For 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.
Leibniz’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.
As 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.
Now, 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?
Larval Subjects . 
May 3, 2009 at 11:02 pm
I’m glad you used Duchamp to illustrate this, given his love for n-dimensional analysis (The “Bride Stripped Bare”). It reminds me of that n-dimensional notion of that a being that expands (grows) and then diminishes (dies) can be seen as a sphere (n + 1 dimensions) that passes through a plane (of n dimensions), and to be experienced planally as a dot growning to an outer limit, and then shrinking back into nothingness. There is something to Leibniz’a view that makes me think of just this sort of transpiercive interaction, revealing the contours of an interaction.
May 3, 2009 at 11:02 pm
I’ve always had trouble distinguishing Leibniz’ metaphysical picture from Spinoza’s for many of the reasons you touch on in this post.
It’s been a while since I reviewed Leibniz’ corpus but I still can’t see a sufficient reason to conclude that monads (as the constituent element of the universe) are in any way different than the ‘substance’ proposed by Spinoza. Indeed, you seem to be making a rather Spinoza-esque reading of Leibniz in trying to understand his picture from the perspective of God (or, as Spinoza would put it, ‘sub specie aeternitatis’).
I always had the impression that Leibniz was reacting to the deterministic consequences of Spinoza’s view, and that monads were a way of preserving the individual sovereignty of agents while also motivating a worldview wholly consistent with the laws of nature and the will of an at least nominally Christian god.
May 3, 2009 at 11:23 pm
Walker,
Kvond is the guy to talk to on this as he’s far more an expert on this period than me. From what I understand, Leibniz was sometimes accused of being a “crypto-Spinozist”, but I think there are significant differences between their positions. For Spinoza there is only one substance and everything else is a predicate of that substance. For Leibniz there are an infinity of substances, all absolutely independent of one another. God is one substance among many. For Spinoza there is no teleology or final causation in the universe, whereas for Leibniz there is purposiveness to the universe. Where Leibniz’s God creates one universe out of the infinite number of possible universes that could have existed, Spinoza’s God creates all of the possible universes that can exist. For example, there is a possible Levi that has bright red hair and that was born in Scotland. Leibniz would say this Levi, while possible, does not exist because he wouldn’t contribute to the “best of all possible universes” for whatever reason. By contrast, for Spinoza if that Levi is possible that Levi does exist by virtue of the infinite fecundity/productivity of substance. I’m sure I’m butchering Spinoza on some points here, but this is, at least, a good indicator of their differences, I think.
I am not sure where Spinoza comes down on the issue of time. Maybe Kevin can illuminate this question. It is worth noting, however, that Einstein said that Spinoza’s conception of the universe is the one that came closest to his own conception of the universe. In writing about Leibniz I wasn’t endorsing Leibniz’s metaphysics but using it as a launching point to elaborate on the strange idea of fixed and frozen substances that don’t change at all.
May 3, 2009 at 11:54 pm
Levi,
I’ve focused much more on Spinoza and his milieu than that of Leibniz (I do just cherish the vision of Leibniz visiting Spinoza, as he did, and bad-mouthing him later, after taking a great deal of inspiration from him, it seems). I agree with Walker that indeed Leibniz’s desire to preserve the sovereignty of agents is largely a Christian Orthodoxy need, as Spinoza decenters the human subject so severely so as to make most of Christian Theology nonsense. Off the top of my head as to the differences between monads and modal essences, Spinoza defines a body (and one must assume its essence in existence) by a preservation of a ration of motion and rest over time, an indistinct defintion which could readily collapse into occasionalism if one torqued it just right. Spinoza’s Time is largely that of Descartes, seemingly the even, mechanical unfolding of extensional/ideational actions (I remember that someone in the early 1900’s tried to postulate that Time was the – suppressed – third Attribute of Spinmoza, an argument that failed). Spinoza would agree that modal essences (monads) are centers of force, but force is read as conatus drives to persist and instead of being defined by their lack of interactions, are defined by them. Ultimately any modal esseence can be and is nested within other modal essences. I suppose one could venture that the “lack of interaction” of the monads, is in Spinoza a “lack of interaction” of the Attributes. Or perhaps turn down to the irreductive “simples” that Spinoza posits make up bodies in combination (and says very little about). I have no real idea what is gained by turning modal essences into windowless monads.
Yes, it is interesting that Einstein turned to Spinoza rather than Leibniz for his affinity of vision. This may have been due to early in life readings of his alienated Jewishness and the way in which Spinoza the person devoted himself to the most important issues of his time in a kind of “outside of time” way. This and Spinoza’s marked determinism, the way in which all things are thus approachable by the mind, perhaps explaining his “God does not play dice”.
