Descartes and Rationalism
René Descartes, 1596-1650 (Latin Renatus Cartesius, hence the term Cartesian)

Descartes’ Project Descartes was a contemporary of Galileo and Kepler. He was born about 50 years after the publication of Copernicus’ De Revolutionibus. Thus he lived right at the beginning of the scientific revolution, as the medieval world view was beginning to collapse. Descartes was a mathematician and physicist, as well as a philosopher. He was the first to offer a system of mechanics that applied both to terrestrial and heavenly bodies. His system was based on a set of laws governing the motions of particles, including various types of collisions. These laws, though unsuccessful, were a precursor of Newton’s laws of motion, and Huygens’ solution to the collision problem. Descartes had the disturbing experience of finding out that everything he learned at school was wrong. From 1604-1612 he was educated at a Jesuit school, where he learned the standard medieval, scholastic, Aristotelian philosophy. In 1619 he had some disturbing dreams, and embarked on his life’s work of rebuilding the whole universe, since the Aristotelian universe was doomed. (Descartes didn’t suffer from lack of ambition!) The problem for Descartes was that he couldn’t merely tinker with the medieval picture, fixing it up here and there, because it was fundamentally wrong. It was rotten to its very foundations. The only way to proceed was to tear it down completely, and start building again from scratch. For an analogy, suppose your computer has been attacked by a virus, so that many important system files have been corrupted. You don’t know which files have been corrupted, so you can’t really trust any of them. The only thing to do is to erase the hard drive completely and re-install everything. How did Descartes “erase his hard drive”? He used what is known as his method of doubt. He tried, as far as was possible, to empty his mind of all beliefs, to suspend judgment about everything. Of course this isn’t easy, as one does not simply choose what to believe. On cannot help believing that things are basically as they seem to be. To help him doubt even things that seem obviously true, Descartes meditated on various possible “sceptical scenarios”. These are situations that cannot be ruled out, i.e. they could be one’s actual situation, yet if they are true then just about all one’s beliefs are false. These are well known. First Descartes considered that, when asleep and dreaming, everything seems just as real and true as when he is awake. So perhaps he is dreaming at this very moment, in which case he may not be sitting in a chair, writing, and so on. To make his doubting even deeper and more radical, Descartes considered the possibility that God is evil (the “evil demon”) and has the aim of deceiving Descartes as much as

possible. All of his sense experience, everything he sees, hears, touches, smells and tastes could be a sophisticated illusion. The demon feeds the fictitious sensory inputs directly to his conscious mind. Even his sense of motion and positions of his limbs could be part of the illusion. (Descartes should have been on the credits of The Matrix! You can also see connections with Berkeley’s later idealism here.) On this scenario, which cannot be ruled out, almost everything he believes is false. An important insight of Descartes, concerning the demon scenario, is that one’s physical body might be an illusion. This extended, geometrical object, with arms, legs, hair, and so on, might not exist. One’s real body might be quite different; perhaps one is really four-legged, feathered, or completely bald? Or perhaps one has no physical body at all! Isn’t it possible that one’s self is a purely thinking “substance” (object) with no geometrical properties like volume and shape? One might be a disembodied soul, receiving fictitious sense experiences from the demon. I cannot be sure, therefore, that I have a physical body. Is there anything I can be sure of? Is there any limit to the method of doubt? Is there any belief that is immune from all possible doubt? Perhaps my conscious mind is also an illusion? Perhaps the demon has deceived me into believing that I exist as a thinking being? Is this conceivable? Descartes finds that he’s not able to even to conceive of this as a possibility. If there’s a deception, then someone must be deceived. Thus the person deceived must exist, and so no one can be fooled into thinking they exist, when really they don’t. Can I be fooled into thinking I’m conscious, when really I’m unconscious? Can I believe that I have conscious experiences, when really I do not? Again, the answer is surely not. Even though my mental images might not be caused by real objects, I cannot doubt that I am aware of mental images. I may not really see a tree, but I certainly seem to see a tree. I cannot be deceived into thinking that I am conscious. In other words, Descartes reasoned that, since I am conscious, I must exist. I think, therefore I am. (Cogito, ergo sum.) Having purged his mind of all error, Descartes set about rebuilding a new view of the world. His approach was foundationalist, which means that one builds a belief system in rather like the way one builds a house. You start by laying foundations, which must be solid and secure. Then you add beliefs that are firmly supported by the foundations, and then further beliefs that are supported by those added beliefs, and so on. So, Descartes laid his solid foundation, that he exists as a thinking being. Now, this might not seem like very much knowledge. If this is all Descartes knows for sure, then what follows from it? What can be built on this foundation? Not very much, it would seem. He can’t even add belief in material objects (his own body, trees, tables and so on) as these might be illusions. Descartes finds a way out of this problem, however, by arguing first for the existence of God.

Descartes’ argument for the existence of God is roughly this: I have a concept of God, as perfect, infinite and so on. This concept is not vague or fuzzy, but quite clear and distinct. An idea must have a cause – even an idea cannot appear from nowhere. Moreover, it is obvious that, while a greater object can cause a lesser one, the reverse is impossible. No object can produce something greater than itself. Thus, my idea of God, which is supremely great, can only have been caused by just such a being. Thus God, as I conceive of him, must exist. Now, since God is perfect, he must be supremely good, containing to evil at all. Since deception is evil, it follows that God is not a deceiver. God would not allow me to be systematically deceived about everything, in such a way that I cannot possibly discover the truth. Thus my sense experiences must in fact be reliable, for the most part. While I am sometimes deceived, I can at least discover these errors by further investigation. For example, a tower may look round from a distance, but when we get closer we see that it is square – we know that the closer view is more authoritative than the distant view, so we end up with a true belief. With his belief in the reliability of his senses restored, Descartes could then acquire common-sense beliefs about material objects. He went on to build an elaborate system of mechanics and a theory of planetary motions, among other things.

