1/10. Descartes and Spinoza on the Laws of Nature

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1 1/10 Descartes and Spinoza on the Laws of Nature Last time we set out the grounds for understanding the general approach to bodies that Descartes provides in the second part of the Principles of Philosophy making clear that he there carefully distinguishes motion from its cause but also bringing out that his discussion of the cause of motion is based on a general conservation principle. This general conservation principle was described and we also looked at Descartes first two laws of nature. We will now focus on the third law of nature Descartes provides before turning to the commentary on these laws that was provided by Spinoza in his early work Principles of Cartesian Philosophy. Descartes third law of nature continues to make clear the consequences of distinguishing between motion and action. It states that a body that comes into contact with another body that is stronger than itself will lose none of its motion. However a body that comes into contact with one that is weaker than itself will act on the latter body and in acting upon it will transmit to it some of its own motion which will hence ensure that it loses some of its own motion. The description of this law that follows makes clear that a body that is weaker than the one it comes into contact with will lose none of its motion but will, due to the effect upon on it of the stronger body, have its direction altered. However a body that is stronger than the one it comes into contact with will transmit motion to the body that is weaker and in so doing will lose as much motion as it transmits to the Gary Banham & Manchester Metropolitan University, 2008 Department of Politics and Philosophy, Manchester Metropolitan University

2 2/10 other. This law thus states a clear correlation whereby to the degree than one body is stronger than another it will have an effect upon the weaker body that will be measurable in the loss of motion suffered by the stronger body. Physical change in terms of the understanding of the motion of body is hence described in its general principle in this third law. Descartes proceeds to give proofs of both parts of the third law, both the part that concerns the fact that a weaker body in coming into contact with a stronger one will lose no motion and the part that asserts that a stronger body in coming into contact with a weaker body will lose motion. In proving the first part of the law Descartes points again back to the difference between motion considered in itself and direction (or determination). The difference between them ensures that the direction of motion can alter without the quantity of motion changing. The important point that Descartes makes here is that motion, considered in itself, is simple, as he described it as being in the defence of the first law of nature. Given its simplicity it will continue to exist as long as an external cause does not destroy it or, put otherwise, there is nothing in its own nature to lead to its cessation. When a weaker body comes into contact with a stronger one all that occurs however is movement meets movement. Since movement is not contrary to movement there is no rationale here for the weaker body to lose motion, only for its direction to be altered. Gary Banham & Manchester Metropolitan University, 2008 Department of Politics and Philosophy, Manchester Metropolitan University

3 3/10 The defence of the second part of the third law that demonstrates that a stronger body in coming into contact with a weaker one will lose as much motion as is transferred involves a more complicated demonstration. Here Descartes appeals to the principle of God s immutability and to the earlier arguments given for assuming that the world is a plenum. The reference to God s immutability is a metaphysical ground for the assumption that the laws of nature have constant operation and that this constant operation is one that is coherently complete. In other words, the laws once set continue in the same manner and do not vary due to their dependence on something that is necessarily unchangeable, namely, God s nature. Since the laws of nature are uniform in operation and since they govern a quantity of motion that is kept constant it must follow that whenever motion is transferred from one to another that as much motion must be lost in one as is gained in the other as otherwise the quantity of motion would not be constant and then the laws of nature would also not be constant. Each thing strives to remain in the same state as it is at present in accordance with the first law of nature and the general principle of conservation of motion. Hence, for Descartes, forces are conservational resistances and are found in two places. Firstly, any body that is moving resists the external imposition of movement and any body that is moving resists the external imposition of rest. Secondly, any body that is moving in Gary Banham & Manchester Metropolitan University, 2008 Department of Politics and Philosophy, Manchester Metropolitan University

