1/9. Leibniz on Descartes Principles

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Bruno Campbell
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1 1/9 Leibniz on Descartes Principles In 1692, or nearly fifty years after the first publication of Descartes Principles of Philosophy, Leibniz wrote his reflections on them indicating the points in which the relationship between physics and metaphysics that Descartes had established should be disputed. Some of Leibniz s criticisms of Descartes are indicated rather than being well developed as when he opens by claiming that Descartes conception of radical doubt is not strictly necessary since all we need to establish is the degree of assent or dissent a matter deserves, not the reasons why we should adopt any given doctrine. Whilst this is not a direct argument against radical doubt further considerations are added by Leibniz which show difficulties with this procedure. So, when commenting further, Leibniz argues that all we can establish with regard to sensible thing concerns consistency with each other as well as with rational principles. This double standard of consistency will suffice for Leibniz but clearly does not reach to a level of demonstrative certainty. Some of the reasons why demonstrative certainty is not an ideal to aim for become clearer when we note Leibniz s responses to specific key Cartesian claims and we will summarize first his responses to key metaphysical claims prior to showing how this affects the basis of Descartes physics. So, in commenting on article seven of the first part of the Principles, Leibniz accepts that the cogito is a key truth. However, despite making this admission, he also claims that it cannot have the specific status Descartes claims for it. Two distinct reasons are given for

2 2/9 Leibniz s view. Firstly, he divides truths into two types, truths of reason and truths of fact. The primary foundation of all truths of reason is then stated to be the principle of contradiction, a principle that, however, Leibniz states is the same thing as the principle of identity. Whether we accept this identification or not the point being made in identifying the primary foundation of all truths of reason would be that without having first assented to this we could not make sense of the cogito so this principle is prior to the cogito and contains its guarantee, showing therefore that the cogito is not the first truth we could hold to be certain. Added to this displacement of the cogito is an argument concerning truths of fact that modifies the sense of the cogito. Leibniz is clear that there are many truths of fact and that the ground of truths of fact is in principle intuitive and he takes the cogito to itself be a truth of fact. Alongside it however is listed another that he argues is just as central, namely the statement that whenever I think, there must be something that is being thought, an argument that points to the centrality of intentionality as something that has to be taken to given alongside the cogito. Leibniz has hence demoted the cogito from a truth of reason to a truth of act and even modified its sense so that it is only if viewed alongside the statement of intentionality as an essential attribute of thought that it can be taken as foundational for truths of fact. Not only does Leibniz object to this element of Descartes metaphysics, he also presents reasons for rejecting Descartes proofs for the existence of God. In his commentary on article 14 of the first part of the Principles Leibniz rejects Descartes version of the ontological argument on

3 3/9 the basic ground that Descartes here assumes certain definitions are given, definitions that allow us to say that an essence is possible from which existence follows. Since we can always deny that such an essence exists the argument is not compelling. Similarly, Leibniz objects to the claim that what is presented to us in the idea of a perfect being is something we understand and having understood have to agree exists. As Leibniz points out it is often the case that in thinking about something that we combine together determinations that are in fact incompatible with each other and in doing so nonetheless appear to have an idea of what we mean. An example Leibniz gives of this is a most rapid motion, an idea that describes something strictly impossible and yet which, given the meaning of the terms involved, we seem to understand. Leibniz also rejects the attempt to show that our continued existence must require the existence of God to guarantee it since, as he points out, we will surely continue to be unless there is a reason why this should change. In making this statement Leibniz is implicitly appealing to a principle of continuity, a principle we shall return to later. Just as Leibniz has modified the sense of the cogito and rejected Descartes arguments for the existence of God, so also he finds fault with the ground alleged for error by Descartes. Descartes argued that the reason we make errors is due to the distinction between our intellect and our will with our will having a greater range than our intellect and making judgments where it has no real data to base these on. Leibniz however states that we give credence to something due to our consciousness or memory of

4 4/9 certain reasons so this does not depend on will. We judge an appearance that is given to us, not one that we will to appear before us. The reason we make errors is thus not due to the disproportion between will and intellect but rather through lack of attention or failure in our memory. Lack of attention is based on distraction of various sorts which leads us to think we have proved something when we have not so the way to avoid error is simply to pay careful attention whilst proceeding slowly in our grasp of a chain of reasoning. This requires, as Leibniz puts it, the development of an inner monitor inside ourselves that can reflect on what we are doing as we do it, a monitor that we can use to check our own conclusions. Added to this is the point that with regard to some things we are ignorant since we can know only a certain amount. Given these corrections of Descartes, it is no surprise that Leibniz also rejects the criterion of clear and distinct ideas as a basis of truth. Rather than try to find these it is best to proceed according to the rules of logic and to admit certain elements of our argument as assumptions. Leibniz corrects the sense of substance also denying that the independence criterion of substance, in Descartes construal of it, can be a basis for finding any substances in the world. No substance can be without an accident though it need not have the particular accidents that it has. Accidents, by contrast, to exist, have to attach to the substances they do and would not be without the substances on which they depend (so there is here some form of independence criterion). Turning to corporeal substance however Leibniz denies that its principal attribute is extension, not least