Descartes and Rationalist Physics Empirical knowledge plays a crucial role in Descartes’ physics. After all, a foundational element of human knowledge is our knowledge of God’s existence, which is mostly required (it seems, for Descartes) to ensure the reliability of our senses. Descartes certainly uses the ‘empirical method’ of using observations to guide and test the theories he constructs. Descartes is not an empiricist in the philosophical sense, however, for he reaches conclusions that do not follow from the empirical evidence alone. He freely uses rational principles, such as symmetry and economy, in addition to empirical data, in formulating his mechanical theories. In doing so he effectively appeals to (supposed) innate knowledge of physics. Here are some examples.

Refraction law It is observed that light bends as it moves from air into something denser like water or glass. Descartes argued that light slows down when it enters such a dense medium, but in a tricky way. Descartes considered the velocity of the light to contain two separate components, one parallel to the surface of the glass and one perpendicular to it (shown as red and green lines below). When the light hits the surface of the glass, only the perpendicular (red) component of its velocity is reduced. It follows that the light bends, as shown below.

Slingshot argument. The ball has no memory, as it were. The instantaneous motion of the ball (if that makes sense) is a tiny straight line. Hence only this motion “remains in the ball”. Once the ball slips out of the sling, therefore, it must continue its present straight line, which is the tangent to the circle at that point.

“The second law of nature {which I observe} is: that each part of matter, considered individually, tends to continue its movement along straight lines, and never along curved ones; even though many of these parts are frequently forced to move aside because they encounter others in their path, and even though, as stated before, in any movement, a circle of matter which moves together is always in some way formed. This rule, like the preceding one, results from the immutability and simplicity of the operation by which God maintains movement in matter; for He only maintains it precisely as it is at the very moment at which He is maintaining it, and not as it may perhaps have been at some earlier time. Of course, no movement is accomplished in an instant; yet it is obvious that every moving body, at any given moment in the course of its movement, is inclined to continue that movement in some direction in a straight line, and never in a curved one. For example, when the stone A is rotated in the sling EA and describes the circle ABF; at the instant at which it is at point A, it is inclined to move along the tangent of the circle toward C. We cannot conceive that it is inclined to any circular movement: for although it will previously have come from L to A along a curved line, none of this circular

movement can be understood to remain in it when it is at point A. Moreover, this is confirmed by experience …” Descartes, Principles of Philosophy, Part II, Article 39.

The cannon ball and small shot argument. According to Aristotle a large cannon ball will fall faster than a small steel shot. But this can’t be right, for imagine that two such balls, one large and one small, are welded together. Then, thinking of the two balls as separate systems, the smaller ball will try to go slower than the larger, and hence will drag on the larger, making the whole system fall slightly slower than the large ball alone. But thinking of them together as a single system, they form a single body of slightly greater mass than the large ball. This should then fall slightly faster than the large ball alone. This is a contradiction. In a similar way, the small ball cannot fall faster than the large one. Hence the two balls must fall at the same speed. The reasoning that “the smaller ball will drag on the larger, making the whole system fall slightly slower than the large ball alone” relies on the idea that the balls in the whole system will try to do exactly what they would if they were not so joined. The whole is just the sum of the parts, so that the nature of the small ball is not changed in any way by being joined to the large ball. Descartes’ collision law. When equal bodies approach along the same line at equal speeds, they rebound at equal speed. (By symmetry: symmetric cause ⇒ symmetric effect) -------------------------------------------Archimedes buoyancy argument. 1. The upthrust on any submerged body should be the same as on the water that would otherwise occupy the same space. But, 2. The water in a tank remains at rest (unless heated, stirred, etc.) Hence, 3. The upthrust on a submerged chunk of water exactly balances its weight. Therefore 4. the upthrust on a submerged body exactly equals the weight of the water it displaces. -----------------------------------------------

Inverse Square Law (for any force field produced by a point particle, e.g. gravitational and electric fields). (Newton claimed to deduce the law from Kepler’s laws)

Since a point is spherically symmetric (invariant under all rotations) it can only cause fields that are also spherically symmetric. (Symmetric cause, symmetric effect.) Thus the emanation from the point that produces the field will, at distance r from the particle, be evenly spread over the surface of a sphere of radius r (centred at the particle). This sphere has a surface area of 4.π.r2, so that the intensity of the field is proportional to 1/r2.

“We find a physical law of reciprocal action applicable to all material nature, the rule of which is that it decreases inversely as the square of the distance from each attracting point—that is, as the spherical surfaces increase over which this force spreads—which law seems to be necessarily inherent in the very nature of things, and hence is usually propounded as knowable a priori.” (Kant, Prolegomena)

Common Rationalist Principles 1. Every event has a cause. (Objects and events don’t appear “from nowhere”, spontaneously, all by themselves.) 2. Exactly similar causes always yield exactly similar effects. 3. If a cause is symmetric (in a certain respect) then its effects must also be symmetric (in the same respect). 4. The parts of a system can be considered as individuals, and will behave independently of each other, unless they exert forces upon each other. (Separability principle) 5. A similar situation holds with respect to instants of time. They can be considered as separate entities, acting independently of each other. 6. Forces on a system can only be exerted by the immediate environment, not by distant objects. (Locality principle) 7. A similar situation holds with respect to instants of time. A physical system “lives in the moment”, as it were, and is directly affected only by what happened just before. It has no “memory” of what occurred before that. (Markov principle.)