4 4/10 a certain direction resists the external imposition of alteration of this direction but this second resistance is weaker than the first since this second change is of a lesser sort than the first. Having expounded Descartes third law of nature let s now look at how Spinoza responds to these laws. Spinoza comments on Descartes Principles of Philosophy in the only work that was published in his lifetime under his own name, the Principles of Cartesian Philosophy, a work published in 1663, 19 years after the first publication of Descartes Principles. This is an early work of Spinoza s and is clearly intended as a careful commentary on Descartes work. It is not, however, set out in the same manner as Descartes work was. Spinoza s work is concerned to comment on Descartes Principles in what is described as a geometric manner and involves the use of definitions, postulates, and axioms prior to statement of proofs. In using these devices Spinoza directly uses the same methods adopted by Euclid in his Elements with the intention, by use of these devices, of making the argument clearer and uncovering implicit assumptions. So the second part of Spinoza s Principles opens with a general postulate requiring that we attend to our perceptions as accurately as possible in order to distinguish in them what is clear and separate it from what is obscure, a general rule that we did note to be important in Descartes work but which Descartes did not set out as a general postulate prior to undertaking the examination of bodies. Gary Banham & Manchester Metropolitan University, 2008 Department of Politics and Philosophy, Manchester Metropolitan University

5 5/10 The definitions that Spinoza next gives are again simply introduced without being placed in the general context of argument as when Spinoza tells us that at the outset of part II that substance is that which needs nothing in order to exist apart from dependence on God or his account of motion in definition eight, a definition that accords with Descartes view of proper motion but, unlike Descartes, Spinoza does not treat the vulgar view of motion at all. What Spinoza does do in his opening treatment of motion is follow Descartes distinction between motion and its cause with the latter described as a force or action. The axioms that Spinoza gives also make more manifest some of the considerations in Descartes work. For example, the second states that if anything can be taken away from a thing without impairing its integrity then this does not belong to the thing s essence which indicates that the essence of something can be expressed by means of a process of isolation of properties until we arrive at those without which the thing would not be or, as Descartes would put it, describe its attributes. Having described this account of essence Spinoza subsequently makes clear a sense of what belongs to the essence of body when he argues in axiom 5 that a part of matter doesn t lose any part of the nature of body whether it gives way or resists the impact of another body and in axiom 6 adds that motion, rest and figure cannot be conceived apart from extension. Similarly, axiom 20 s statement that a change in any thing proceeds from a stronger force already points in the direction of the third law of nature. Gary Banham & Manchester Metropolitan University, 2008 Department of Politics and Philosophy, Manchester Metropolitan University

6 6/10 The subsequent argument of the Principles depends in Spinoza s construction on reference to the definitions and axioms with which he has begun the second part in conjunction with others that are drawn from the first part. So, the initial argument to the effect that where there is extension there is necessarily substance which supports the Cartesian conception of a plenum, is supported by reference to the first axiom concerning nothingness, the second definition of substance, and two propositions concerning God proved in the first part. The first proposition that detaches the sensible qualities from body also relates to the second axiom concerning essence in conjunction with the description of hardness given in the third axiom and this leads once again to the claim that the nature of body is based only on extension. Spinoza begins to consider motion in the Scholium to proposition 6 which concerned the reason for thinking that the matter of the world is indefinitely extended whereas Descartes distinctly separates these topics from each other treating one in one section and the other in the next. As in Descartes work Spinoza introduces motion to account for diversification of matter in the sense of individuation of discreet bodies. What Spinoza includes here that Descartes did not is a serious treatment of Zeno s paradoxes, ancient problems concerning the nature of change. Spinoza treats these paradoxes on the grounds that they draw on the data of sense in such a way that we might be confused by this data concerning our intellectual Gary Banham & Manchester Metropolitan University, 2008 Department of Politics and Philosophy, Manchester Metropolitan University