May 4, 2009 at 12:12 am
I think, again, that Leibniz is led to the “windowless monad” thesis by considerations pertaining to the principle of identity and the principle of non-contradiction. If you begin from the premise that every substance must contain all predicates that it will ever have past, present, and future then you’re led to the conclusion that there can’t be any causal interaction among substances because were one substance to modify another substance this would constitute a change in that substance and therefore a violation of its identity and the principle of non-contradiction. Ergo we get the thesis that each monad or substance expresses the entirety of the universe without there being any interaction between monads and that God created all the monads in such a way as to correspond with one another. Thus, were I to have a little lightbulb on my forehead and you had a little lightbulb on your forehead we can imagine a scenario in which my lightbulb blinks red and then yours blinks green. We might conclude that there is some sort of causal interaction between the two of us (the sending of a message) that makes the lightbulbs oscillate in this way, when in fact we both just have an internal “program” that, at the beginning of creation, was created to correlate with one another without any interaction with one another. We’re Leibniz’s God to get really pissed at you and smite you from existence, I would still have all the future discussions with you that were in me at the beginning of time because your end of the dialogue doesn’t come from you but is already in me as a way in which my monad expresses the universe. The obvious contradiction in all this is that God seems to violate the principle of being “windowless” insofar as he creates all these other monads and correlates them with one another. Long and short, though, he seems to be led to the windowless thesis as a logical consequence of his considerations about the identity of substances. Wild stuff.
May 4, 2009 at 12:20 am
Levi: “I think, again, that Leibniz is led to the “windowless monad” thesis by considerations pertaining to the principle of identity and the principle of non-contradiction.”
Kvond: Perhaps this is in support of my thought that for Spinoza there is no such thing as a completely adequate idea being held by a person. As Leibniz wants all the properties of individual substances being deducible from them like in a circle, Spinoza is ever driving awareness outside of the limits of any finitude. Any property is in relation to what lies outside of it. When Spinoza turns to the illustrative powers of a circle, it is to say that the infinite number of rectangles that are contained within a circle (modal expressions) are deducible from it, it would make no sense to see these dependent forms in any sense self-contained. His entire point is that there is only one thing self-contained, and thus self-caused.
I would have loved it if Deleuze would have written a contrast between these two.
May 4, 2009 at 12:40 am
I don’t think Leibniz is suggesting that we can have an adequate idea of any substance. His thesis is metaphysical, not epistemological.
May 4, 2009 at 12:50 am
I think Leibniz addresses this epistemological point in paragraph 24 of the Discourse:
http://www.class.uidaho.edu/mickelsen/texts/Leibniz%20-%20Discourse%20on%20Metaphysics.htm#XXIV:
May 4, 2009 at 1:07 am
I agree with your wish about Deleuze. Likewise, just as you’ve made Spinoza’s lens-grinding central to his philosophical practice, I’d like to see someone write a study of Leibniz that makes his work as a diplomat central to his philosophical project (and such a work perhaps already exists). It seems to me that the spirit of the diplomat pervades everything he’s trying to theorize– almost like what D&G would call a “conceptual personae” –and that he’s perpetually trying to juggle and integrate all points of view at once. When I’m reading Leibniz I sometimes get the image of a guy trying to play hacky sac with five different hacky sacs at once, trying to balance the kernel of truth in each position he addresses within his own position just as a diplomat tries to balance the various “points of view” among the parties he’s engaged with.
May 4, 2009 at 1:43 am
just a couple of quick thoughts:
1) Deleuze talks about Leibniz v. Spinoza quite a bit in the Expressionism book.
2) I have always had the impression the God is most decidely NOT a monad in Leibniz. (monads MUST have bodies, and God does not have a body – there may be an overarching universe-monad, but that’s not God, according to Leibniz – thus, it is illegitimate to accuse him of a contradiction if God isn’t windowless)
3) in the CD analogy, the stereo could be a world, since a monad is inseparable from a world… maybe a CD player that could hold infinitely many discs, with God as the DJ who puts together the best of all possible tracklists?
May 4, 2009 at 1:47 am
Caemeron,
As I said, I’m no Leibniz scholar, but it seems to me that our having a body is, for Leibniz, a sort of illusion. We have a sort of “phenomenological” body, but no real material body. I don’t know if your take on the CD analogy quite works because the thesis isn’t that monads are inseparable from the world, but that each monad contains the entire world from a particular point of view. In other words, there isn’t, for Leibniz, any “out there” but only all these coordinated monads that each contain their entire world compossible with the worlds of all the others. Leibniz likes to give the example of points of view on a city. The city itself doesn’t exist. It is the compossibility of all these monads. Deleuze tries to one-up Leibniz by arguing that all incompossible worlds exist as well.
May 4, 2009 at 2:44 am
Levi: “Likewise, just as you’ve made Spinoza’s lens-grinding central to his philosophical practice, I’d like to see someone write a study of Leibniz that makes his work as a diplomat central to his philosophical project (and such a work perhaps already exists).”
