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16 Descartes, Principles II.33-40,
64; IV.189-99, 203-4; Discourse VI [AT VI: 63-65] Cartesian science is built on the equation of
space and body established over the opening articles of Principles II. Given that equation, it follows that there is such a thing as absolute density (for any body, there is a
point beyond which it cannot be further condensed or compressed), that matter
is indefinitely divisible (since body just is extension and any extension,
however, small, is still extended, any body, however small, must be at least
in principle separable into spatially distinct parts), and that nature does
not contain qualitatively different kinds of material. Lead, gold, salt, sulphur, mercury, water, air,
fire are all made of the same material, and the only thing that makes them
different from one another is how this material is cut up into parts and how
these parts are arranged and moving.
There are no qualities, forces, or powers in nature other than those
that arise from the size, shape, arrangement, and motion of otherwise
homogeneous particles. Consequently,
we shouldn’t need to do any more to understand what bodies are and how they
behave than to understand the principles of geometry, which tell us how
bodies can be shaped and divided, and the laws of motion and collision, which
tell us how they will act over time. In
building on these foundations, Descartes’s first
project was to determine what the laws of motion and collision are, something
he attempted to do solely by reference to how God could be presumed to act in
recreating the world from moment to moment.
Applying these laws to a universe that is everywhere full of matter
led him to develop a theory of the origin of the universe and of the
regularities in nature that made heavy use of the notion that matter is
swirling around in vortices. However,
he recognized that he was only able to discover the most general things
simply by deduction from metaphysical first principles. When it comes to accounting for the
specifics of how bodies interact, experience has an important role to play. At
the close of the Principles,
having, as he believed, successfully shown how all the phenomena of nature
could be explained by mechanical principles, Descartes returned to the topic
of sensible qualities, and offered a final set of reasons for concluding that
these qualities should not be attributed to material things. QUESTIONS
ON THE
1. What relevance does
the fact that there can be no vacuum and no rarefaction or condensation (in
the sense of a gain or loss of volume by a material that completely fills the
space it occupies throughout the change) have for the theory of motion?
2. Why must matter be
indefinitely divisible?
3. What might the “bodies
as wide as the space at E” referred to in article II.35 be?
4. What might Descartes
be referring to when he speaks in article II.36 of changes (sc. in the quantity of motion in the
universe) that we know to take place either by experience or revelation?
5. Why must the quantity of
motion in the universe be preserved?
6. Is it natural for
bodies that have been set in motion to slow down and stop? What is it that teaches us the answer to
this, sense experience or understanding? Note: Descartes’s 3rd
law of motion. This law was almost
immediately criticized on the ground that it violates the principle that
natural phenomena are continuous in their variations (it instead postulates a
sudden and radical change in the way colliding bodies behave at the point
where the resistance of the impacted body becomes less that that of the body
that hits it, from reflection without any transmission of motion to
transmission of motion to the impacted body).
What may have led Descartes into this mistake was focusing on case of
the reflection of light.
7. What is the result of
movements caused in the brain by the nerves?
8. Propose a Cartesian
remedy for depression (sadness not caused by any obvious misfortune). Note: “Globules of the
second element” Art. 195. Descartes thought
there were three elements, which he called gross matter, intermediate matter,
and subtle matter. Since all materials
are made of the same stuff, the only difference between these elements is the
size of the particles that make them up.
The second element, or intermediate matter, is comprised of the
particles of light. Subtle matter is
yet finer, and gross matter is the stuff that all visible bodies, from the
stars and planets to grains of sand are made of.
9. What conclusion should
be drawn from the fact that people complain of feeling pains in a limb that
has been amputated? 10.
Why should we think that the nerves do not transmit
anything but motion to the brain (e.g., that the visual nerves do not
transmit colour, the olfactory nerves smell, the tactile nerves heat)? 11.
Where does the feeling of titillation or pain, and the
appearance of light and sounds originate? 12.
What makes it unlikely that the colours we sense are
produced by colours actually existing on the surfaces of bodies? 13.
What is the major guide Descartes relied upon when
deciding what hypotheses to formulate about the workings of the small parts
of nature? 14.