7 7/10 understanding of motion. Spinoza describes two paradoxes from Zeno but we will only consider the first, which concerns the motion of a wheel. If we isolate three points on a wheel then it is possible, suggests Zeno, to show that there is no difference concerning the motion of a body moving at high speed from that which would pertain to a wheel at rest. Since this would be absurd it shows that motion is absurd and cannot take place. The basis of the argument is that if a point remains in the same place it is at rest. All the points of a body moving at high speed must remain at rest however so the body is at rest. If we take 3 points of the body then we can see that A would complete a circle more quickly at a higher speed than a lower one. Suppose it moves slowly and takes an hour to go from its starting point to back to where it began, then speed up so that it takes only half an hour at twice the speed, quarter of an hour at quadruple speed and so on. If the speed is increased infinitely then we will be dealing with infinitesimal moments and in that case it will always be in the same place at each moment and so could not move. This must apply to all parts of the wheel so the wheel can t move. In reply Spinoza points out that the argument supposes that bodies can be conceived as having a highest speed and assumes time to be made up of moments. In response Spinoza suggests that any speed can be assumed to overtaken by a further one and any slow speed can also be conceived to have one slower still. Similarly, time can always be conceived of having an instant smaller even than the previous one measured. He illustrates these Gary Banham & Manchester Metropolitan University, 2008 Department of Politics and Philosophy, Manchester Metropolitan University

8 8/10 claims by attaching a second wheel to the first which is smaller than the first but which, by means of a belt, is connected to it. As the larger wheel keeps increasing in speed so the smaller wheel must be proportionately faster still which shows that however fast the points of the first wheel are run through those of the second must be greater which establishes that there is motion in the first as a proportion can be established between it and something else. Here what Spinoza has done in responding to this paradox is change one element of Descartes view as he here has argued that time is infinitely divisible whilst Descartes took it that although bodies where infinitely divisible that there is a lowest limit of divisibility of time. If Descartes assumption was granted there would be no reply to Zeno s argument so here Spinoza improves on Descartes. Proposition 12 of Spinoza s Principles restates the claim that God is the principal cause of motion and proposition 13 adds that God ensures the conservation of the total quantity of motion. These two points added together produce Spinoza s restatement of the first law of nature but the first law is given slightly differently by him to how it was described by Descartes. Whilst Descartes gave the first law as saying that each thing remained in the same state so far as this was in its power, Spinoza states that it preserves the same state insofar as it is simple and considered only in itself. The proof that Descartes gave of the first law depended on the argument that the thing in question was simple and undivided but these Gary Banham & Manchester Metropolitan University, 2008 Department of Politics and Philosophy, Manchester Metropolitan University

9 9/10 points are instead lifted into the principle of the first law by Spinoza. The effect of this change is to make the first law refer, on Spinoza s account, directly back to the point concerning God from proposition 13 whilst Descartes, by contrast, made no direct reference to God in his proof of the first law. The second law of nature is treated to a much lengthier demonstration in Spinoza than in Descartes taking up propositions 15-17, each of which concerns part of the law. Again, Spinoza refers directly back to the importance of God s conservational power as proved in proposition 13 although to this is added some lengthy geometrical demonstrations that Descartes did not give. The third law is stated in proposition 18 where the first part of the third law is given and in proposition 21 where the second part is given. Spinoza derives from the third law a consequence which again is not directly specified in Descartes when he states in the proof of proposition 22 that in bodies at rest we understand by force of resistance the quantity of rest. This suggests a specification of the quantity of rest that Descartes did not give as he rather contented himself with a notion of the quantity of force in terms of conservational resistance whereas here the resistance would appear to itself be considered as capable of being quantified. So it would appear that despite the fact that Spinoza s work is set out as a commentary on Descartes that there is some divergence between them Gary Banham & Manchester Metropolitan University, 2008 Department of Politics and Philosophy, Manchester Metropolitan University

10 10/10 both in terms of the role of God in the principles and in terms of the precise understanding of body. We will uncover next week, in looking more closely at Spinoza some of the ways these differences are justified and how they are developed. Gary Banham & Manchester Metropolitan University, 2008 Department of Politics and Philosophy, Manchester Metropolitan University

1/10. Descartes Laws of Nature

1/10. Descartes Laws of Nature 1/10 Descartes Laws of Nature Having traced some of the essential elements of his view of knowledge in the first part of the Principles of Philosophy Descartes turns, in the second part, to a discussion