On Monadology

In an effort to place science on religious foundations, Leibniz introduces the concept of a “monad” as the basic quantum of reality. Although, initially, monads appear to be no more than a philosophical rendering of the atomic model of the Universe, soon it becomes apparent that a monad - a non-physical atom - is a baffling concept, and much care is required to avoid oversimplifying, or, indeed, overcomplicating of the far reaching implications not dreamt of in the physical counterparts. Although I believe that, towards the end of the essay, Leibniz falls into the later trap, overall, much can be made of the interesting concept developed throughout Monadology (Leibniz, 1714).

The concept of a “monad”, as defined in the introductory paragraphs of Monadology, is nothing more than that of an elementary, indivisible object forming the world. Although far from being original, atomic models have often before proved their successfulness. Therefore, although §2 of Monadology is an obvious fallacy, as, from an empirical evidence for existence of compounds we can only reason as to an existence of, at most, simpler compounds, and certainly not deduct an existence of anything fundamentally simple, Leibniz is nevertheless justified in taking his “monads” as an axiomatic fact, an a priori, knowledge.

According to Leibniz, all monads have a common origin of creation and destruction, if indeed there is one at all, and these points can be identified with the origin and cessation of time respectively. If compounding and division are the solemn sources of an on-going change in the world, as assumed by Monadology, this is indeed a correct and important observation.

§3 of Monadology amends the definition by an important qualifier. Each monad, being completely context-free and self-contained, is not subject to a macroscopic, or, if we were allowed the term, inter-monad transformations. It must be noted that, contrary to Leibnz' own believes, once again this postulate cannot be derived from the definition in §1, and must be treated as an axiom. It must also be noted that the claim made in this paragraph, although important, is apparently contradicted lated in the essay. In paragraph §23 Leibniz talks of “receiving perceptions”, an obvious contradiction to his claims from §14 where he describes “perception” as an intrinsic aspect of most monads, in which case “receiving perceptions” from an external agent violates the claim that a change in a monad can only occur as a product of internal factors. Later, in §56, Leibniz discusses “connexion, or adaptation, of all created things with each”. This implies either overlapping of monads or some kind of inter-monadal force, either contradicting the concept of a monad's autonomy. Incidentally, Leibniz does not make it clear which of these two alternative is preferred in his essay, and indeed seems to ignore the difference and alterate between the two throughout the text.

The initial simple picture does not justify the reasoning that, later in Monadology, leads to the necessity of being attributed to God, amongst other important results. Therefore, the advancements of §9-16, although superficially inconsistent with the defining §3, are necessary to distinguish monads from the traditional physically atomic objects. In §9 and §10, Leibniz suggests that a typical monad is not a particle-like objects with few distinct attributes which distinguish it from other similar particles, but rather a complex entity resembling Plato's pure forms more than traditional elements of nature.

Probably the best way to understand the apparently inconsistent concept of an active monad is to view it as a process more than as an entity. For, although Leibniz' overview of internal change thought intrinsic to monads is flawed in that there is no reason, least of all an analytic one, to support his central claim that “every natural change takes place by degrees”, the notion of change within monads is not only plausible, but remains at the centre of effectiveness of the concept. While “trivial” physical monads are accounted for in Monadology, Leibniz concerns himself chiefly with abstract, conceptual rather than factual monads such as the souls presumably underlying every animal and human body. For the purposes of the remainder of this essay, I assert the existence of such souls without proof, and while keeping in mind that such souls do not constitute all of the monads, I will restrict the discussion only to them.

The first achievement of Monadology which Leibniz is quick to boast about, is a clever definition of perception in §14. I must admit to objections against identifying “the passing state”, or the “incorporeal automata” within monads with “perception”, the later being a concept which I find equally applicable to a corresponding state of composite bodies. Once again Leibniz demonstrates that monads are not merely concepts underlying individual objects, but more so spreading across objects to cover their external interactions and processes in which they take part. Novel to philosophy, entities formed from monads contain the interactions and processes to which they are being subjected.

While the above view is sharply different from any competing philosophy, and, arguably, Cartesian perception is a concept with different definition of applicability, Leibniz believes himself justified in using it to falsify Cartesian views of perceptions and souls (“And herein lies the great mistake of the Cartesians, that they took no account of perceptions which are not apperceived.”, etc., in Monadology, § 14).

Definition of perception is followed by a number of various definitions of varying credibility. I must admit that for me Leibniz' assignment of popular concepts to various aspects of the monads appears highly arbitrary and unjustified. I will therefore refrain from treating each of these concepts separately, instead using them in Leibniz' sense without further objections.

