My purpose today will be to relate some information about the methods of science that Descartes advocated and used during his lifetime. I hope that you will see this talk as a continuation of the one delivered two months ago which focused upon Copernicus and the problems of astronomy in his time. That talk attempted to show how inappropriate it would be to expect that Copernicus' near contemporaries should have accepted his theory. Partly because the scientific evidence for the theory was not unequivocally on his side, especially for physics and astronomy. And partly because it seemed quite right to many of them on both sides of the Copernican debates to find a role for the Bible in their assessments of scientific value.

This discussion of the character of scientific reasoning will consider Descartes, a particularly interesting figure. Not only was he a historically important mathematician and scientist, developing theories about physics, cosmology, optics, physiology, psychology, and more; he also was a philosopher, and particularly important to this presentation, a philosopher of science.

So, something about his science itself, to give some idea of what the science he put forward was like; and a view about his philosophy of science and his ideas about how science should be pursued. And, with any luck, to complete the parallels with the earlier talk, there will be an opportunity to mention another interesting and enjoyable squabble between religion and science in which Descartes was involved.

An Introduction to Descartes' Early Life

Rene Descartes (1596-1650) was, as a youth, a bright but not an especially noteworthy character. He studied at the College of La Fleche, a boys' school, until about 1613; he then attended law school at Poitiers. After law school, by his own reckoning, he was a licentious young rake of a soldier. He found an intellectual companion in Holland late in 1618 in Isaac Beeckman, who encouraged him to pursue studies in music and mathematics (for which he showed a great aptitude), as well as physics, navigation, and many other scientific investigations. We find in his notebooks a very self assured young man; the author of a small collection of notes and thoughts, one of which is the abstract for the 'Treasure Trove of Polybius', a book that most doubt was ever written. I think this piece of text provides a fair enough vignette of the young M. Descartes:

"This work lays down the true means of solving all the difficulties in the science of mathematics, and demonstrates that the human intellect can achieve nothing further on these questions. The work is aimed at certain people who promise to show us miraculous discoveries in all the sciences, its purpose being to chide them for their sluggishness and to expose the emptiness of their boasts."

Descartes was working upon problems of mathematics and methods for scientific inquiry, though finding little success with anything so ambitious as the treasure trove. On the 10th of November, 1619, Descartes had a dream/vision that apparently changed his life. Among the visions was one of a book with 'what road shall in life shall I follow?' written on it. Looking back in his autobiography of 1637, perhaps embroidering on his experiences a little, Descartes explains the change in his thoughts:

"I stayed all day shut up alone in a stove-heated room, where I was completely free to converse with myself about my own thoughts. Among the first to occur to me was the thought that there is not usually so much perfection in works composed of several parts and produced by various different craftsmen as in the works composed of one man...And so I thought that since the sciences contained in books...is compounded and amassed little by little from the opinions of many different persons, it never comes so close to the truth as the simple reasoning which a man of good sense naturally makes concerning whatever he comes across.

"Admittedly, we never see people pulling down all the houses of a city for the sole purpose of rebuilding them in a different style to make the streets more attractive...But regarding the opinions to which I had hitherto given credence, I thought that I could not do better than undertake to get rid of them, all at one go, in order to replace them afterwards with better ones, or with the same ones once I had squared them with the standards of reason."

This passage suggests several of the essential elements of Descartes' method. He chooses what road he will take, and is set to rebuild opinion into knowledge; but first he pauses: his autobiography continues with a bit of the Cartesian humility we find in the passage about 'Polybius':

"I thought that first of all I had to try to establish some certain principles in philosophy. And since this is the most important task of all, and the one in which precipitate conclusions and preconceptions are most to be feared, I thought that I ought not try accomplish it until I had reached a more mature age than twenty three..."

Method and the Meditations

After a few more years of travel during which Descartes performed more scientific investigations on such diverse topics as anatomy, rainbows, and physics, he felt able to publish his musings on method along with the autobiography, at the ripe age of forty one.

