hierarchies of monads populate the continuum of all created things, each one mirroring the rest of the universe from its own unique point of view, expressing every other monad with a greater or lesser degree of clarity. Monads are the "metaphysical points", so to speak, which are the indivisible, unified, and simple substances that are the foundation of the created world. (Mercer)

Distinguishing Features of Leibniz's Ontology

There are two particularly significant distinguishing features of Leibniz's ontology as a whole. In brief, Leibniz's ontology remains as true to his desire to be the great reconciler as it does to his expectations for substance, epistemology, and the problem of the continuum. This ought not be forgotten amidst the details that follow.

Monads are a Synthesis of Old and New
It is not surprising, in light of Leibniz's reconciliatory nature, that monads bear hallmarks of both Aristotelian and mechanistic philosophy. In terms of the former, they do the work of substantial forms, possessing an entelechy which guarantees that they unfold through time as they ought. In terms of the latter, they do the work of atoms, explaining how features in the phenomenal world (i.e., the macro-level world) come about as a result of changes of state in the real world of monads (i.e., the micro-level world). The monad is, by its very definition, designed to leverage the strengths of the two opposing theories, while simultaneously inheriting none of their defects. (Mercer)

From this it is clear that Leibniz's theory of substance is determined by his expectations, and by the perceived failures of mechanism. In assembling it, Leibniz borrows liberally from what he considers the best features of the old and the new. Regarding those aspects in which Leibniz finds either of them inadequate, he crafts his own philosophy so that it avoids said inadequacies, essentially by definition.

Qualitative, not Quantitative
What is arguably most interesting and quite unique about this synthesis of systems is the shift in focus. To elucidate, Leibniz sees the mechanist philosophy as a fundamentally quantitative and extensive endeavor. The Cartesian defines the very essence of body as extension, which is quantitative in its extensive nature. Similarly, the atomist cannot help but construct the macro-level world by aggregation, through the grouping of many extended entities in the micro-level world, which is also quantitative by nature. Both variants of mechanism therefore sustain a quantitative and extensive view of the relationships between wholes and parts, explaining or reducing qualitative features of the macro-level world in light of or to quantitative features of the micro-level world. (Mercer)

Given the problems he finds with quantitative theories, Leibniz concludes that that the correct theory must instead be uniquely qualitative and intensive, rather than quantitative and extensive, and this unique notion is given flesh along very Aristotelian lines. Latta (1965) provides the following apt description:

Accordingly, the essence of Leibniz's argument is that a quantitative conception of the relation of whole and parts affords an inadequate theory of substance. The common element in the contrary positions of the Cartesians and the Atomists is the explicit or implicit reduction of qualitative to quantitative differences. And it appears to Leibniz that the solution of the dilemma is to be found in the opposite hypothesis, namely, that the essence of substance is non-quantitative, and that the relation of whole and parts must be conceived as intensive rather than extensive. Thus a 'simple substance' has no parts, i.e. no quantitative elements, and yet it must comprehend a manifold in unity; that is to say, it must be real, it must be something, it must be qualitative, specifically determined. (p. 27).

The suggested intensive view of the relations between parts and wholes is noteworthy for its novelty if nothing else. What Leibniz seems to have in mind is that the parts of a whole somehow "participate" in that whole, and similarly that the whole somehow "participates" in all of its parts. The nature of this participation isn't entirely clear, but it is certain that the conception Leibniz holds is not the traditional understanding of the part-whole relation. There is something deeper at work here, some understanding that is intended to allow both the parts and the whole to remain distinct and unified, the parts in themselves and the whole through its special relationship to the parts. (Thompson)

What Leibniz seeks is some sense in which the whole somehow mirrors or expresses all of its parts, containing within itself the explanation for why the parts are precisely as they are. And similarly, the parts must somehow mirror or express the larger whole as well, containing within themselves their explanations, while also mirroring the explanation of the whole, albeit with a lesser degree of clarity. The important degree of mutual inter-participation is what is key to the more organic or holistic relationship Leibniz intends. (Swoyer)

Despite the present vagueness, however, this much remains clear: Leibniz believes that the part-whole relation in genuine unities must be something far more special than other philosophical systems have taken it to be. Leibniz's use of monads is therefore intended not only to reconcile Aristotle with the mechanists, but also to lay the groundwork necessary to make such a special relationship logically possible and plausible. (Thompson)

The Argument From "The Monadology"

