Leibniz and Newton disagreed profoundly about the nature of space and time, and the excerpts we read come from a series of exchanges between Leibniz and Newton's friend Samuel, Clarke, whom we have met earlier in the course.

The easiest way to put the disagreement would be this: for Leibniz, there are spatial and temporal relations (this is longer than that, this happened before that...) but there is no space nor time as such. For Newton, space and time are substances -- they are fundamental parts of reality. For Leibniz, the idea that there might be space or time apart from things that have spatial or temporal relations is unacceptable. But the disagreement goes further than that; on Leibniz's view space and time are not even "modifications" of objects, in the way that qualities. etc. are for Aristotle. Once all of the particular spatio-temporal facts have been enumerated, there is nothing left to say or refer to.

There are two questions we might ask here. The first is: why does Leibniz disagree with Newton? The second is: which view is more plausible? We will concentrate mainly on the first issue in these notes.

Leibniz offers two related reasons for rejecting the existence of space and time. One is an appeal to the Principle of Sufficient Reason; the other is an appeal to the principle of the Identity of Indiscernibles. We begin with the first.

Suppose that there really is such a thing as space, above and beyond the spatial relations that things possess. Suppose, in particular, that there is such a thing as absolute location. Then God could have created the universe five miles to the left (from the point of view occupied by facing Chapel Drive from Skinner Hall) of where He created it. But God could have had no reason for doing that; one part of space is intrinsically just like another. And since God never acts without a sufficient reason, it follows that there is no absolute space.

The reasoning might seem a bit quick here. But the point is this. If there were a system of absolute locations, God could not possibly have a sufficient reason for putting the universe in one place rather than another. So absolute space is incompatible with God's wisdom, if you will; absolute space would render some of God's decisions completely arbitrary.

This issue, in fact, is at the center of a dispute between Leibniz and Clarke. In earlier exchanges (not included in our selection) Clarke has argued thus: the placement of the world in absolute space would indeed have a sufficient reason, the reason being God's will. But Leibniz replies that this is to misunderstand the concept of sufficient reason. A sufficient reason is a reason; it is not a mere arbitrary choice. If space is as Newton says it is, God could not have a reason for picking one location rather than another, because there is nothing to distinguish one location from another, and hence, no difference that God's reason could be based on.

The same applies to time, of course. If time is as Newton says, then God could have had no reason for creating the universe when he did, rather than at some earlier or later time. So time, too, is not a real thing accordign to Leibniz. What is real, if anything, are the temporal relations among events in the world.

In the later sections included in our collection, Leibniz makes much the same point by appeal to the Identity of Indiscernibles. To understand this idea, let us begin with one that is much less controversial: the Indiscernibility of Identicals.

Take one thing that is called by two names. For example, the Evening Star is the same object that is called the Morning Star: both are just the planet Venus. Whatever is true of the Evening Star is therefore true of the Morning Star; we are talking about one and the same thing, and the name doesn't change the thing at all. Because the Evening Star is identical with the Morning Star, it is indiscernible from the morning star. (Both are planets, both have a mass of thus-and-such, both follow one and the same particular orbit, ...) Although there are some technical issues that are beyond our scope here, it seems reasonable to say that identicals are indiscernible. But are indiscernibles identical? That is, if two things share all their properties, are they really just one thing?

Leibniz thought that the answer should be yes. If, for example, someone claimed that they had found two absolutely identical leaves, Leibniz would insist: either the leaves are not absolutely identical, or they are not literally two leaves, but only one. The principle of the Identity of Indiscernibles says that if there is no way, even in principle, to tell one thing from another, then the "two" things are just one.

Why does Leibniz believe this?

It's not altogether clear, but in some applications, the difference between this principle and the principle of sufficient reason is very slender. However, we won't worry about the relationship between the two principles. We can see how the principle of the Identity of Indiscernibles works easily enough. Suppose there is such a thing as absolute space. Then from Leibniz's point of view, there are two problems. The first is that the points of space are indiscernible, which already violates the principle. But we can go further. If there is absolute space, then we have indiscernible, distinct possibilities. The possibility that God created the world "here" differs from the possibility that He created it five miles to the left of here. But these two possibilities are absolutely indistinguishable. And so they cannot be two possibilities at all. This is a different way of seeing the same point that was made in the similar, earlier argument.

