70106_duchamp_nude_staircaseFor the last few weeks I’ve been teaching Leibniz in my Intro to Philosophy courses. In my view, Leibniz has to be one of the most audacious and creative metaphysicians that ever walked the earth. Regardless of whether or not you vehemently disagree with him, it is difficult, I think, not to come away with a deep appreciation for his philosophical creativity and ability to think outside constraints of “everydayness” or lived common sense. As you first begin reading texts like the Discourse on Metaphysics or the Monadology it is difficult to escape the impression that these are the ravings of a lunatic. Yet as you begin to understand the logical considerations that motivate his position (in particular, the principle of identity and the principle of non-contradiction as criteria to which any substance or object must conform) you start to appreciate his line of reasoning and what leads him to such strange conclusions.

Take, for example, §13 of the Discourse on Metaphysics. Leibniz calmly remarks, as if it were obvious, that,

We have said that the notion of an individual substance includes once and for all everything that can ever happen to it and that, by considering this notion, one can see there everything that can truly be said of it, just as we can see in the nature of a circle all the properties that can be deduced from it.

In short, Leibniz is claiming that every substance, every thing that exists, already includes all of the qualities, events, and properties that will ever occur to it. When my hair turns completely gray, as it is beginning to do now, this is not a new property of my being, but was already contained in my being from all eternity. Even more bizarrely, when I get into a frustrating flame war or blog battle, there is not someone else that is impacting my being in a particular way, there is no causal interaction between myself and other persons and objects. Rather, these events that befall me are already contained in my being for all eternity and arise from me in a movement from the virtual to the actual. As Leibniz puts it in the Monadology, the monads (substances, objects, entities, etc.,) have no windows by which anything could come in or go out (§7), and any change that takes place within a monad is the result of an internal principle (§11), not a cause and effect interaction between substances. For Leibniz, then, substances are a bit like compact disks. As I listen to my favorite CD, I might think something new is taking place as I hear the notes unfold (especially if I’ve never been acquainted with this technology). Moreover, I might think the notes disappear as the song continues to wind its course throughout time. However, this is only a sort of illusion. The notes are already all there inscribed on the CD and remain the same through each performance. This analogy, of course, breaks down when we observe that the CD has to be played on a stereo. That aside, for Leibniz substances are something like CDs in that just as CD’s already contain all their music on them, each substance or entity in the universe already contains all of the events, properties, qualities, etc., within it.

read on!

I am, by no means, a Leibniz scholar, but when I try to reconstruct his argument for this jaw-dropping and outlandish position, it seems to me that ultimately it has to do with logical and mathematical considerations about the principle of identity (A = A) and the principle of non-contradiction (~(A & ~A)) coupled with considerations about the nature of time. The problem is that in order for an entity to count as an entity, according to Leibniz, it must be identical to itself. Indeed, Leibniz presents a new concept of truth wherein truth is conceived as the identity of the subject with its predicates. The problem is, as we readily observe, that substances change in time. I am taller than I was when I was a wee little knee biter at the tender age of seven. My hair goes from being the auburn it is now to gray. When I have a conversation with someone I have undergone a new event that leaves me different than I was before.

Insofar as substances change, they become other than themselves and thus appear to violate the law of non-contradiction. It thus seems that we’re faced with an alternative: Either the principle of identity and the principle of non-contradiction are mistaken, or our common sense understanding of substances is mistaken. While there’s certainly plenty of perceptual evidence that substances change, we should nonetheless side, according to Leibniz, with the principle of identity and the principle of non-contradiction. In the first place, these principles are the ground or foundation of all rationality. However, more speculatively, God would not create a universe in which the principle of non-contradiction and the principle of identity do not hold sway because, by definition or in his essence, God is a perfect being. Now, since it is more perfect to be rational than to be irrational, the argument goes, God would not create a universe or world in which these principles did not hold sway. Consequently, the philosopher’s job is to correct our understanding of substance so that it might conform to these principles.

leibnizacta1684-2Leibniz’s solution is as elegant and simple as it is audacious: Substances contain all of the predicates they will ever have past, present, and future at the very moment of their creation. In this way, Leibniz is able to preserve the principle of identity and non-contradiction because when we attribute a predicate of a substance we are not adding anything new to it, but simply listing off that which is already contained in the substance. The result of Leibniz’s line of reasoning– if I’ve reconstructed it accurately –is that time becomes an illusion unique to our partial experience of the world. Where we are inclined to think of objects in time as being like snapshots or frozen postures where the past has disappeared and the future is yet to come, Leibniz thinks of objects as threads where all the predicates are already there on the thread. Were we able to adopt the perspective of the “super-monad” or God in Leibniz’s universe, we would not see a universe filled with buzzing and moving objects or substances, but rather we would see something akin to a four-dimension tapestry composed of threads all beautifully intertwined with one another without any of these threads directly interacting with one another (recall that God is omnitemporal and thus does not experience time as unfolding but as something more akin to a flat geometrical surface). Like a curve on a graph where all the changes and points on the line nonetheless belong to that line– i.e., the line is identical to itself and “exhausted” or completed –each substance is still and completed for Leibniz in this sense. Thus, although we find becoming and change all over the place in Leibniz’s writings– he was one of the inventors of calculus or the mathematics of things undergoing continuous rates of change, after all –metaphysically it would seem that everything in Leibniz’s universe is essentially still. It is only from our perspective that things appear to change or become.

laurel-and-hardyAs outlandish as Leibniz’s understanding of substances and time are, they do appear to have some experimental support in Einstein’s theories of special and general relativity. It could be said that Einstein effected a radical egalitarianism of space-time perspectives where one space-time perspective is no more true or right than another space-time perspective. Thus, for example, should Laurel be moving in a space ship close to a speed of light, time is far more dilated for him, moving much slower than it does for Hardy who remains back on earth. The key point here is that this dilation and contraction of time (time moves more quickly for Hardy) is not a matter of perception. When Laurel returns to earth he will have aged much less than his good friend Hardy and his watch will show that much less time has elapsed. For Einstein, these contractions and dilations of time are real phenomena (that have been well substantiated experimentally). However, the key point here is that neither Hardy’s perspective or Laurel’s perspective is more correct than the other. We have to adopt an egalitarian position of affirming all these different space-time perspectives.

6a00d83451b13569e200e54fdb15ad8834-800wiNow, the real weirdness of Einstein’s relativity arises when we begin to think of simultaneity. For Hardy who remains on earth, all sorts of events elapse such as his aging that don’t elapse at all for Laurel looking back on Hardy from his space ship. As Hardy, from earth, observes Laurel moving near the speed of light in his space ship, all sorts of things elapse that don’t elapse for Hardy himself. If this is the case, how are we to understand the nature of time? Given that Einstein’s theory of relativity requires a radical egalitarianism where space-time perspectives occur, does it turn out that Leibniz (and for that matter Whitehead) were right and that somehow every event that has ever taken place and will ever taken place is frozen as an entity for all time because it continues to exist at that moment for some space-time perspective or another? Where we think of the past as something that elapses or disappears, such that only the “moving present” can truly be said to exist, is it the case that the time I cut my leg with an axe when I was eleven still exists and is still taking place like some frozen pose for all eternity? I don’t know. But here is one place where philosophy and science meet. The scientists give us experimental confirmation of this space-time weirdness. If this is true– and all the measurements and experiments strongly suggest that it is true –what must time be if it is anything at all?