Banham Gary, Leibniz on Descartes' Principles

8/22/2019 Banham Gary, Leibniz on Descartes' Principles

1/9

1/9

Gary Banham & Manchester Metropolitan University, 2009Metaphysics, Level II, Lecture 15: Leibniz on Descartes Principles,

Department of Politics and Philosophy, Manchester Metropolitan University

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 Leibnizs 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 Leibnizs 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

thePrinciples, Leibniz accepts that the cogitois 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


2/9

2/9



Leibnizs 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 cogitoso this principle is prior to the

cogitoand contains its guarantee, showing therefore that the cogitois not

the first truth we could hold to be certain. Added to this displacement of the

cogitois 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 cogitoto 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 cogitofrom 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

PrinciplesLeibniz rejects Descartes version of the ontological argument on


3/9

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 cogitoand 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


4/9

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


5/9

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


6/9

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 Leibnizs objections to Descartes view

of body. This objection is described in his response to paragraph 36 of the

second part of thePrincipleswhere Descartes stated the principle of the

conservation of the quantity of motion. The crux of Leibnizs 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 Leibnizs 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


7/9

7/9



velocity 4. So the increase in velocity is proportionate to the decrease in the

quantity of mass of the body. Leibnizs 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 giveBthe same force asAis for itBto have a velocity that is

double its mass as the velocity ofAwas a quarter of itsmass. 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 Leibnizs 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


8/9

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

continuityto 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.

Leibnizs 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

9/9



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.

Documents

Banham Gary, Leibniz on Descartes' Principles