Is there a role for experimentation in Cartesian science,
and if so what is it? NOTES
ON THE Cartesian
physics. In discussing Descartes
proofs for the existence of God in the chapter on Principles I.1-23 I made reference to the doctrine of constant
creation. Recall that according to
that doctrine God must constantly recreate the world from one moment of time
to the next. Since it is of the nature
of time that the past no longer exists, a bare tick of the clock, meaning
that the present moment has become past, signifies that everything that now
exists has been annihilated as a necessary result of the passage of time. It must, therefore, be recreated in order
to be sustained in existence. God is
constantly doing this, and it is the manner in which he does this that
accounts for the laws of motion and collision. According to Descartes, God is supremely
constant in all his operations. This
is a consequence of the perfection of the Divine nature. An all-perfect being would not change his
mind, since that would show indecision, uncertainty, or lack of
foresight. Accordingly, when
recreating the world from moment to moment, God always operates in the same
way. He conserves everything,
recreating each body that existed at the previous moment and putting into it
just those modifications it possessed at the previous moment. Among these modifications would be a state
of motion. Descartes thought that
having once injected a certain quantity of motion into a body God would
recreate that motion from moment to moment in an unchanging way, just as he
would recreate the body itself. This
means conserving both the direction and the speed of the motion and so
recreating the body just slightly further down on a straight line path. The effect of this operation is to enforce
what was later called the principle of inertia: the principle that each body
in the universe, once set in motion, will continue in that motion in the same
direction and at the same speed, unless something special happens to alter
that state. Descartes recognized only two such special
causes of a change of motion: collision and the free wills of minds that have
been joined to particular bodies. From
time to time, as a body moves, it will run into other bodies standing in its
path. Indeed, in a plenum, that is, a
world that contains no void, this will happen in no time at all. When running into an impediment, a body
cannot simply pass through, since we very clearly
and distinctly perceive that two different bodies cannot occupy the same
place at the same time. Consequently
it must either drive the impediment on in front of it, or bounce back, or
come to rest and transfer its motion to the impediment (or, more precisely
God must so recreate it), and whichever of these cases occurs, the overall
quantity of motion cannot be increased or diminished. Descartes took the quantity of a body’s
motion to be the product of its size — effectively, of how many bits of space
it consists of — and its speed. And he
maintained that as much motion as a body loses in collision it must transmit
to other bodies. Just which of the three cases occurs —
rebound, stopping and transmitting all motion, or pushing the body that was
hit on in front while continuing in the same direction with proportionately
diminished speed — is also something Descartes thought he could also deduce
from the constancy of the Divine operations, and his attempt to do so led to
one of the more incongruous features of his physics. He maintained that when a moving body hits
a “stronger” body, it loses none of its motion, but rebounds away from the
stronger body, whereas when it encounters one that is “weaker” it continues
in the same direction, but transmits as much of its motion to the body that
it hits as it requires to drive that body on in front of it. This law of motion was the foundation for
seven specific laws of collision that he went on to state, all but one of
which are wrong.
The specific laws, and the general law they were deduced from, were
quickly condemned by Descartes’s successors on the
ground that they violate the “principle of continuity” — the principle that
all changes in nature are continuous.
According to this principle, as the difference between the “strength”
of bodies diminishes, the effect of the collision of one with the other
should likewise continuously change.
There should not be an arbitrary point where suddenly something comes
about that is radically distinct from what happened in an almost identical
situation, as Descartes supposed would in fact happen if we compare the case
where the moving body is infinitesimally “weaker” than the body it hits (in
which case it rebounds) with the case where it is infinitesimally “stronger”
(where it does not rebound but pushes the other body on in front of it). This mistake aside, the main point to
appreciate for purposes here is just that, on this scheme, the motions of the
parts of matter are rigorously determined by the laws of inertia and
collision. The one exception to these
rules concerns the motions of those bodies that finite minds are
substantially united to (i.e., human bodies).
God is willing to move these bodies in ways projected by the wills of
the minds that they are attached to. On the basis of nothing more than this simple
physics, Descartes proposed to explain the evolution of the solar system from
an original, chaotic state, the formation and burning of the sun, the
formation of the planets and evolution of the various minerals on earth, and
even the evolution of life and such physiological processes as the beating of
the heart and the circulation of the blood.
