Commencement Address by Dr. Klaus Brinkmann, May 16, 2010

Commencement Address delivered by Dr. Klaus Brinkmann
Law School Auditorium, Boston University, May 16, 2010

Dear graduates, dear parents, dear guests,
When I was asked to be the Faculty speaker today, I had the spontaneous idea that I would take you on a journey into the infinitely small and the infinitely large and that I would introduce you to these topics by talking about the mysterious world of Leibnizian monads. Now why might you, or anyone else, ever develop an interest in Leibnizian monads? Well, I hope that this will become clearer as we go along.

Leibniz (1646-1716) was a German philosopher of the 17th and beginning 18th century, a true polymath, a logician, mathematician, metaphysician, diplomat, an expert in constitutional law, even an engineer. Independently of Newton, he invented the infinitesimal calculus. He also invented the so-called binary system (the representation of numeric values by zeros and ones) on which our modern computer architecture is based. Still, he is relatively little known outside of philosophy, although you may be familiar with one idea for which he is famous, and that is that this world, the world we live in, is the best of all possible worlds. To many, this has seemed a statement that jars with our experience and the facts. Another philosopher, Arthur Schopenhauer, quipped that this world must be not the best, but surely the worst of all possible worlds, and if it was even a tad worse than it already is, it would completely collapse. The truth, as we say, may be somewhere in the middle. The American composer Leonard Bernstein (of West Side Story fame) composed an opera titled Candide (1954) which in turn is based on Voltaire’s satirical novel of the same name. In it, the idea of this being the best of all possible worlds is savagely ridiculed and made fun of. So you see, Leibniz has had some influence even on American culture.

But I wanted to talk specifically about this other famous concept of Leibniz: the monad, from the Greek monas, meaning the One, or unit). Leibniz received his Bachelor’s degree at the age of 16 and soon afterwards defended a Master’s thesis on the principle of individuation. It seems that this is a topic that occupied his philosophical mind throughout his life. Why, you might ask, is individuation, or: what it means to be an individual, an interesting concept, not just for philosophers but potentially for anybody? Well, it raises the question precisely of “What makes me me?” And that seems to be an intriguing question that everybody might at some point ask of themselves: Who am I, really? Incidentally, very recently there was an exhibition at the Museum of Science here in Boston with the title “Identity: An exhibition of You”, and it was advertized under the slogan “What makes you you?”. And in the magazine Discover I saw an article entitled “What makes you uniquely you?”. So the question seems to be attractive enough to devote magazine articles to it and organize exhibitions around it, attractive enough to become the object of public attention.

Leibniz was fascinated by the very same question, but he understood it in a broader sense, not just in the sense of “What makes me me?” but in the sense of “What makes anything the unique thing that it is?” And to this he gives essentially a twofold answer: First, for a thing to be what it is it must be one. And second, for a thing to be what it is it must be unique, an individual that cannot be mistaken for any other individual, be they ever so much alike.

Now it seems to be obvious that in order for something to be an individual it must be one thing, so we would normally take it for granted that anything that is an individual is in virtue of that very fact also one thing. But Leibniz didn’t think that we could take being one for granted so easily, because he believed that something may exist and yet not be one. And, more importantly, he believed that if something is not one thing, it is not even real. In a letter to the French logician and theologian Antoine Arnauld (1612-1694), Leibniz wrote: If something is not one thing, it is not one thing, meaning thereby that if something is not one unified thing or individual then it is not even real. So, for something to be an individual, it must be one thing, and only if it is one thing is it also real.

But why would it even be a problem to explain why an individual thing is one thing? Isn’t that obvious?

Well, not really. It turns out that Leibniz’ line of thought goes back to an old problem that already plagued the ancient Pre-Socratic philosophers. The problem has to do with the divisibility of things. If things are divisible, are they divisible infinitely, without end, i.e. ad infinitum, or does the division necessarily stop somewhere and arrive at indivisible elements, which already the ancient Greeks called atoms? Others thought it hard to believe that there are any indivisible building blocks, so they argued the division must eventually terminate in nothing, or at least in nothing that would still be spatial, so that things could be divided until there is nothing left to divide. Infinite division would ultimately ends with points, they argued, and as points are no longer spatial, there is nothing to divide anymore. In either case, division comes to an end.

But this is not a happy ending. For it generates a paradox that was made famous by another pre-Socratic philosopher, Zeno of Elea: a so-called antinomy, the worst form of self-contradiction. It goes like this. If things are finite in number, then they must be infinite in number. That’s an antinomy. If something has one property, then it cannot have this property, by must have the opposite property. It’s as if thinking seizes up in a kind of paralysis. The argument goes somewhat as follows. If things are finite in number, they must be many. If they are many, they must be distinguishable. If they are distinguishable, they must be separate from one another. So between any two things there must be a separator that keeps them separate (be that another solid thing or air, or just space). But then the separator must be separate from what it distinguishes and thus there must be another separator between the separator and what it separates … You get the idea. So if you start with only two distinct things you end up with infinitely many distinct things. Alternatively, if the division ends in points which are not spatial anymore, then everything zips together into nothing, because no matter how many points you add up, the result will always be nothing. So, if there are a finite number of things and things are divisible until we reach the point that no longer possesses spatial extension, then the finite number of things will suddenly turn out to be a sum of zeros, and that sum will always also be zero, even if we were to gather together infinitely many of them.

