I came across Richard Halpern's book on Leibniz in the old fashioned way -- by perusing the shelves at my local bookstore. While I'm not normally a big reader of academic secondary literature (unless we're counting Deleuze's readings in this category) I thought I'd bow to serendipity and take in a contemporary perspective before returning to The Fold. It turns out that Halpern has concocted an interesting and vaguely Deleuzian reading of Leibiniz that focuses on the use of analogy in his philosophy. Since Halpern is a retired literature professor, it's not surprising that he begins by examining the explicit metaphors that appear frequently in everything from Leibniz's letters to his most abstract writings. But Halpern's thesis is much broader than a merely literary one. He wants to connect Leibniz's writing style to the content of his philosophy and show us how one of the distinctive things about Leibniz is the way he maps different areas of knowledge onto one another, folding them over, as it were, till they productively touch, thereby creating synthetic concepts that borrow from the many disciplines that interested him. It's a convincing portrait of "a philosopher in motion" (as the subtitle has it) -- an intellectually restless man often called the last "universal genius", who made major contributions in many fields, and yet who curiously never produced anything like a magnum opus comparable to Spinoza's Ethics. If there's anything like a flaw in the book, it would be Halpern's own restlessness and corresponding lack of depth. Not infrequently, he will open up an interesting and complex issue only to make a fairly summary pronouncement about it before moving on (eg. the discussion of panpsychism on pg. 134). In fairness though, this approach not only suits his own thesis, but keeps the book to manageable dimensions. Overall then, the book didn't do that much to deepen my understanding of any particular concept Leibniz created, but it did give me a better appreciation of his breadth of thought, as well as make me consider his style of writing for the first time. I think it could also be a useful and accessible (if somewhat unusual) introduction to Leibniz for someone who isn't going to read the primary material.
One of the reasons that Deleuze associates Leibniz with the Baroque is his aesthetic and philosophical obsession with the concept of unity-in-variety. The way this description applies to the monad is pretty obvious, but it fits just about every metaphysical concept Leibniz created as well. This is the best of all possible worlds because it harmoniously includes maximal diversity. Every body supports an entire world of smaller bodies within it ad infinitum. A single clear perception is a selection or highlighting or synthesis of the confused murmur of an infinity of tiny microperceptions that extend to the whole universe. While Leibniz himself always seems sanguine about the coexistence of these two dimensions, we might say that the book's main aim is to show us the many ways in which the principles of unity and variety tug him in opposite directions without pulling him apart.
Accordingly, Halpern provides us with a variety of illustrations of how this tension works. For example, he shows us how Leibniz has a tendency to overload his writing by "clumping" metaphors. Instead of just picking one analogy to illustrate some philosophical point, he provides a whole related group of them. Yet instead of simply reinforcing his main point, these metaphors often end up complicating it in unexpected ways. Each of them is different enough that what is supposedly a literary device for reducing abstraction and confusion can actually generate even more of it. For Halpern though, this is not merely a literary quirk. It's indicative of a whole style of thinking that he calls "conceptual blending". Leibniz is constantly mapping different areas of knowledge onto one another even when he doesn't always develop these connections as explicit analogies. But these isomorphisms don't end up repeating an idea so much as putting it in variation. Just like with the literary analogies, we're soon confused about which domain provides the canonical model of a concept, and which constitutes its copy. There are so many analogies that theoretically converge on a single point that in practice we are led off in divergent directions.
To illustrate this effect, Halpern devotes a long chapter to comparing the monad to an infinite mathematical series (eg. the harmonic series). The analogy is fairly obvious. Each monad perceives the entire world. But this world is constructed of other monads with the same type of perception. So the internal state of each monad at a given moment would consist in certain large clear terms that correspond to other monads it finds itself closely connected to, together with a whole infinity of smaller confused terms that correspond to monads that are 'further away' (in some topological sense -- monads have no extension and no location in extensive spacetime). And we can redouble the same analogy by considering the second (and third, and n-th) order effect whereby each 'other' monad contains a perception of the 'original' one, which 'original' in turn contains a perception of this image of itself ... creating an infinite series like the reflections of two mirrors facing one another. In fact, the monad is analogous to an infinite series of infinite series of ... remarkably like Indra's net. This already makes the monad pretty complicated.