Bogged down in identifying the three nested types of monads - simple monads, or entelechies, souls being monads possessing more distinct perceptions accompanied by memory, and minds which are made distinct by their capacity for knowledge - Leibniz has overlooked a clean and logically appealing development. More than the outward perception from within a monad, the internal change within the monads is the inward perception of the monad or compositum by other, monads external to it. Did Leibniz choose such a path, he would arrive at the modal picture of §56 by a direct route that was both more convincing and appealing. Should he, by definition, make interactions to which a body is subjected an intrinsic part of the corresponding monad, the picture in which a monolithic, immutable monad encloses an internal flux, would be a much less clouded one.

To fully acknowledge Leibniz' intended application of “monadology”, and demonstrate its coherence when stripped from its weaknesses, I will explore the broad outlines of the interpretation sketched above.

To consider perceptions of an object its attributes does not attempt to attribute any extraordinary meaning to these perceptions. Should a patch of red be a monad, a colour-blind person's perception of it as gray does not give it an attribute of grayness, but merely an attribute of being perceived as gray. Where this, after all not so original, view shows its usefulness is when, as Leibniz correctly notes in §14, we attribute to every monad all possible, and not merely actual, perceptions of it. Such monads, consisting of fluctuating and often contradicting perceptions, some of them describing the true nature of the monad more accurately then others, are natural raw materials for a multitude of possible universes. In fact this approach is suggested throughout David Lewis's work on the plurality of worlds, although it is never, to the best of my knowledge, spelt out as acutely as it is above.

It must be noted that a monad multiplied in perspective does not in any way limit the freedom of interpretation by others. Even if the range of possible perspectives is finite, it is nevertheless large, and the choice of actualising any particular perspective may well remain entirely under control of the perceiver.

Although I will not extend my treatment of the plurality of perception to other processes that a monad may be subjected to, it should remain clear that such an extension is by all means possible. For example, a monad may be attributed all its possible ages, from negative to positive infinity inclusive, thus modelling the behaviour of personal identity throughout time, and developing Leibniz' belief in the immortality of souls and their passing into a stupor.

All such extensions increase the usefulness of the monads as tools for understanding modality. Essentially, a monad provides an immutable conceptual invariant around which modality and change can be accumulated. By capturing and isolating the difficult concepts within the elementary structures, we increase the level of abstraction of the resulting picture of the world, thus rendering it more open to our analysis.

Although Leibniz does not attribute perceptions to their subjects, he achieves a similar result by a complex picture of interacting monads. Essentially, he draws boundaries between monads as so to attribute the monad's perception of the world to itself (§56-57). The approach has a serious drawback which, despite its superficial plausibility, makes it more chaotic than the one initially outlined by myself, in that Leibniz never explains the place of unactualized perceptions in the model.

Leibniz further complicates his discussion by introducing the concept of a perfect monad - God - together with two distinct definitions of perfection, reconciliation of which is beyond me. In §41 he states that “perfection is nothing but the magnitude of positive reality”, only to retract from the view in §50, which reads “And one created thing is more perfect than another when it is found in it that which explains a priori what happens in the other; and it is because of this that we say that it acts upon the other.” Although Leibniz' formalised treatment of the concept of God in §32 through §39 are interesting, they contribute little to the general theme of Monadology, and build on even less of it.

As a final complaint to Leibniz' methods, I would like to discuss §44, which states that “For if there is a reality in essences or possibilities, or indeed in eternal truths, this reality must be founded on something existent or actual; and consequently on the existence of the Necessary Being in whom essence involves existence, or in whom it is enough to be possible in order to be actual.” It seems that, having just ventured into the modal philosophy, Leibniz fears to attribute too much reality to possibilities themselves. Instead, being unable to actualise possibilities immediately, he invents an external agent actualising them indirectly. I cannot agree with Leibniz who strives to prove the possible with and as the actual. If indeed God is a logically necessary being, His necessity surely is not the factor necessitating the existence of the possible.

An important achievement of Monadology is to provide a strong link between separate possible universes, a core of necessary abstract entities which allow us to solve such problems as the maintenance of personal identity through possible worlds. Leibniz also avoids an unmanageable randomness through his principle of sufficient reason (§32), which, although of questionable universality, leads to the “best possible universe” theme for which Leibniz is famous. In Leibniz model, all the possible worlds contain precisely the same amount of reality captured in precisely the same monads, without regard for its even most bizzare appearance.

Although much of Monadology represents a highly comparative philosophy, where similes are used frequently and often taken either too far or too literally, it serves Leibniz to introduce and develop a very novel concept which, well ahead of its times, has pioneered the way into modern modal philosophy. Ironically, Monadology is impressive for its potential, for what it could have been. Although cluttered by unnecessary axioms and controversial conclusions, it remains a novel and powerful vision of reality centred around conceptual more than physical entities.

Patryk Zadarnowski, Sydney 1998