# 1/6. Space and Time in Leibniz and Newton (2)

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1 1/6 Space and Time in Leibniz and Newton (2) Leibniz s fourth letter to Clarke begins by returning to the question of the principle of sufficient reason and contrasting it with Clarke s view that some of God s actions may, in themselves, be indifferent. Leibniz argues that if God acted without a sufficient reason and took something to be indifferent in itself then this would be contrary to the understanding of him as a perfect being. The defence of the principle of sufficient reason is also connected to Leibniz s argument for the principle of the identity of indiscernibles. The latter principle is based on the conception that there are no two things in nature that are absolutely alike in all respects and connects to the question of indifference in that it provides a reason for objecting to the view that there could be two parts of matter that were alike in every way except in having distinct locations. On the view of the principle of the identity of indiscernibles this could not be the case, there must be something different in the two pieces of matter over and above their location. On the basis of the principle of sufficient reason, it also follows that there must always be a reason why any given piece of matter is where it is when it is, so it cannot be a matter of indifference. The argument for the principle of the identity of indiscernibles also weighs, in Leibniz s view, against a material conception of atoms as such atoms are meant to be indistinguishable elements of matter. The principles of sufficient reason and the identity of indiscernibles are metaphysical principles which, Leibniz believes, help science to be real and demonstrative.

2 2/6 Returning next to the understanding of space, Leibniz discusses the question of whether space is a property and argues that if it is, then it must be a property of some substance. However if it is possible for space to be empty, for there to be a vacuum, then it follows that there is some space that seems to belong to no substance in which case it is unclear how such space could be a property of anything. Further, since even empty space will be extended, it follows that there can be such a thing as an extension which is not related to anything that is extended, a conception that seems contradictory. If space is really a property then it seems impossible for it to be absolute. Rather, if space is absolute, it is not a property but something even greater than substance. Also, if space is absolute, then it follows that it is infinite and has no real parts in the sense that it cannot be made up of subelements that are finite as it would have to be infinite in itself. The principle of the identity of indiscernibles is also used by Leibniz to demonstrate that it must be false to claim where things are is a matter that is indifferent. If God were able to move the universe without affecting where any two things were then it would be indifferent were they are. However, since there must be a discernible difference if things alter situation, then God could not do this and so it is not indifferent where things are. The principle of sufficient reason provides a further argument against this supposed indifference attaching to the properties of bodies. Leibniz also argues against the very conception that God could possibly have created the world at a different point to when he did, a conception that was important in

3 3/6 Clarke s response to the relativist view of time. In responding to this claim Leibniz emphasizes the principle of sufficient reason to the effect that God would not have created the world at any other time without some reason for so doing but no reason why he would do this has been given. In the post-script to this letter Leibniz adds an argument against the possibility of there being a vacuum. The argument presented against its possibility begins again from the principle of sufficient reason using the point that every perfection that can belong to things without running into conflict with other perfections will belong to them. If we assume that there is a space that is completely empty the point is that such a space could have been filled without God thereby taking anything away from the perfection of things. So there is no reason to assume that God has not filled every space since this accords better with the understanding of things than otherwise. To this argument Leibniz adds a further one to the effect that there is no reason why the amount of matter in the world should be limited. Clarke s fourth reply to Leibniz begins by responding to the question of the understanding of God s will indicating that on Leibniz s account there is no real difference between this will and the operation of weights in a balance. When we place weights in a balance it has to occur that the balance goes one way or the other or becomes equal. The balance cannot act otherwise so there is nothing indifferent for it. Balances are naturally operated however only by mathematical combinations which produce outcomes of this kind. However, God is not such a mechanism but possesses

4 4/6 a will which is inclined by reasons which move themselves and for which things can be indifferent. When things are indifferent there can be reasons for different actions but none which are determinative so that there has to be one set outcome. This is the way that Clarke suggests a reconciliation between the principle of sufficient reason and the possibility that some things are indifferent in themselves. The next point that Clarke makes in support of this argument is to the effect that the parts of matter are homogeneous as is revealed in their mathematical treatment and this indicates that their placing is necessarily one that is indifferent. In response to Leibniz s argument that there are no two things in nature absolutely alike Clarke states that this may be so with compound bodies such as leaves and drops of water but not with regard to simple parts of matter. Even with compound bodies Clarke sees no reason why they should not be absolutely alike without thereby becoming equivalent to each other. In support of this stronger contention that there can be two things absolutely alike and yet still numerically distinguishable Clarke adduces the example of the parts of time and space. Both time and space have parts that are indistinguishable but two moments are not thereby made into one moment or two parts of space into one part of space. Clarke next moves on to the question of the vacuum. On Clarke s conception of a vacuum, what happens here is that we have a space in which there is nothing present capable of exercising the resistance that solid parts of matter are all equally capable of exerting. So there could be rays of light

5 5/6 or other elements of matter present there in some minute form but the want of the resistance we naturally attribute to the presence of matter shows that in no meaningful way could there be said to be matter present. Clarke also disagrees with Leibniz s contention that the view that there is no matter present in a space is based on an appeal to the gross action of the senses. As Clarke puts it, some things divide in finer ways than others whilst still exercising action so the degree of resistance a body possesses does not concern the grossness of its matter and is not based on it. Rather the attribution of a degree of resistance to matter is based on the quantity of the matter in question. Should there be such a thing as a vacuum then there can be a space which has no bodies in it. Space is not something only bounded by bodies, it exists equally well both within and without bodies. Bodies exist in an unbounded space rather than space being bounded by bodies. Space that is empty is not absolutely empty but it is empty of all body (or, at any rate, of any body that can exercise resistance). Such space still has God present in it and perhaps substances that are not material but it includes nothing sensible. In response to Leibniz s questions concerning the parts of space Clarke argues that the parts of space are improperly named such since these parts cannot be separated from each other. So space is essentially all one and is not divisible in itself. In response to Leibniz s view that space and time are reducible to situation and order Clarke makes the point that space and time are quantifiable whereas situation and order are not so there is an

6 6/6 essential difference between space and time and situation and order. The uniformity of space does not provide a reason why God could have put things in any place equally. Since all places are of the same sort it is indifferent to God where they are and if were not indifferent to him then it would follow that all that is where it is could not be differently disposed so the world would include no freedom. Under these arguments, says Clarke, God will not be a free actor but simply be identical with fate. The order of succession is not the same thing as time states Clarke since the order of succession can be faster or slower considered simply as an order of succession but cannot be faster or slower considered as time which shows the amount of time is distinguishable from the order of it. The arguments alleged by Clarke in the fourth reply to Leibniz hence indicate grounds for thinking that the principle of sufficient reason does not constrain God s action in the manner in which it would seem to need to for Leibniz whilst the principle of the identity of indiscernibles is one that Clarke, by contrast, has denied to have any real purchase since he denies its consequence that if two things are indiscernible from each other that they are identical with each other. In admitting the principle of sufficient reason but providing arguments that still allow for indifference of outcome on the one hand and denying the principle of the identity of indiscernibles on the other Clarke attempts to defuse the metaphysical thrust of Leibniz s argument.

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