Descartes distilled his method into four rules, quite reminiscent of his musings concerning his experiences of eight years before:

"The first was never to accept anything as true if I did not have evident knowledge of its truth: that is, carefully to avoid precipitate conclusions and preconceptions, and to include nothing more in my judgements than what presented itself to my mind so clearly and so distinctly that I had no occasion to doubt it.

"The second, to divide each of the difficulties I examined into as many parts as possible and as may be required in order to resolve them better.

"The third, to direct my thoughts in an orderly manner, by beginning with the simplest and most easily known objects in order to ascend little by little, step by step, to knowledge of the most complex, and by supposing some order even among objects that have no natural order of precedence.

"And the last, throughout to make enumerations so complete, and reviews so comprehensive, that I could be sure of leaving nothing out."

Descartes' Meditations are an attempt to carry out such a project, showing a sort of order of re-discovery for newly-secure knowledge on new foundations. As he stated in another passage of writing, it was to be a method like dumping all of the apples out of a basket, replacing them one-by-one so that none would get by that could spoil the rest: no rot at the base of knowledge. He attempted to provide secure foundations of knowledge by instituting the following test: for any candidate for the beginning of a chain of knowledge, can I doubt it?

On these ground rules, Descartes comes to doubt almost everything we would consider ourselves to know. The work is divided into six sections, six meditations. In the first, he brings this project of doubt to its full development. In the second part, he finds one thing he can be certain of: that he himself exists, whenever he is thinking that he exists; for how else could the thinking occur without a thinker? Hence the famous dictum: "I think, therefore I exist."

An interesting point, for how can one doubt it?

Method, Order, and Science

The point is not to tell all of Descartes' metaphysics nor all of his science; it is to clearly represent his professed method and the way in which this method affected his progress in science. The method is to allow doubt to intrude wherever it may and build certain knowledge only upon the basis of prior certainties. These prior certainties came to be delineated in a very particular order, however. Descartes felt reason to believe that they had to be; and so there is much to tell about the influence of his method on his scientific thought.

We can see the importance of this method when we consider the next several certainties that Descartes develops in the Meditations, and how they affect the rest of his scientific system. After the certainty of his own existence, Descartes came to the certainty that he was not a body: for since he knew through thinking that he was, and yet did not know on this account anything about his body, or even that he had a body (for example, he did not know that his 'body' wasn't just the result of a bad dream), it seemed reasonable to him to conclude that this thing that he did know wasn't a body. This was the (unfortunately bad) argument that Descartes used to show that he was an immaterial soul: the argument that lies at the center of the famous 'Cartesian Dualism' of body and soul. Of course, Descartes did not invent the dualist conception of the person, but he played a great role in entrenching this belief in our culture. He wove much of his scientific investigation of psychology, morality, and physiology around this prior certainty; for if it was built first in Descartes' system of knowledge, it remained a tenet to be built around thereafter.

Descartes' second certainty about the world around him also had great scientific significance, for it was his certainty about God's existence. Descartes felt it necessary to prove God's existence and explain God's nature before proving anything further since the existence of a good God would ensure that what his senses told him about the world was neither erroneous nor fantasy. Indeed, he appears to have honestly felt that a divine being's power might be so great as to allow that being to change the truths of mathematics from what they are. Descartes, then, had to prove the existence of a good God who wouldn't try to deceive us in this way, in order for any further knowledge (in the sciences, for example) to be certain. Proving the existence of no Gods at all might have done the job for him, but that wasn't an advisable approach in 17th century Europe.

Cartesian Science

Descartes' systematic construction plan for certainty should certainly not be taken to be representative of how he in fact inquired into subjects of science; at least, not entirely. He certainly was engaged in scientific activity long before he proved his own or God's existence, and we should not really believe that he went about destroying all of his knowledge about science and built it up again upon these certain foundations when he did finally come to these conclusions. Nonetheless, this method that he espouses in his writings does stand, for him, as an ideal for all knowledge, including scientific knowledge. Ideally, all knowledge would be connected back to indubitable first principles, and any that is not is that much the less certain, and that much the less worthy of the title 'knowledge'.

