I think it’s possible to have studied Aristotle and still get confused on that point— at least, I found many objections to the Monadology on a recent rereading, but that wasn’t one of them, at least not directly.

I mean, atomism is very tempting, philosophically, for a lot of reasons. I was thinking recently about the modern scientific atomism, and how it is both appealing and inadequate as a philosophy. It is appealing because what philosophy likes to do is generalize (in a sense, that’s all it can do), and atomism is a wonderful generalization. Everything is made up of near-identical parts (and someday we will find the smallest, truly identical parts! goes the mythology) arranged in this uniform stuff called space-time (this is probably not a subtle understanding of physics, but I’m after philosophical intuition here, not accurate physics) which glues them together and (I think) gets around your objection by allowing them to be in relation to one another. You can’t get more general, while still explaining the diversity of things around us. And certainly it is a practical view of the world, since it lets us blow things up.

It is inadequate because while it is easy to visualize how a heap of atoms can make a glass of water, it is very difficult to understand how a heap of atoms can be a complex experience. Leibniz obviously gives his atoms experiential qualities, but does that help? How does an experiential atom combine with another experiential atom?

My main problem, and I’m not sure if it’s the same as your problem, is this: say you posit some sort of atom, monad, quantum, moment, what have you. Each monad is nothing special in itself, outside its relation to other monads. But those other monads are also nothing in themselves. Relatedness is all-important, but if all you have is monads, how does relatedness even begin?

It’s not quite accurate to say that by omitting to lay out a case for atomism, Leibniz is simply ignoring Aristotle’s arguments. After all, Spinoza and Descartes (for their own reasons) also rejected atomism. Leibniz doesn’t address their arguments any more than he does Aristotles’, notwithstanding that they fall within your two-generation radius of engagement. (Leibniz spent several days in company with Spinoza and corresponded with him as well.)

Leibniz’s well-known regard for Aristotle (he appropriates Aristotles’ term entelechy, he attempted to update Aristotles’s logic instead of discarding it [& scholasticism] as antiquated and irrelevant as many of his contemporaries and immediate predecessors had done) also makes it doubtful that he simply rejects Aristotles’ arguments on this or any other point.

There is another way to interpret his lack of explicit engagement. According to one conception of philosophy, we, starting from indubitable premises, argue ourselves into new truths by means of cross-checked, incremental steps. But isn’t the way an individual comes to believe or accept a philosophy like this as well: you try on the philosophy like clothing, you “wear it around” in different situations (using it to think through things known to you). Or again, isn’t a work of philosophy also something like a collection of photographs someone else has taken of a place you love or a person you know well. There is much that you recognize, much that (on first looking) strikes you as new or strange while remaining familiar. Examination of a collection of photographs of something familiar by a talented photographer can end with your seeing the thing itself differently. (And your own photographs, or those of your favorite photographer up until now, may seem hopelessly shallow or inadequate; conversely they may gain something by the interaction.)

In that case, couldn’t Leibniz’s style be saying to us: here, try this thought on. What if the world were like this? - or, I say the world is like this, why don’t you try to think in this way? When I read Leibniz, I feel more like I am reading a novel than a treatise: I take what he gives me, I try to live inside it and let it do its work on me, instead of trying to work on it; or to let my imagination work on imagining the whole world instead of assembling it from pieces. At any rate he appeals strongly to my imagination, and my imagination is content to let him set the premises, and tag along behind.

Erica wrote:

“It is inadequate because while it is easy to visualize how a heap of atoms can make a glass of water, it is very difficult to understand how a heap of atoms can be a complex experience. Leibniz obviously gives his atoms experiential qualities, but does that help? How does an experiential atom combine with another experiential atom?

“My main problem… is this: say you posit some sort of atom, monad, quantum, moment, what have you. Each monad is nothing special in itself, outside its relation to other monads. But those other monads are also nothing in themselves. Relatedness is all-important, but if all you have is monads, how does relatedness even begin?”

Very well said. But isn’t this view of monads somewhat contrary to Leibniz’s own?

8. Yet the Monads must have some qualities, otherwise they would not even be existing things. And if simple substances did not differ in quality, there would be absolutely no means of perceiving any change in things. For what is in the compound can come only from the simple elements it contains, and the Monads, if they had no qualities, would be indistinguishable from one another, since they do not differ in quantity. Consequently, space being a plenum, each part of space would always receive, in any motion, exactly the equivalent of what it already had, and no one state of things would be discernible from another.

9. Indeed, each Monad must be different from every other. For in nature there are never two beings which are perfectly alike and in which it is not possible to find an internal difference, or at least a difference founded upon an intrinsic quality [denomination].

I’ve always taken this to mean that Leibniz perceives his version of atoms as being infinitely various, all uniquely souled. It is these differences in quality, I thought, that gave rise to relatedness.