All of these phenomena, he claimed, originate from nothing more than
the motion and collision of otherwise uniform and undifferentiated particles
of matter. There is no need to invoke
forces of impenetrability, chemical bonding, electromagnetic or gravitational
attraction, radioactive decay, or notions of variations in mass, and
certainly no need to ascribe different sensible qualities to bodies. Descartes took the fact that there is no empty
space to entail that all motion must be rotary in nature. After all, if the world is full of body,
then the only way anything can move is if a whole ring or sphere or cylinder
or other cyclical form rotates. It
helps greatly that matter is indefinitely divisible. In a universe composed of a solid mass of
cubes, motion can occur as long as the cubes slide past one another in a
line. But if the cubes must move in a
curve, as they must if motion is to occur without leaving empty spaces in
behind, they could not pass one another without creating gaps, that is, empty
spaces. Since that is impossible, the
pieces of extension must constantly be bending and breaking as they move past
one another, in order to generate little pieces to fill the interstices that
would otherwise form, and these pieces must be
arbitrarily small.
Descartes supposed that the universe consists
of three different kinds of matter: gross matter (which goes to make up very
large bodies like the planets and the bodies on the planets like our own
bodies, the water, and the air), intermediate matter (which goes to make up
things like light), and subtle matter (which goes to make up the aether in the heavens).
Intermediate matter is composed of very tiny, approximately spherical bodies,
and is the original form of matter.
Subtle matter is created when the pieces of intermediate matter move
and some of them break into extremely tiny, spiky pieces that fill in the
interstices that would otherwise form between the particles of subtle
matter. Gross matter is composed of
pieces of subtle matter that get stuck together to form jagged, twisted
shapes that readily interlock with one another to form arbitrarily large
chunks. Originally, when God created the universe he
just created intermediate matter in a very compact form (squashed into cubes,
as it were). But then God injected a
certain quantity of motion into the universe, and, being supremely constant
in his operations, preserves this same quantity of motion through the rest of
time. The moving pieces of
intermediate matter quickly generate subtle matter, which generates stars and
suns, which in turn generate gross matter, which generates the planets and
the minerals, vegetables and animals on the Earth. As noted earlier, vortex mechanics is
supposed to take care of all the details. While Descartes paid lip service to the
Christian dogma that God spent six days creating the world out of nothing and
ordering all its parts, he also observed that God could have simply injected
a certain quantity of motion into a chaotically arranged mass of
particles. Simply as a result of the
necessities of vortex mechanics, systems of stars and planets, and worlds
like our own would very quickly evolve.
Be this as it may, he added that the doctrine of constant creation
makes it sufficiently evident that God is required to sustain the universe
from moment to moment, and indeed, make the laws of physics possible. So we need not worry that casting doubt on
the creation story will in any way damage the need to accept the existence of
God. One final feature of Descartes’s
physics deserves some consideration: its position on the role of experiment
and hypothesis. As so far described, Descartes’s science proceeded in what might be described
as an exclusively top-down fashion.
From metaphysical first principles concerning the nature of God and
matter, Descartes proceeded to derive the laws of motion, to deduce the
necessity of the existence of vortices and the three main kinds of matter,
and to account for the origin of the general kinds of things: the Sun,
planets, minerals, winds, tides, and so on.
But Descartes noted that this exclusively
top-down procedure could not suffice to explain the nature and operations of
more particular objects, like the particular species of animal and vegetable
life. The reason for this is that the
first principles and what follows from them are too simple and general. They tell us that everything that happens
must be the result of rolling vortices and the impact of particles. But what vortices and particles, moving in
what ways? Just as it is possible to
compose an infinite variety of novels with the few letters of the alphabet,
so it is possible to account for the generation of an infinite variety of
different species of things from the mechanical principles. To discover what species actually exist, as
opposed to what ones might possibly exist, we appear to need recourse to
experience. But this is just one respect in which it
appears we must have recourse to experience.