In the first few sentences of "The Monadology", Leibniz gives one formulation of his argument for the existence of monads, a formulation which might be described most charitably as terse. Though this is not the only argument Leibniz gives for monads, it is probably the most well known. As early as 1671, for example, Leibniz argues for monads qua indivisible unextended things, though in a much different fashion involving the proper beginnings of extended entities. (1969, p. 139-140)

Because his earlier argument is even more terse than the later argument it shall not be discussed any further. It is worth mentioning only because its similarities mark it as a clear precursor for Leibniz's later thinking on the subject. Further, Leibniz claims elsewhere that the existence of monads may be inferred from his doctrine of the pre-established harmony, though his reasons for this remain obscure. (1985, p.80)

Returning to the better known argument of "The Monadology", while it would be unreasonable to fault Leibniz for his brevity in making the argument, it is nevertheless the case that much remains to be said before the argument can be accepted, rejected, or even understood adequately. Because the monad is at the very heart of Leibniz's metaphysics, one might reasonably expect a more complete formulation of his argument to be possible, just as one might expect Leibniz's critics to focus their attacks upon that argument if monads qua simple substances are to be rejected.

For the purposes of this essay, it is necessary to understand this argument and the issues underlying it in order to make clear precisely how Leibniz takes the monad to be united and simple. The following is Leibniz's argument for the existence of monads as given in "The Monadology":

The Monad, of which we shall here speak, is nothing but a simple substance, which enters into compounds. By 'simple' is meant 'without parts.'
2.   And there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregatum of simple things. (1989, p.213)

Common Sense Observations

Relevant Observations
For Leibniz, the observations relevant to a theory of substance are those of entities in the world. As established already, Leibniz simply looks at the world and takes inventory of what he sees. Among the entities perceived he finds what might be called "macro entities" of a relatively mundane variety such as tables, chairs, rocks, streams, etc., as well as perhaps not so mundane macro entities such as plants, animals and persons. With the aid of the microscope, one may similarly perceive "micro entities" both mundane (e.g., crystals) and not so mundane (e.g., unicellular organisms). Further, with the aid of a telescope, one may perceive entities at the large end of the macro scale, if not, in fact, objects of an altogether different order of size. (Mercer)

There are two primary points of interest as regards this body of observations. The first is that each entity, because it has extension, is divisible into parts. The second is that despite this divisibility into parts, the entities in question are more or less unities in some sense; i.e., each entity is numerically one, and it is what it is rather than something else.

To put these two points a bit differently, this body of observations indicates that for all such objects there seems to be a unified whole, just as there seems also to be discernable parts, which are similarly real and unified. A third less interesting but important point is that in each case one seems to find entities at every scale. No matter how high one turns up the telescope or the microscope, one never reaches the end of things. Wherever one looks, one finds worlds within worlds.

Existing Theories

This body of observations requires explanation. More to the point, Leibniz takes this body of observations to require an explanation in terms of some sort of substance. In virtue of what is it the case that some particular entity is a whole? In virtue of what is it the case that the parts of that entity are themselves both unified and real? Further, what relations are sustained between the wholes and their parts? And finally, what conclusions may be drawn more generally once answers to these questions have been established?

These are the sorts of questions Leibniz has in mind when considering existing theories. A successful theory must address them adequately without falling into either internal conceptual contradiction or external contradiction. That is, the theory must cohere with the present body of observations, just as its predictions (if any may be made) must also cohere with both present and future observations. (Thompson)

In terms of evaluating mechanist theories, there are only two that Leibniz takes as plausible candidates, Cartesianism and atomism. As established already, Leibniz considers both of these views to be inadequate for explaining the body of observations under consideration. Having already examined Leibniz's reasons for rejecting these systems in some detail we may move directly to the next step, which involves synthesizing a new theory that avoids the inadequacies of mechanism while embracing its strengths.

A Novel Theory of Substance

If both ends of the spectrum of mechanist philosophy are unacceptable, then why not head for the middle? Leibniz is convinced of unities in the world because of a wealth of observations, and he believes both the Cartesians and the atomists to be unable to explain such unities with their theories. (Thompson, p. 24-6) What is needed according to Leibniz is a theory whose fundamental unit of substance is both real and indivisible. It must be real for the obvious reason that it simply will not do to explain what does exist by appeal to what does not, and it must be indivisible in such a fashion that it may explain the genuine unity of the observed entities in the world.

