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Descartes - Study Notes

DESCARTES by Tom Sorell

Tom Sorell is Professor of Philosophy at the University of Essex. His book on French philosopher René Descartes is divided into 20 chapters which take us through Descartes’ life, side by side with how his work and thinking developed in mathematics and philosophy. He was a major and original thinker in both these fields, with important contributions to physics and optics. His best known publications were his Discourse on Method (1637), the Meditations (1641) and the Principles of Philosophy (1644). He lived from 1596 to 1650.

Chapter 1 of Sorell’s book is entitled ‘Matter and Metaphysics’.
Descartes is probably best known as the man who said ‘cogito, ergo sum’, Latin for ‘I think, therefore I am’, an obvious, almost trite piece of reasoning which was the basic principle of his theory of what has to be known for ‘stable and exact science to be possible at all’. Also, by a very abstract argument Descartes tried to prove that only the geometrical properties of length, depth and breadth, plus motion, were needed to explain natural phenomena.

Galileo had pioneered this approach, so had Francis Bacon to an extent, but Descartes wanted to establish the primary cause of nature, God, and to deduce the causes and effects of all other natural phenomena. He only concerned himself with what could be described mathematically such as size, shape, speed etc., whilst other sorts of facts about things such as colour or smell were relative to the sensory powers of human beings. So there was a distinction between the exact, objective way of describing phenomena and the sense based conception which was more open to interpretation and doubt. But Descartes’ conception of mathematical physics has subsequently been proved to be remarkably successful.

Chapter 2, ‘The Discovery of a Vocation’, starts with a brief summary of Descartes’ early life.
Born into an educated background (mostly lawyers), Descartes was sent to a Jesuit college at age 10 where he was taught science and mathematics (in which he was particularly good). Although the college was generally scholastic in its approach to science, there was an awareness of astronomy and the work of Galileo. After leaving college Descartes went to Holland where he subsequently spent most of his life, on and off. He became a friend of a Doctor Beeckman who greatly encouraged his enthusiasm for science. In 1619, whilst dozing by a hot stove, he had a ‘daytime vision’ which seemed to be a sudden insight into the outlines of the scientific and mathematical research to which he would devote his life.

Chapter 3, ‘One Science, One Method’, relates how Descartes became ‘increasingly receptive to the possibility of a master science, or a master method of scientific discovery’.
In this way there would be a unity, under mathematics, of a long list of sciences previously regarded as distinct such as arithmetic, geometry, astronomy, optics, mechanics etc.. He borrowed from but did entirely accept the ideas of a 13th century writer, Raymond Lull; likewise he considered but subsequently disowned the ideas of the Rosicrucians.

He realized he could only achieve this aim, the unity of the sciences, if he had a systematic method of doing so. He could also see it would take him many years of thought and preparation to formulate such a method. In fact it took him nine years, until 1628.

Chapter 4 is ‘Absolutes, Simple Natures and Problems’.
He aimed at a comprehensive list of all the precepts or rules that should be followed in pursuing scientific enquiries. He never completed this list, the Regulae, written in the 1620’s but not published until 1701. He noted that there are determinate methods for settling questions in the mathematical sciences, and he wanted to apply this to other disciplines. He favoured this approach in Rule Four, observing that mathematics is concerned with numerical ‘order or measure’ in the most general sense; the question of what is being counted, ordered or measured being irrelevant. He believed in the unity of science, that ‘all the sciences are interconnected’.

Rule Five tells the enquirer to reduce complex or obscure questions step by step to simpler ones. Other rules elaborate this, and he shows how this method can be applied in optics among other examples. His aim was to develop a procedure for ‘translating scientific problems that were not ostensibly about number and figure into ones that were’. Along the way he introduced co-ordinate geometry, changes in algebraic notation that are still in use today, as well as how lines and curves can be represented in algebraic notation.