When we attempt to explain why particular species behave as they do,
we find ourselves not so much as at a loss for an explanation as overwhelmed
with the number of different possible explanations. Just as it is possible to make clocks with
many different arrangements of gears and wheels that will all tell the same
time, so it often appears possible to conceive of many different mechanical
devices that could all just as well produce the same visible effect. Sunlight
melts wax but hardens clay. How are we
to account for this? Shall we say that
the clay is composed of particles of sticky, gross matter between which
particles of round, aetherial matter have been
trapped, so that the round particles grease the sticky ones and make the clay
malleable, but that the particles of sunlight knock the watery particles out,
so that the remaining particles of gross matter cohere strongly? Shall we say that the wax contains gross
matter and that the sunlight exercises a pulverizing action that has the
effect of turning the wax fluid? These
explanations would work, but we can readily conceive of a number of different
“machines” that could produce the same visible effect. Perhaps the sunlight causes the clay
particles to merely vibrate and rearrange themselves in such a way as to
enclose the water particles in chambers, rather than knock the water
particles out. Perhaps the wax
particles are of a type that can slide past one another when they are set
into vibration by incoming fire particles, but that, when moving slowly,
readily get caught and hooked into one another. Since we do not have microscopical eyes we have no way of seeing the fine,
corpuscular structure of these different materials in order to determine
exactly what machine makes them behave as they do. How, therefore are we to proceed? Under these circumstances, Descartes thought
that we have no recourse but to consult our experience with the operations of
the larger-scale objects whose parts we very readily can see, particularly
the machines of our own invention. To
understand the operation of the muscles for instance, we must consider how we
would construct devices to alternatively draw strings together and release
them. We must then provisionally
suppose that some such machine is the one that actually produces muscular
motion. That is, we must formulate a
hypothesis. And then, if there are
rival, alternative hypotheses that both seem to be likely ways of explaining
the phenomenon, we must look for some respect in which they are different and
devise some sort of experiment that, when performed, would yield one type of
result when one machine is responsible, but another if a different one is
responsible. We must then choose in favour
of that machine that our experience of the results of the experiment
indicates. For example, in the case of
the two rival explanations for why it is that the Sun melts wax mentioned
earlier, we could consider that if the first explanation is correct, then the
wax ought to remain fluid when it is removed from the sunlight, whereas if
the second is correct the wax should quickly solidify again. We could perform the experiment of removing
the wax from the sunlight to determine which in fact occurs, and then accept
or reject the indicated hypothesis. Of course, our hypotheses cannot be wild: they
have to conform to the things Descartes claims to have established so
far. They cannot involve postulating
unextended bodies, forces, real qualities, or other non-mechanical modes of
explanation, and they cannot violate the laws of motion or collision. But
within these broad bounds, we are free to speculate about precisely what
mechanism may be producing the phenomena we observe. Cartesian science may accordingly be viewed as
a three-tiered structure. On the top tier is
metaphysics and first philosophy and all of the things we clearly and
distinctly perceive. It is there that
we do the exercise of the first part of the Principles and establish the fundamental laws of physics. It is there that we learn of the existence
of God, of the equation of body and extension, and of the laws of motion and
collision. On the bottom tier is sensory experience. It is there that we learn, more or less
accurately, what particular sorts of objects there are in the regions
immediately around us and what sorts of effects these objects have on
us. It is experience that teaches us
such things as that there are planets that are carried in circles through the
constellations, that there are tides, that iron is attracted towards the
magnet, and that bodies that feel heavy in our hands tend towards the centre
of the earth. In between the top tier and the bottom there
is a gap. Descartes recognized that
science cannot proceed in a purely top-down fashion to derive all the particular
features of the world from general principles. From first principles we can only carry our
deductions so far, to draw conclusions about general laws and
structures. After that, we must go
down to the sensory level, accept what it tells us about what the particular
phenomena of nature are, and construct hypotheses that connect the general
principles found at the top level with the phenomena observed at the sensory
level. These hypotheses must be
consistent with the general principles and of such a nature as to allow us to
see how the specific phenomena follow.