Leibniz doesn't claim that it is an absolute impossibility that there should be two indiscernible things; it is not, as it were, a matter of the definition of "thing." But he does believe that indiscernible but distinct things would be "contrary to the divine wisdom."

What are we to make of this? In particular, what are we to make of such overtly theological arguments used to settle questions that seem much broader? Interestingly enough, there is a way of understanding Leibniz in which the theology is more or less incidental.

There is an intellectual maxim that applies in just about any field. It is sometimes called Ockham's Razor (after the medieval philosopher William of Ockham) and sometimes called the Principle of Parsimony. The idea is: dispense with what you don't need intellectually. The principle says, in Ockham's version, "Don't multiply entities beyond necessity." What this means is: if you can make do with fewer things in your explanations, then do so. Seen in this light, the objection to absolute space and time is that it doesn't add anything to the story. If we assume that there are things and events, and that they are related in various ways (some events are earlier, some later, some things are longer, shorter, etc...) then there is no advantage in adding space and time as separate entities. Furthermore, doing so leads to pointless questions such as "Why is the matter in the universe in one location rather than another?" On Leibniz's view, there are no absolute locations nor times, and so such questions can't arise. On Leibniz's view, as filtered through the Principle of Parsimony, absolute space and time are idle wheels. They have no genuine intellectual work to do, and so they should not be believed in.

Still, it might seem that we run into problems if we reject absolute space and time. Remember: for Leibniz there is no such thing as empty space. For one thing, spatial points are supposed to be intrinsically indiscernible, and so they are ruled out by the Identity of Indiscernibles. But more generally, if all that exists are things, events and their relations, then there is no space to be empty. This might lead to a puzzle. Suppose there is only a finite amount of matter in the universe. Then if we travel far enough, we must come to a region beyond which there is no matter:

        . ,
       . . .
      . ...';
    . .. , , ..
     .. . , ; . :
   . . .  , . ;  x
  ' " . , . . , , 
    . . , ^ ' ; 
      . ; . .
        ,  .

In fact, however, this is a confusion. To say that there is no empty space is to say that there is nothing real other than matter and its relations. But if you went to the spot marked x, there would be no force repelling you. If you kept on going, there would simply be a new set of relations among the bits of matter in the world. Nothing in Leibniz's doctrine says that the relations among things have to remain static. In fact, for there to be time, change of some sort will have to occur. And change of location is as good a form of change as any.

There might seem to be a similar puzzle about time. If there is a first event -- the creation of the physical world -- then it might seem that there could be no time before that event. In one sense, this is right. There is no empty time before the first event. Time begins when the first event occurs. But in another sense, there could have been an event before the first event. As we noted in class, if the first event was God saying "Let there be light!" God could have done something else first (cleared his throat, for example) and then said "let there be light!" As with space, the fact that there is no time as such doesn't put any restrictions on what range of events is possible. There could have been more events. There could have been all the events that there are in this universe, plus some earlier ones. Nothing Leibniz says rules this out.

Does Leibniz's view have any consequences for how the world works?

It's not clear that it needs to. It's point is mainly to say that we can make do with less than Newton thought. But if we accept his version of the Identity of Indiscernibles, there are some peculiar consequences. One is that no matter how hard we try, we will never be able to make two things that are exactly alike. That this is true in practice is not surprising; that it is true as a matter of metaphysical principle is another matter. In fact, on Leibniz's view of the matter, if you had a ball bearing and I had one too, and we kept making them more and more alike, something would prevent us from ever making them exactly alike. It would be almost as though there were a force at work.

There is some controversy about whether Leibniz's own version of his principle is the most plausible version. And in any case, the argument against space and time can appeal to the Principle of Sufficient Reason or, better yet, the Principle of Parsimony (even though this is not Leibniz's principle.) Thus, we can sidestep the more general puzzles of Indiscernibility.

A more interesting question, perhaps, is whether there is any way to settle the dispute between Leibniz and Newton. Though the answer may ultimately be no, the question becomes more complicated once we consider the theory of relativity.

© Allen Stairs, 1998
stairs@glue.umd.edu