Chapter 5, ‘Roaming about in the World’, relates how Descartes travelled outside France in the earlier to middle 1620’s.
During this period he did a lot of thinking and seemed to be systematizing what he thought into some sort of order. Firstly there is logic, then mathematics, then philosophy, followed by physics, mechanics, medicine and morals. His general procedure was to reject whatever seemed to him to be doubtful, but he retained belief in a moral code, religion and his country’s laws and customs. After visiting various countries, in 1626 he settled in Paris where he became quite well known as a thinker.

In Chapter 6, ‘Paris’, Sorell notes that Descartes chose to remain neutral in the current debates and discussions of that period.
But he did take part in a public debate where he said that although something was needed to replace scholastic philosophy, whatever it was would have to be guided by a method of reasoning capable of leading to certainty, not merely probable conclusions.

Chapter 7, ‘The Suppressed Physics’, relates a curious but important episode.
By the end of the 1620’s the Paris intellectuals were eagerly awaiting Descartes’ latest thinking on science and philosophy. So from 1629 Descartes worked on a major treatise, Le Monde (“The World”), which was intended to outline a unified explanation of all natural phenomena. It was nearly ready in 1632 and it included a complete theory on the origins and workings of the solar system incorporating the Copernican hypothesis that the earth moves annually around the sun. The kind of explanations which Descartes gave in physics were completely different from the ancient Aristotelian account which was full of qualitative explanations, e.g. a body falls because it possesses the ‘quality’ of heaviness. Instead, Descartes’ account consisted of mathematical statements about the quantifiable, that is, the sizes, shapes, motions and velocities of matter.

However, the work was not completed on schedule; corrections were still being made in 1633, and when it was finally ready Descartes heard that Galileo had been condemned by the Inquisition at Rome. So in 1634 Descartes decided not to publish. It was finally published in 1664, thirty years later and fourteen years after Descartes’ death.

Conciliating the Church was a problem for Descartes. He could see that his physics, based strictly upon logic and mathematics, was radically contrary to the Aristotelian scholasticism which was the Church’s official doctrine. But he too was a religious man, and he sought to show that ‘scientific knowledge of the physical world depended on the existence of a mind or soul, distinct from the body, that had to know God before it could grasp the principles of sound physics’. Hence, the origin of ‘Cartesian dualism’ which we shall look at later.

Chapter 8 is ‘Three Specimens of a Method’.
Once Descartes had decided not to publish his work on physics, he decided not to publish his Treatise on Man, for much the same reasons. However, he completed the Dioptrics which dealt with optics by 1635; another essay, the Meteors which dealt with meteorology, was also completed; and his Geometry was also completed by 1637. His Discourse on Method was completed last, and all four works were published as a single work in 1637. By unveiling disparate specimens of his work, he could ‘advertise his method without revealing its controversial applications in connection with planetary motion’ – which would have offended the Church, of course. Sorell does not put it this way, but it seems that Descartes was doing a bit of intellectual ‘ducking and diving’ – for perfectly understandable reasons. His friend Marin Mersenne urged him to publish his physics, but Descartes declined, waiting for the ‘intellectual climate’ to be more favourable.

In Chapter 9, ‘A New Logic’, it appears that Descartes’ philosophy began to go off the rails, in my view, at a critical point – although it began quite favourably.
From Sorell’s account his Discourse on Method incorporated four important precepts from the earlier Regulae:-
1. Never to accept anything as true if he did not have evident knowledge of its truth.
2. To divide difficulties into as many parts as possible so as to resolve them better.
3. To begin his thoughts with the simplest objects in order to ascend step by step to the more complex.
4. To ensure that enumerations are so complete as to leave nothing out.