Realistically, we can also see much of his reasoning in science as representative of the ideal of systematicity: for his science is quite systematic. It is a reasoning from rational principles, from the simple towards the complex, from mystery towards truth. Descartes presents in his writings something of a deductive analysis of science from prior principles, but not the strict deduction of a logician. Observation, he finds, is only necessary for determining the details of science and is not relevant to decision regarding framework.

A quick example of this aspect of Descartes' science can be found in his arguments concerning the 'geometricization' of matter. Descartes presents a striking effort to explain what matter is, and he finds, partly on the basis of his understanding of geometry, that the 'essential property' of matter (or 'corporeal substance') is extension. This leads him to the conclusion that space and matter are only different modes (modifications) of the same thing. Space is a 'corporeal substance', a corporeal substance lacking most but not all corporeal properties.

Another reason behind these conclusions runs as follows: each of the other characteristics normal to matter can be found to be missing from some. Glass is colorless. Fire is not hard. But all matter must have extension. Further, since space doesn't disappear when a stone is moved out of it to another place, matter must just be space, with some different (extra) qualities added in.

Very odd and interesting reasoning but it does represent some of Descartes' 'scientific method' and argument from first principles rather well.

Descartes' approach should not be considered a 'failure' because it is superseded by the quantitative approach of Newton. Descartes did do useful, quantitative, more long-standing work in optics. His approach to physics (dynamics, terrestrial and celestial) and astronomy was grand and fascinating. It was a great system, but less worked out and less detailed for it did not come into close contact with the details of observational astronomy at Descartes' time. Newton exploited this mismatch very well in his theoretical reply to Descartes in the Principia Mathematica.

Descartes and the Eucharist

There is much to be considered regarding Descartes' scientific findings. I would like to close by offering a little extra, interesting piece of history concerning one of his scientific battles just to show how some of the connection between religion and science mentioned in the Copernicus lecture still hangs on for Descartes.

You have already heard about how Descartes felt it necessary to prove the existence of God before many other things, and you also heard, I hope, an interesting logical reason for his doing so. Another area in which Descartes' science and theology connected, perhaps even clashed, is the miracle of the Eucharist. That miracle, as any good Catholic will tell you, is the genuine change of substance, or transubstantiation, of the eucharist cracker and holy wine into the body and blood of Christ. It is supposed to be a genuine miracle, one that happens (according to one account) as the host hits the tongue.

But how could this intersect with Cartesian science? If matter and space are indistinguishable, excepting certain accidental physical properties, and if body and animate soul are as distinct as Descartes' arguments suggest they are, then how could such a transformation take place? That is, if matter only has a 'geometric' essence and properties added on, how could anything, once it is detached from Christ himself, be legitimately considered to be 'Christ's body'? At best, the only way to distinguish a piece of Christ's body, without a soul attached from anything else, would be to find out whether it once was attached to Christ's body. But a cracker is a cracker, not Christ's body--so how does it become so? This problem, at the interface of religion and science, was one that exercised Descartes a great deal, and one that he could not solve to the satisfaction of many intellectuals of his time.

So runs a rather interesting scientific problem of the 17th century concerning a specific phenomenon that a physical theory of the time would have to be designed to accommodate. And it is not a minor one, since, as one historian has argued, the problem of the Eucharist, and not Copernicanism, may have been at the root of Galileo's condemnation by the Church.

A note on useful sources

Quotations from Descartes' writings are from the translation of Cottingham et. al., in Descartes, The Philosophical Writings of Descartes. J. Cottingham, R. Stoothoff, D. Murdoch, and A. Kenny, translators and editors, 3 vols., Cambridge, U. K., Cambridge University Press 1984-91. William Shea, The Magic of Numbers and Motion, gives a fine intellectual biography of Descartes and his times.

--Dr, Eric Palmer