Patrick,

my criticism here is less about the development of Leibniz’s thought and more about the opening of the Monadology itself. The author was certainly familiar with other thinkers, and certainly had more respect for philosophical tradition than his contemporaries, but the work gives the impression of appearing in more of a vaccuum than it really does, whereas in fact it can less be read independently than works which explicitly engage contrary arguments. In this regard it is similar to Descartes et al.

Your point about trying philosophies on for size like hats is a very accurate description of what it’s like to read modern philosophy. The aesthetic dimension of thought-constructs like Berkeleyan philosophy, for instance, is about the only thing which redeems it. If addressed on strictly rational grounds it’s absurd, but as a what-if? scenario it has its own kind of beauty. It’s a little like non-Euclidean geometry.

This quality however is much less apparant in medieval philosophy, however, for reasons I was already planning to make the subject of a future post, so I’ll leave it at that for now.

Erika,

Leibniz of course is not an atomist the way Democritus and Lucretius were atomists. In fact I don’t know if there have been any pure atomists in the classical sense (what exists is bits of solid matter and their motion, period) since Newton, anyway. Modern physics certainly seems often to presuppose a kind of atomistic philosophy, but finds it has to have all these bizarre, ill-defined notions like energy and force as well. I think the problem of continguity and composition is less strong for modern physics for that reason.

In fact this problem is stronger for Leibniz than for Lucretius, even, because Lucretius’ atoms were real material objects which had size (though why they couldn’t be broken down further was obscure), whereas the monads have no extension and are more like mathematical points.

Michael,

“Your point about trying philosophies on for size like hats is a very accurate description of what it’s like to read modern philosophy. The aesthetic dimension of thought-constructs like Berkeleyan philosophy, for instance, is about the only thing which redeems it. If addressed on strictly rational grounds it’s absurd, but as a what-if? scenario it has its own kind of beauty. It’s a little like non-Euclidean geometry.”

One small point: non-Euclidean geometry may have begun as a try-it-on-for-size endeavor, but it then changed to a full blown this-in-fact-needs-to-be-true if traditional Euclidean geometry is to be true at all (as a special case of non-Euclidean geometry). My take home message is that apparent absurdity may become more real than the initially obvious, revisedly incomplete.

Mr Gaudinsky,

my example wasn’t clear. What I meant was that a non-Euclidean geometry, like some philosophies, is a rationally consistent thought-construct which does not agree with the reality of our experience but is interesting and valuable for other reasons. I didn’t mean that it wasn’t true on its own terms, which clearly it is! (An important point and useful for refuting Kant on the transcendental aesthetic.) In this it is distinguished from the same philosophies, which, given that they make claims about the reality we experience, rather than merely being deductions from thought-provoking but ultimately arbitrary first principles, means that they are *not* true on their own terms.

If addressed on strictly rational grounds it’s absurd, but as a what-if? scenario it has its own kind of beauty.

I don’t think that this is quite what Patrick meant (though of course, he can speak for himself).

The distinction you draw is between, let’s say, two ways of appreciating philosophy: either as a sort of amusing aesthetic conceit, or as something genuinely proposed to be true. But I think Patrick is talking about ways of engaging with philosophy—of examining it, understanding it, and trying to better grasp the truth.

The reason to try taking on a philosophy altogether, rather than building it up point by point, is that it’s often impossible to go in reasoned steps from one world-view to another. By taking the new world-view as a whole (even just tentatively), you may be better able to see how it does and doesn’t reflect the truth of the world than if you had to judge each part of it from the point of view of your own presuppositions.

In this view, Leibniz is saying not “come look at this clever and amusing way of seeing things”, but rather, “try looking at things in this way, and see if it doesn’t reveal them more fully and accurately.”

What I meant was that a non-Euclidean geometry, like some philosophies, is a rationally consistent thought-construct which does not agree with the reality of our experience but is interesting and valuable for other reasons.

Would you say it is like Euclidean geometry in this respect, or that Euclidean geometry is different?

Well, I can’t claim to be a serious student of philosophy, or anything else. I am looking forward to hear what you have to say about medieval philosophy. I did sweat a few nights over Aquinas, and I found Ockham and Scotus more accessible and enjoyable than I had expected, but I’ve retained very little. One figure I’m curious about: Suarez. Know much about him? Worth the candle? (Came across the name a few times, reading about Leibniz and Descartes. Never followed up.)

Moss puts my original point nicely.

The method of engagement Moss and Mr Findler mention is fine as a way of engaging a philosophy in the sense of coming to grips with its innards and trying to understand it. As a way of evaluating its truth, however, I find it extremely dangerous. Hume in his Enquiry notes that in philosophy as in religion there is a constant danger of “trying them on” and then choosing to accept the one which most comports with one’s pre-rational opinions, preferences, and habits; a given philosophy seems more true or more consistent with experience than another largely depending on how one has already interpreted that experience or unthinkingly accepted certain principles. Thus the importance of carefully and impartially judging the principles and arguments of philosophy apart from this other holistic sense of weiging it in its entirety as a worldview.