These are excellent precepts of method when it comes to acquiring and analysing complex data. But Descartes claimed they supersede Aristotelian logic, which he must have misunderstood. Sorell should have mentioned that logic is not about acquiring data at all; it is simply a set of rules about valid deduction from the premises of an argument to a conclusion, as in ‘all A’s are B’s, all B’s are C, therefore all A’s are C’. Descartes was correct in rejecting Aristotle’s physics which was out of date and erroneous, but his logic was ‘right first time’, subsequently endorsed and absorbed in the mathematical logic of Frege and Russell in the 19th and 20th centuries.

Descartes claimed that the certainty of a piece of reasoning depended not on the formal or structural relations between premisses and conclusions, but on the ‘impact the propositions made on a mind that had perfected itself sufficiently to reach ideal levels of attentiveness and controlled assent’. Sorell says ‘the introduction into logic of psychological criteria of conclusiveness is now often thought of as a retrograde step’. I would put it more strongly: it was a major mistake which Frege called psychologism. By this Frege meant that a statement such as ‘2+3=5’ is true not because ‘it’s crystal clear’ or ‘it’s obvious’ but because it is true by definition. Feelings of certainty are not relevant.

To be fair to Descartes, he recognized the problem facing his method. He could see ‘that only purely mathematical reasoning could really be regarded as incontrovertible. Once reasoning relied on extramathematical assumptions about matters of fact [as in the Meteors or the Dipotrics]..... it lost the rigour necessary to put it beyond dispute’. So he concluded that nothing would solve this problem except a ‘demonstration of the principles of physics by metaphysics’. Some would say that this is only another mistake.

At the beginning of chapter 10, ‘The Need for Metaphysics’, Sorell explains that basic to Descartes’ argument is ‘the proposition that human beings are the creation of a supremely benevolent God who has given us a version of his own intelligence’.
But by what process of reasoning does Descartes make this assertion? He starts with the assertion of ‘a necessary connection between his thinking and his existing’ – ‘I think, therefore I am’. I think we can accept this as true by definition; it would be implicitly self-contradictory to assert ‘I think and I do not exist’. But the critical question is, how does Descartes move from the truism that he exists to the assertion that God exists?

Regrettably his arguments appear to be brief, and not very clear. For example he asserted that certainty about the existence of God was greater than that about material objects, but (from Sorell’s account, at any rate) it is not clear why. Most people would say it’s the other way round. Another difficulty is that ‘certainty’ is a very subjective and indeterminate notion - why should my feeling of certainty be any ‘truer’ than your feeling of doubt?

Rather a curious ‘thought-experiment’ which Descartes conducted was the imaginary supposition that everything he perceived or thought he perceived was the creation of a malevolent demon who was deceiving him all the time. Such a scenario, he thought, could not possibly be true. Maybe not, but it is not clear why not, nor is it clear why it follows that there must be a God who would not have deceived him in this way. What if there is neither God nor demon? I do not know whether Descartes considered this possibility or not.

Descartes does however give two ‘proofs’ for God’s existence, both very debatable. The first is that we know we are imperfect creatures, so it follows that we must have an idea of ‘perfection’. But ‘perfection’ can only come from a perfect being, God. The difficulty is that if this argument is correct, then we can argue anything at all into existence by having an idea of it.... The second argument, often called the ‘ontological argument’, is that ‘existence’ is a perfection, so there must be a supremely perfect being which must by definition exist. But nothing can exist by definition because ‘existence’ is not a predicate.
Just to explain that point, in order to describe something you simply list all its attributes. That is not the same as saying that it exists, which is a separate question - you can have a perfectly accurate description or definition of a unicorn for example without saying or implying that it exists in reality. Questions of definition and of existence are entirely different things. That is why existential statements cannot follow from definitions.

But we are still a very long way from establishing the sort of metaphysics Descartes was seeking to justify his physics. Somewhere along the line, he must have taken a wrong turning.

Chapter 11, ‘The Meditations’, takes us no further forward.
Started in 1639, published in 1641, the book seemed to have a dual purpose. Officially it was ‘billed’ as a demonstration of ‘some truths of Christianity’, but it also had a ‘crypto-programme of destroying the principles of Aristotle’, the scholastic physics we have already encountered.