Further, it must provide a qualitative and intensive, rather than quantitative and extensive, construal of the part-whole relation, as previously discussed. Leibniz concludes, therefore, that what is needed is a new, basic unit of substance: ...physical points are indivisible only in appearance; mathematical points are exact, but they are merely modalities. Only metaphysical points or points of substance (constituted by forms or souls) are exact and real, and without them there would be nothing real, since without true unities there would be no multitude. (1989, 142)

This conclusion, which lays the foundation for the development of the remainder of Leibniz's metaphysics, owes its support to the two factors given earlier as motivations. Most central to it is the fundamental assumption that monadic unity is necessary "at bottom" for the production of all compound things. In light of this, it is possible to summarize the more complete formulation of Leibniz's argument for monads as follows:

P1       Common sense observations show that real, unified entities exist.

P2       What is real may be explained only by appeal to something real.

P3       What is unified may be explained only by appeal to something indivisible.

C         Therefore, the explanation for such entities in the world must involve real and indivisible substances, namely, monads.

This bears little relation, prima facie, to the less detailed argument given in the first two sections of "The Monadology", but it is nevertheless reducible to that argument. P1 amounts to nothing more than the initial premise that compounds exist. P2 and P3 do not appear at all in "The Monadology", but it is tolerably clear from the preceding discussion that these principles are indeed assumed by Leibniz. Finally, the conclusion is just a restatement of the conclusion that monads exist. Again, to restate the argument more succinctly: compounds exist, therefore simples exist.

The remainder of Leibniz's metaphysical deductions in "The Monadology" follow from this more complete formulation at least as well as they follow the abbreviated version. Because monads must be both real and indivisible, Leibniz may argue that they can have neither extension nor form and must therefore be immaterial. Because they cannot be divided, Leibniz may still maintain that they cannot go out of existence in any natural way, by the dissolution of parts. Similarly, they cannot come into existence in any natural way, by the aggregation of parts, and so forth. Thus, this more complete formulation of the argument acts as a "drop in replacement" for its far more concise sibling.

Conclusion

To summarize, Leibniz's argument for monads is an enthymeme, an argument with an implied premise. Examining the logical derivation suggests a line of thought that Leibniz's other writings explicitly affirm, namely, that there is no reality without unity. With this additional premise in hand, the argument for monads is rendered formally valid. What's more, this additional premise provides a starting point for untangling the issues previously suggested as problems for monadic simplicity.

The close tie between reality and unity prompts one to consider what Leibniz means by 'simple' in a different light. It seems that what he intends in his argument for monads is not merely that they have no parts, but rather that they also include a kind of indivisibility, an inability to be divided in any way that destroys them. If there is no reality without unity, then things that are fatally separable and thus not unified are not intrinsically real. The relation between reality and unity helps suggest the fatal inseparability criterion for simplicity.

Further, it also seems that mereological simplicity and fatal inseparability are but negative entailments of a more positive construal of simplicity, namely, ontological simplicity. A thing is ontologically simple if it stands alone, or described negatively if it is self sufficient in the sense that it bears no internal relations of ontological dependence to any other thing. Such an understanding of simplicity resolves the problems raised previously for the mereological construal, helps to make sense of Leibniz's argument for monads, and coheres nicely with the various other texts in which Leibniz uses the term.

References

Brown, Stuart. The Young Leibniz and His Philosophy. Dordrecht: Kluwer AcademicPublishers, 1999.

Leibniz, Gottfried Wilhelm. (1969) Philosophical Papers and Letters, 2d ed. Translated and edited by Leroy E. Loemker. Boston: D. Reidel Publishing Company,

Leibniz, Gottfried Wilhelm. (1985) Theodicy. Translated by E. M. Huggard, edited by Austin Farrer. Open Court Publishing Company.

Leibniz, Gottfried Wilhelm. (1965) The Monadology and other Philosophical Writings. Translated and edited by Robert Latta. London: Oxford University Press.

Leibniz, Gottfried Wilhelm. (1989) Philosophical Essays. Translated and edited by Roger Ariew and Daniel Garber. Indianapolis: Hackett Publishing Company.

Mercer, Christia. Leibniz's Metaphysics. Cambridge: Cambridge University Press, 2001.

Swoyer, Chris. (1995) Leibnizian Expression. Journal of the History of Philosophy 33 (1), 65-99.

Thompson, Garrett. On Leibniz. Belmont: Wadsworth Publishing Company, 2001.

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