5 5/9 because we cannot derive motion or resistance from extension. Anything that is extended is so relative to something and furthermore it is not evident that something extended cannot think as Descartes suggests. Just as Leibniz has rejected Descartes search for demonstrative certainty so also does he think the arguments by which Descartes aims to prove the existence of material things fail and do not refute the sceptical hypothesis of the evil demon that Descartes himself conjured up in the Meditations. Similarly, Leibniz does not accept that Descartes argument from subtraction is accurate since he points out that impenetrability of a body involves it not giving to another unless it moves elsewhere, a quality not derivable from extension and yet which belongs universally to all bodies. The most important divergence Leibniz makes from Descartes physics concerns the understanding of motion. Rejecting Descartes conception of proper motion Leibniz states that on this view we can never define which thing is moved since different hypotheses can be set up with regard to vicinity always arbitrarily taking something to be at rest. So there is no more reason to attribute motion to one thing than to another and on this view it follows that there is no real motion. In order to have such a view we need to ascribe a cause of change to something, a cause that attributes a force to it. In stating this Leibniz rejects Descartes attempt to describe motion in itself separately from its cause. On these grounds Leibniz argues that to say something is at rest requires us to state a difference in the force within such a body comparable to one that is in motion. The body that is at

6 6/9 rest is one that has no force in itself as it is caused to be at rest by the bodies surrounding it which, due to the force of their own motion, hold it in rest. The argument concerning force and motion is subsequently expanded into the most important of Leibniz s objections to Descartes view of body. This objection is described in his response to paragraph 36 of the second part of the Principles where Descartes stated the principle of the conservation of the quantity of motion. The crux of Leibniz s objection should be clear from his response to the Cartesian conception of proper motion. Rather than arguing for a principle of the conservation of the quantity of motion we should adopt a difference view of what is fundamentally conserved, a view that is centred not on the quantity of force. The quantity of force, on Leibniz s view, remains permanent, whilst the quantity of motion is susceptible to change. In his commentary on this paragraph Leibniz gives a number of examples to prove this point. Let us just focus on the initial example as the principle that is at work in it is the same as that in the other examples. The first example involves two bodies, one of which has a mass of 4 and a velocity of 1 whilst the other has a mass of 1 and a velocity of 0 or, in other words, the first is moving, the second is at rest. The next point is to imagine that the moving body comes to rest and transfers all its force to the one that was previously at rest. The question then concerns what velocity the previously resting body will then have. On Descartes conception the newly moving body will have a velocity of 4 since the original quantity of motion and the present one would then be equal as mass 4 multiplied by velocity 1 is equal to mass 1 multiplied by

7 7/9 velocity 4. So the increase in velocity is proportionate to the decrease in the quantity of mass of the body. Leibniz s answer, by contrast, is that the second body (B) should now have a velocity of 2 in order to have the same quantity of force as the first body. Force is doubled when its quantity is repeated twice as we can see when we think that two bodies of equal mass and velocity have twice as much force as one of them would have. However the two bodies in our example are not completely homogeneous in the sense that their masses are distinct from each other. What we can see is that a body of four pound one foot requires the same amount of force as raising a body of one pound four foot. So to give B the same force as A is for it B to have a velocity that is double its mass as the velocity of A was a quarter of its mass. The difference between Descartes and Leibniz here is that on Descartes view the quantity of motion is conserved where motion is a product of mass and velocity whilst on Leibniz s view the quantity of force is conserved where force is a combination of mass with not just velocity but the square of the velocity. The consequence of the dispute between Descartes and Leibniz is seen when we look at how they view the three laws of nature. Whilst Leibniz admits the first two of Descartes laws he rejects the third, a rejection that leads him to evaluate the question of impact quite differently than Descartes did. On Descartes third law when two bodies collide, a weaker one hitting a stronger keeps its motion constant but changes direction but can increase in motion. When a stronger body hits a weaker body however the stronger body loses as much motion as it imparts to the

8 8/9 weaker one. Leibniz reformulates this to state that it is only in cases where bodies are moving in opposite directions that a body colliding with another that is stronger than itself retains or increases its velocity. Leibniz agrees that quantity and direction of motion should be distinguished and that one of these can change whilst the other remains constant. But both can also change together. The problem Leibniz has with Descartes third law is summarized by him as involving the fact that there are no leaps in nature. Every body, which collides with another, must, before being repelled by the body with which it has collided, first reduce its advance, then come to a stop, and only later turned back so that it moves from one direction to the other, not all at once, but only by degrees. So all bodies are fundamentally elastic, that is, not is completely hard. The law of continuity to which Leibniz appeals indicates that things only by degree and understands the coherence of nature to be an expression of this change in degree. Gradually decreasing motion finally disappears in rest whilst gradually diminishes inequality finally reaches a state of equality which entails that in the true sense there is no absolute rest but only infinitely slow motion. Leibniz s departure from both Descartes metaphysics and the physics that is built upon it consists in an appeal to a different set of criteria for judgment than is offered by Descartes as can be seen in this principle of continuity. Rather than think of the relationship between principles as either demonstrative in terms of deduction or intuitive in terms of immediate certainty Leibniz is arguing for a continuous degree as required to link

9 9/9 principles to each other and as governing the way in which phenomena are related to each other. This difference in degree is one that is generally ordered but which enables this order to be assessed through minute distinctions rather than in terms of radical divisions of type. There are effectively no radical distinctions in type for Leibniz just gradations in degree.

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

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