There was a Pre-Socratic philosopher, however, who called Zeno’s bluff, if we want to call it that. His name was Anaxagoras. He reasoned that there cannot be indivisible ultimate physical units that make up reality, presumably because as long as they are spatial they should still be divisible. So it would be arbitrary to just posit the existence of indivisibles in space. Nor can the ultimate units be points without extension. Was there another possibility? It takes a really smart person to solve an antinomy, and Anaxagoras was that smart person. He concluded that there are no ultimate indivisibles, no atoms. Nor does division end in non-spatial points. Instead, things get infinitesimally small as you keep dividing them, such that there is always a smaller one, until the end of time. So in fact there are infinitely many ever smaller things, none of them being the smallest, and this getting smaller of things continues infinitely.

This is the conclusion that Leibniz reached also. But he went a step further. If this is true, he thought, then matter must not only be infinitely divisible but in fact infinitely divided. If it were only infinitely divisible, then it would come in aggregates and composites, in actual wholes that are potentially divisible into infinitely many parts. But why would there be wholes, unities of parts, in the first place? It would be more rational to assume that matter by itself does not form wholes, it only consists of parts. Which means: taken by itself, matter will forever fall apart into smaller and smaller bits and pieces and if there were only matter, there would be no wholes, no composites, no aggregates, and no individuals. And without wholes and individuals, there would be nothing really real, because there would be nothing really there – there would be no ‘there’ there, only an endless diminution of less and less. Reality would simply fritter away, disperse, and become infinitely rarified.

So there must be something that keeps things together, that prevents the parts from falling apart, something that explains the existence of wholes and individuals. Again, that something cannot be matter itself since matter will forever fall apart, dissolve, not into nothing, but coming closer and closer to nothing. But there would never be one thing. This something that holds the parts together is the monad. The monad is the unifier, the glue that keeps the parts unified. And if it is not matter, something physical, then it must be something like a soul, or a mind. And so, according to Leibniz at least, minds are the true realities that hold our bodies together. In fact, each person is a monad that sits at the center of an infinite aggregate of other monads that form the body of the person. We could also say that this central monad represents our individual personality.

Also note: If there are infinitely many parts of matter, there must also be infinitely many monads that bind the parts together. Look at it this way: For every two parts there must be a monad that holds them together. And because there are infinitely many such pairs of parts there must be infinitely many monads. Now we see why Leibniz wrote to Arnauld that unless something is one thing, it is not even a thing, something that is really a whole and really exists, because it does not forever fall apart.

But remember, Leibniz also maintained that for something to be an individual also means for it to be unique, that is, unmistakably different from all other individuals. If monads are these individual souls or minds, then how are they unique? So we return to the earlier question: What makes us uniquely who we are? What makes me me?

Normally we would assume that an individual is unique, if it possesses just one thing, one characteristic that it does not share with anything else. But this turns out to be difficult to maintain, because none of our traits or characteristics is really unique. None of them is really owned by exactly one person only. Take the talents or character traits people have – one is good at math, another good at playing a musical instrument, yet another is always generous, and yet another is funny, one is smart, the other is melancholy, one is business savvy, another is a great athlete … and so on and so forth. But, there is no person who is the only person ever to have had one of these traits or characteristics. So, none of these traits can really make us unique.

The only unique thing about us would be that we are we, and not someone else. But again, just being us, or just being me, is not enough to distinguish me from anybody else because everybody else is also a ‘me’. When we ask “Who is there?”, we all say “It’s me”.

Uniqueness is a tricky concept. Leibniz believes that in order to capture the uniqueness of a monad, or the uniqueness of a person, we would need to be able to give a description that completely exhausts a person’s traits and characteristics and relationships. It soon turns out, however, that such a description would be infinitely long so that we could never get to the end of it. For, in order to uniquely determine who I am I would have to know my place in the history of the universe, and that would include a description not only of myself, but of all the people who are related to me, and all the people to which those people are related, including their forebears right until the beginning of mankind.

Leibniz really thought that it would take a description of the whole history of the universe and of everything that ever happened in it and would happen in it in the future, if one wanted to describe the uniqueness of just one individual. The reason for this is that in his world everything is connected with everything else, nothing is entirely isolated. So everything stands in some relationship to everything else. Surprisingly, then, to describe exhaustively just one individual would require to describe them all, past, present, and future.