As for medieval philosophy, that’s my academic specialty and the locus of my knowledge, and readers of this blog may eventually get a lot more of it than they bargained for. Suarez, although in the scholastic tradition of the medievals, is chronologically more of an early modern, and I’ve read little of him. My understanding is that his thought is a lot of Aquinas, radically modified by certain principles from Scotus, filtered through his own unique viewpoint, and on the whole much less medieval really than his vocabulary sounds. As a Jesuit he’s supposed to have been an important influence on the Jesuit-educated Descartes. But this is mostly hearsay.

As a way of evaluating its truth, however, I find it extremely dangerous.

I think I’d agree with this, or at least agree that it’s dangerous to use it as your only way of evaluating truth. Though I’m not sure philosophy has any good way of consistently avoiding this danger—certainly logical argument from first principles is subject to the same risk.

Certainly logical argument from first principles has its share of risks, but not, I think, the *same* risks, unless you refer to the method by which the principles are chosen.

I didn’t mean that it [non-Euclidean geometry] wasn’t true on its own terms, which clearly it is! (An important point and useful for refuting Kant on the transcendental aesthetic.)

I would be interested to hear more on this point; I’m not sure Euclidean geometry’s failure affects anything but the details of Kant’s argument.

For Kant Euclidean geometry is entirely a priori. The fact that our experience conforms to it is not evidence of the validity of its premises; rather, the premises are given in the structures of consciousness as a pure intuition determining the necessary preconditions of any possible experience. But the equal validity of non-Euclidean geometries seems to me to prove that in fact there are no such pre-given pure forms of consciousness, but that the specifically Euclidean premises—the parallel postulate etc.—are in fact empirically derived. There seems to me to be no rational reason why Lobachevskian space couldn’t underly some set of experiences; except that isn’t in fact the data given to the senses. Sure, we can’t intuit Lobachevskian forms in the imagination, and can only conceive them in the intellect: but that seems to show only that the imaginative power is formed by experience, rather than possible experience being determined by the form of the imagination, whereas the intellect is subject to no such restrictions.

In other words, the fact that we can see that Euclidean geometry necessarily follows from its premises, but that these premises are contingent and known to apply only because we in fact experience things that way, seems to me to indicate grounds for believing that Kant’s transcendental aesthetic fails in claiming to show that our experience of Euclidean objects tells us only about the forms of consciousness and nothing about the things in themselves. But I’m willing to listen to arguments going the other way.

Mr. Sullivan, I gather from a few things you’ve said that you consider the geometry of our sense experience to be Euclidean. Is this really so clear? In theory, all the geometries are alike on a suitably small scale, so it’s impossible to say definitely that space is Euclidean with only finite observations. In practice, science appears to show that space isn’t Euclidean, or at least isn’t Euclidean everywhere.

I’ll agree that Euclidean geometry does come more naturally to the human mind. But is this because it’s closer to our sense experience, or just because it’s mathematically simpler?

“so it’s impossible to say definitely that space is Euclidean with only finite observations”

On this criterion it will be always be impossible, given the unlikelihood of infinite observations being made.

It seems to me that physics is more or less irrelevant here. Even if it could definitively prove that on the macro level or in some other part of the universe another geometry obtained, this would presumably not alter our actual experience, which seems definitively Euclidean.

What if I put it like this? One set of observations, our day to day experience, physical measurements with things like rulers and compasses, etc., show the experienced world as unabashedly Euclidean. Another set of observations, i.e. whatever physics happens to be doing, might show the world or some part or level of it to be “really” non-Euclidean. But wouldn’t this merely go to show that our day-to-day sense experience was inadequate or misleading? Or that our induction of postulates had been hasty and overgeneral? It wouldn’t show that our acceptance of the parallel postulate was not based on empirical rather than a priori grounds, which is the real point of my argument.

“Space, represented as object (as we are required to do in geometry), contains more than mere form of intuition; it also contains combination of the manifold, given according to the form of sensibility, in an intuitive representation, so that the form of intuition gives only a manifold, the formal intuition gives unity of representation. In the Aesthetic I have treated this unity as belonging merely to sensibility, simply in order to emphasize that it precedes any concept, although, as a matter of fact, it presupposes a synthesis which does not belong to the senses but through which all concepts of space and time first become possible. For since by its means (in that the understanding determines the sensibility) space and time are first given as intuitions, the unity of this a priori intuition belongs to space and time, and not to the concept of the understanding.”

Apologies for lengthy quoting, but this is more or less the crux of the Kantian matter for me. While the day-to-day experience of space may give us to believe that it’s Euclidean (and I’m certainly willing to admit that, in the absence of other evidence, I’d have no cause to accept a non-Euclidean geometry), that’s space as object. Space qua a priori form of outer intuition is something closer to ‘magnitude’ or ‘extension’. How it works in the real world is only one possible experience of space; the a priori form of outer intuition can admit of innumerable variations of these experiences.