Kvond: This is a very interesting point. I did run into an incredible confluence of these two aspects, Spinoza’s lens grinding and Leibniz’s view of politics. Leibniz actually had an overly enthused respect for Spinoza’s optics, and even sent around a rather neglected and very short optical treatise, which proposed a new kind of lens that he had designed (in his head), an optical kind of “response” to Spinoza’s very controversial Theological-Political Treatise. He sent this treatise actually to Spinoza, and it seemed to suggest (imply) that somehow perfect optical vision would result in perfect political agreement at a time a very great strife.
I write about it here:
http://kvond.wordpress.com/2008/09/08/leibniz-optical-response-to-the-theological-political-treatise/
In this small attempt Leibniz’s diplomacy (he urged that it be sent to Hudde, the soon to be Burgomaster of Amsterdam, and he sent it to Oldenburg in England), and Spinoza’s lens-making coincide.
As to Adequate Ideas and Leibniz I only meant that Spinoza may not have been led down the same path as Leibniz because he did not have the same view of linguistic identity and contradiction. I’ll look at the link you give.
May 4, 2009 at 2:46 am
Caemeron,
Thanks for the look up on Expressionism and Leibniz. I’ll dig in there for the contrast between the two.
May 4, 2009 at 3:15 am
Kevin, I suspect you’ll love Stephenson’s Baroque Cycle when you get around to reading it. One of the things I think I appreciate most about them is how deeply they’re informed by Braudel’s history.
May 4, 2009 at 3:19 am
Levi, Thanks. I have to say that I read very little fiction, and even less non-fiction, unless it is specific to research these days. But I will keep it on my long list, which goes into effect when deep changes come. I do appreciate the recommendation.
May 4, 2009 at 4:33 am
you’re right, the analogy breaks down. one would have to say that the CD player only exists in the CDs… whatever. I take it this kind of analogy is at best pedagogically useful and ultimately to be discarded anyway…
as to the point about having a body, I think you are missing a couple of aspects of Leibniz’s thought that he is pretty straightforward about:
a monad is a principle of unity, right? what does it unify? a material body
each monad expresses the universe from its own point of view. this point of view is defined in terms of clear and distinct expression of the universe. what determines which aspects of the universe are expressed at what level of clarity? the body
the body is all over the monadology. indeed, anything Leibniz says about the monad he must give a parallel to in the body because of his pre-established harmony thesis. so, in the same way that each monad expresses the entire universe, each body is in a material relation to every other body in the universe (it is so far away, or stabbing my leg, whatever).
which is why he replies to Locke’s claim that saying the soul always thinks is as absurd as saying the body is always in motion by saying – Yes, the soul always thinks and the body is always in motion, and, moreover, the thought of the one is strictly parallel to the motion of the other.
now, I don’t know how “thick” his notion of the body is… and it should also be emphasized that bodies and monads don’t interact (but anything that happens to the body is mirrored in the monad)… but I do not think the body can be an “illusion” if his system is going to function.
I also don’t think I agree with your claim that the city doesn’t exist. I get what you mean, I think (that the city doesn’t exist in itself apart from the monads which constitute it), but there still must be a sense in which the city exists for Leibniz. but this would mean that the city is a monad, has a perspective, and so on. in other words, this is, for me, where things start to get truly weird. I don’t know, maybe I’m wrong. “is the world a monad?” is a tough question, and Leibniz is usually concerned to say that God isn’t a monad (which is an answer to a different question) when this question comes up (I’m thinking here, particularly, of the correspondence with Clarke).
anyway, reading back over this it strikes me as having an overly strident tone. sorry about that. I just have a perverse love for Leibniz…
and I second the recommendation of Neal Stephenson in general, and the Baroque Cycle in particular.
May 4, 2009 at 8:53 pm
Try Mathew Stewart’s ‘The Courtier and the Heretic’ (subtitle is’Leibnitz, Spinoza, and the fate of god in the modern world…’) it might fulfil some of your desire… interested in hearing what you think of it anyway.
May 8, 2009 at 1:07 am
Thanks a lot! I was writing a paper about Leibniz and how I think he was ahead of his time in multiple ways. Reading your blog just affirmed my own thoughts and gave me the confidence to write the paper. :) Hope I get a good grade. :S
May 8, 2009 at 4:38 am
Glad you enjoyed the post, Dotty. I hope your paper turns out well. Let me know.
November 21, 2009 at 3:52 am
Time is an emergent concept which results from presence of motion and forces. Time is caused by expansion of space. Time is slow where expansion of space is slow like around massive bodies. Amount of motion and forces induced into a given mass by expanding space is a constant, therefore when we increase external motion of an object, its internal motion slows down. This we see as slowing of time.
May 27, 2010 at 12:01 am
The most real feel of time “the present” is infinitesimal. It cannot be measured. Measurement of time is mostly an afterthought. Time also has similarity to recording devices where “the present” resembles the sharp recording point like laser and past is comparable to the recorded material while future is the unrecorded portion. In this way past is just a memory. Similar thoughts were expressed by Mc Taggart when he described the similarity between written history and stories in their time characteristics suggesting that past is just like recorded material.