That sounds fantastical, but it is perfectly logical from Leibniz’ point of view. It goes without saying that no human being would ever be capable of completing such a task. Not even the most powerful computer of all times could ever finish it. But this is alright, because if we could completely decode our uniqueness, the mystery of being me, the mystery of being human would be lost. To be me is in part to be prevented from fully knowing who I am.

But we haven’t quite finished our exploration of what it means to be uniquely me yet. What Leibniz has told us so far is by no means sufficient to make each one of us unique. To the contrary, he has just done the opposite; he has made us all the same. For we have just seen that to describe exhaustively one individual means to describe the entire universe. But we have only one universe, and so the exhaustive description of each individual will always be the same – the description of the one universe of which we are all just one tiny little part. And so Leibniz does indeed conclude that each monad is a “living mirror of the universe”. Each monad, each individual, each person, carries the entire universe within themselves. And it is the very same universe for each of them, for all of us. Strangely enough, it seems that being unique and being the same as everybody else are not two incompatible things. On the contrary, it is because we all carry the same world within ourselves that we can communicate with each other about a shared reality and yet remain uniquely individual at the same time.

Still, we must ask once more: What makes us uniquely who we are? In the wonderful world of Leibnizian monads, it is the biography of each individual that does so, but also the particular perspective from which each one of us views the world, as well as the scope and clarity of our perception of the world. These factors taken together define the unique personalities that we all are. They distinguish us from everybody else, but they also ensure that there is a reality that we all share with one another. Or, to take up the argument again that I offered earlier about what makes us unique, we could say: We are all, each one of us, a world of infinite possibilities of which each one of us uniquely activates a particular combination at a particular time in the history of the world, and this conjunction of a set of possibilities at a certain juncture in the larger scheme of things is what makes us unique.

The world of Leibnizian monads is much more mysterious than I have let on, but I cannot really go into it much further. Just two more things: The monads are always active, because they are alive. There are no dead monads. Their activity consists in a striving towards ever more clarity of perception and understanding. They always seek to realize a built-in measure of perfection, which is why Leibniz calls them entelechies, a word borrowed from the ancient Greeks meaning things that have a standard of perfection or a goal built into them.

He also says, that all monads are windowless, nothing comes in or goes out. He means to say that there is no real physical interaction between bodies and minds, there is only mental interaction. And since every monad, every individual, is a universe unto itself, all interaction is internal to each monad. So, when you are sad and your sadness affects me, this is not because I simply register the sadness on your face, but because my mind understands the sadness expressed through your face. My mind feels your sadness, so to speak, because your sadness affects me internally. And it affects me internally, because it is part of my world which is also your world, even though we all live in our own unique worlds. In other words, when we look at each other or at the world around us, what we really do according to Leibniz is to look at what goes on inside of us.

Let me conclude with two beautiful analogies Leibniz offers to explain this exquisite balance of uniqueness and sameness. The first is meant to show how it is that although we all possess a unique outlook onto the world, we yet live in a common shared reality so that we can actually know that we talk about the same things despite coming at them from different perspectives. Picture the circumference of a circle and imagine that at each of the infinitely many points along the circumference there sits a monad looking into the inner of the circle. Each monad has its own particular angle with which it views things, each sees some things clearly, others not so clearly, and much remains obscure. But they are all looking at the same universe. To quote Leibniz:

Just as the same city, regarded from different sides, offers quite different aspects, and thus appears multiplied by the perspective, so it also happens that the infinite multitude of [monads] creates the appearance of as many different universes. Yet they are but perspectives of a single universe, varied according to the points of view, which differ in each monad (Monadology, § 57).

The other analogy Leibniz offers emphasizes more the idea that the common reality we all share because we all carry it within ourselves is just as much the result of our activities as it is the foundation upon which we stand. Picture an orchestra performing a symphony. Each musician has their own part to play. None of them actually has the whole score in front of him or her, except for the conductor. But we can ignore the conductor for now. There are groups of musicians that have no conductor, small chamber music ensembles, for instance. But despite the fact that each one only sees their particular score, yet together they produce with their unique voice something that sounds together, some kind of harmony or euphony, something that is larger than each one of them – a whole of wholes.

So, one little piece of philosophical wisdom Leibniz can give us is this: Find the right score that is the basis for the part you are going to play, and try to avoid cacophony. Be dissonant when required, yes! – all harmony becomes stale without dissonance. But cacophony is like matter without monads, things falling apart forever.

And: Try to be one, an individual. We need to integrate our traits and beliefs and convictions into a coherent whole. And the better everything in our thoughts and actions coheres, the more unique we become, the more unmistakable we become as persons. The less integrated, the more scattered, the more erratic, the less we are one person. Others don’t know who we are, if we behave in one way today and in another tomorrow. Integrity means being one, having a coherent set of beliefs (think of Socrates here!), it means finding a match between beliefs and actions, words and deeds. That is something worth striving for. So, just be the entelechies Leibniz says you are.