Halpern carries this analogy deeper by pointing out that so far we haven't actually characterized the monad in itself, but just its series of perceptions. The monad itself would be the law that defines the successive terms in the series (eg. ∑(1/n) in the case of the harmonic series). This law lays out the entire series of the monad's perceptions all at once from the beginning. It unifies the monad as a substantial entity with a predetermined set of perceptions that are a consequence of its essence, and not simply the result of randomly bumping into other monads. This is a crucial feature of Leibniz's "windowless" monad, which somehow packs its entire history -- the sum total of everything that will happen to it and everything that can be truly predicated of it -- into a simple definition. In itself, each monad is a soul existing outside of space and time, but it unfolds in a law-like manner within it. Perhaps led by my mention of the harmonic series, the mathematically inclined may justifiably wonder how any such series of series could converge and how any such law could be specified. It seems to strain credulity to suggest that the infinite variety of a single monad's predetermined perceptions could be unified by a single formula, and yet we need an endlessly reflecting infinity of these to compose a harmonious world. In short, the monad seems to be an almost impossibly perfect concept.
Halpern completes the analogy between the monad and an infinite series by suggesting that this ideal completeness gives the monad precisely the ontological status often attributed to mathematical objects themselves. They exist outside of space and time, in some noumenal realm, and yet they can be realized approximately within it, in exactly the way a vibrating string realizes the harmonic series. So perhaps a monad is not so much like an infinite series as it is an infinite series -- its substance is mathematical. What begins as a straightforward analogy carries us to the point where we become confused about which of its terms is the 'real' one. And yet Halpern concludes by observing that even at this point, we cannot simply identify a monad with a mathematical series. There's still more to the concept than this. In particular, it's not clear what it would mean for a mathematical object to be free, as Leibniz believes the monad to be. The isomorphism between the monad and an infinite series is not the only possible perspective on the concept. As deep as they may go, for Halpern, Leibniz's analogies never provide a definitive perspective. No analogy is perfect, which is why he adds another and another, in an infinite series whose path to convergence gets more and more complicated.
We could read through Halpern's whole book by duplicating examples like this one. The very substance of Leibniz's concepts are these harmonious isomorphisms, and yet their endless multiplication seems to suggest that there's really no 'best' analogy. Despite these spiraling levels of complexity and recursion, he always seems to complacently believe that everything will converge in the end. There's a striving towards unity that is perpetually mired in detour. But in the interests of time, let me skip to what I thought was the best chapter in the book, which I also think most cleanly illustrates this war between the centripetal force of unity and the centrifugal force of variety. Chapter 19 is entitled: "Dark Leibniz".
Leibniz was, infamously, an optimist. He claimed we live in the "best of all possible worlds". God has created the world in such a way that every part of it, every monad, is harmoniously adjusted to every other according to a principle of maximization. This is the famous doctrine of "pre-established harmony" that explains not only how an infinity of different monads can coexist, and even how an extensionless monad's perceptions can miraculously correspond to a soulless and mechanical matter's motion without any possibility of causal interaction between these. Halpern, however, shows us a number of passages where the sunny Leibniz seems to have a pretty dark imagination. His Theodicy particularly seems to rather vividly imagine the sufferings of the world before rather blandly defending the idea that they must all be for the best. In fact, there even appear to be moments in which Leibniz imagines a somewhat sadistic God who voluntarily adds suffering to his creation to enhance its overall aesthetic effect in the way a composer enhances the glory of a harmonic resolution by a preceding dissonance. This immediately brings up the question of which metric we use to judge this world 'the best'. We can think of any number of things that could be maximized, and it's hard to see how even God could make it all optimal on every dimension all the time. As a result, it's easy to turn Leibnizian optimism inside out -- "the best of all possible worlds" can quickly become "this world is as good as it gets". The latter implies a sort of dark optimism that borders on Stoic fatalism. This world is constant suffering and misery, but rejoice, ... any other would be even worse! Here it feels like the sheer variety of possible worlds threatens to totally overwhelm us, and the harmonious unity we're promised acts almost like a consolation prize. And indeed, this is how Leibniz's pre-established harmony appears to many folks. Which leads Halpern to astutely observe that, "Leibniz's genius was to have produced an almost universally repellent form of optimism -- one that is therefore productive of pessimism" (pg. 195). The precarious balance between unity and variety can end as a moral war between light and dark. And Leibniz chose both sides in different ways.