But because there will typically be alternative, rival hypotheses, all
apparently capable of connecting the general principles with the observed
phenomena, we cannot simply accept the hypotheses as statements of the truth
of the matter. We instead have to rely
on sensory experience of the results of crucial experiments to help at least
narrow down the range of alternative hypotheses. The middle tier of Descartes’s
system, the tier where the gap in the deduction occurs and at which
hypotheses are made, is therefore simultaneously determined by both the lower
and the upper tiers. The hypotheses
that are arrived at must be consistent with the principles discovered at the
upper tier, but it is the lower tier that tells us what these hypotheses have
to explain, and it is the lower tier that judges their adequacy. In this way, we might hope to eventually
arrive at the correct hypothesis. The
physiology of sensation. The Principles concludes with some
important remarks on human nature and sensation. Descartes considered it to be obvious that
human beings are minds that have been intimately conjoined with particular
bodies. But minds are not extended,
which means that they cannot be spread out over the space that human bodies
occupy. Instead, he claimed, there
must be a point somewhere in the body through which bodies and minds
communicate. Information would have to
flow from all the parts of the body to this point and directions to move
would have to be transmitted from this point to all the parts of the
body. Anatomy seems to confirm this,
because it has revealed that the body is full of nerves that all appear to
lead to some point in the brain. Not
surprisingly, Descartes considered the messages that flow along these nerves
to be mechanical. The nerves are
“cords” or “tubes” that are “pulled” or “plucked” or that carry streams of
“animal spirits” that operate like a kind of hydraulic fluid. Given that minds can only communicate with the
remote parts of bodies by means of the mechanism of nerves the possibility of
sensory illusion arises. Due to
amputations, injuries, diseases, or other causes, nerves might be moved
somewhere along their length in just the way they are moved when struck by external
objects and so might send the same signals to the brain that they would send
if affected by external objects. This
is what happens when we feel pain in an amputated limb, or when our eyes are
stuck in the dark. God is not to be
blamed for these sorts of illusions because there is no way to join a mind to
a body without using nerves and so without creating the possibility for this
sort of sensory deception. But God
does what he can to mitigate it. He
designs us so that, in the vast number of “normal” circumstances where our
sensory nerves are affected by objects, we are given ideas that accurately
inform us where those objects are, how they are moving, and whether they are
harmful or beneficial to the state of continued union of the mind with its
body. Descartes’s principal argument
for the ideality of sensible qualities proceeds from these observations,
together with the further observation that the sensory nerves seem to be all
alike, rather than formed in different ways that we might conjecture to be
adequate for conveying different kinds of sensible quality to the brain. As this argument was closely examined in
the Chapter on Principles I.51-76 I
will not review it here. However, I
will add, as a note that what Descartes had to say on this topic goes some
way to address the objections raised by Foucher and
Bayle against his attempt to prove that material things must exist (as
discussed in the previous chapter). Recall that the point of those objections was
that there is little difference between accepting that extended bodies exist
on the ground that we were given a strong natural impulse to believe that our
ideas of extended things are caused by objects that resemble them and
accepting that coloured bodies exist on the ground that we have a strong
natural impulse to believe that our ideas of colours are caused by objects
that resemble them. The one impulse is
as strong and as natural as the other, and if we have recently discovered
that the one is mistaken, we could well sometime discover that the other is
as well. If God is no deceiver for
allowing hundreds of generations to be tricked on the former score, then he
would be no deceiver if he were to allow us to be tricked on the latter as
well. The answer that Descartes could now give to
this objection is that the cases of colour and extension are not at all
alike. God would only be a deceiver
for giving us a natural impulse to make judgments without at the same time
giving us some means for discovering the error. But in the case of sensible qualities we
are given a means to discover the error, namely attention to cases like that
of the phantom limb and blows to the eyes, which give us reason to think that
we experience the sensible qualities that we do because objects touch the
nerves rather than because they transmit qualities to them. This should lead us to the conclusion that
the qualities that we experience in sensation are not like their causes and
that we can therefore not safely assume that objects have those
qualities. The case with extension is
entirely different as motion and impact of objects on the nerves requires
extension. ESSAY QUESTIONS AND
RESEARCH PROJECTS
1. Leibniz’s view that
repulsive force is responsible for the transmission of motion upon impact
naturally led him to suppose that collisions would always have to be
elastic. This is turn led him to
attack Descartes’s account of the laws of collision
on the ground that they violate a fundamental metaphysical principle, the law
of continuity. Outline Descartes’s account of the laws of collision as stated
over Part II, Articles 46-53 of his Principles
of philosophy and Leibniz’s
critique, given over Part II, Articles 46-53 of his “Critical remarks on Descartes’s principles.”
2. In Part II, Article 36
of his Principles of philosophy Descartes maintained
that the same quantity of motion is present after collision as before, so
that quantity of motion is conserved through collision. Leibniz objected to this view, maintaining that
it is rather the quantity of moving force in bodies that is conserved through
collision. (The moving force or “vis viva” is another of the forces
Leibniz attributed to bodies.)
Descartes considered the quantity of motion to be the product of the
quantity of matter and its speed, a formula very close to that |