There are six ‘meditations’. The First sets out his original doubt; the Second relates to the ‘demon deceiver’, and the Third sets out a concept of God as a supremely good creator who would never let falsehoods seem evident ‘to an attentive human mind intent on finding the truth’. This enables us to be confident that material objects and their mathematical properties exist, so that mathematical physics is possible. I would suggest that his line of reasoning is ingenious but basically flawed because its ‘lynchpin’ is fallacious. As we have seen, existential assertions about God or anything else cannot follow from definitions (particularly a rather conjectural definition which Descartes seems to have devised himself).

Oddly, Sorell does not seem to summarize the Fourth, Fifth or Sixth Meditations. In Chapter 12, ‘Doubt without Scepticism?’, he briefly relates how the Meditations was not well received by many of its readers. There was much misunderstanding. In particular Descartes deliberately outlined sceptical arguments in detail not to advocate scepticism but to criticize it and to illustrate its shortcomings – but many readers jumped to the conclusion that he was advocating scepticism himself.

For example he set out the ‘dreaming conundrum’. How can I tell if I’m not dreaming right now? If I cannot tell, then maybe the beliefs I form in my present experience are all false. This is quite a good case for scepticism about the reality of the external world and its contents which I think I perceive. It is not easy to refute. Descartes argued that even if scepticism could not be conclusively refuted, we still have the basic concepts of matter, shape, number, space, time etc., which are what counts. But is this sufficient to refute scepticism?

The basic problem was that Descartes wanted to argue that we cannot trust our senses, so we must doubt them – but if so, how can we avoid scepticism? It is as if Descartes is walking a philosophical tightrope; he wants to avoid outright scepticism at all costs. The only way out was to argue that although the mind relied on the senses for some of its thoughts and ideas, it ‘possessed other information independently’ by the light of divinely inspired reason. In this way the elementary truths of mathematics and physics are known to human beings. Whether this account is convincing or not is debatable.

Chapter 13 is entitled ‘The Theologians and the God of Physics’. The arguments of the Meditations were supposed to lay foundations for physics that would be acceptable to theologians and ‘to answer influential people who claimed that the new Cartesian science was atheistic’. The chapter relates how Descartes’ philosophy became a public issue, and how it was condemned and banned at the University of Utrecht in 1642.

Descartes claimed that his philosophy ‘either left matters of orthodox theology undisturbed or gave them better backing than was available in scholastic philosophy’. He argued ‘the mind cannot make mistakes when it does everything possible to avoid error, for then the mind would suffer from a defect that would argue for imperfection in its Maker, and its Maker, God, is perfect, without defects. The mind’s clear and distinct ideas must then be true’.

As Sorell comments, Descartes’ argument involves a circularity. ‘In order to prove that God exists, he has to use premisses that are supposed to be true in virtue of their clarity and distinctness, and it is not until God’s existence is proved that anyone can be sure that clear and distinct perceptions are true’. But apart from this chicken-and-egg situation, there are other difficulties as with the ontological argument, already mentioned, and variants of it such as the ‘causal argument’. ‘The idea of God has to be caused by an infinite substance, namely God. So, given an idea of God, God must exist to cause the idea’. But this is only another circular argument, of course, a variation on the same theme.

Chapter 14 is ‘Ideas’.
Descartes ‘theory of ideas’ involves the basic notion that the source or cause of an idea can be different from the idea itself or what it represents. He denied that our scientific understanding of the world around us depends upon the operations of the sense-organs; he maintained that the action of bodies on the sense-organs was entirely a matter of impact, with after-effects in the nervous system and in a gland in the region of the brain called the ‘pineal gland’. The rational soul was supposed to be joined with the body at the pineal gland, located somewhere in the brain.

Only things that exist in the mind and represent other things should be called ‘ideas’, although ideas could include non-representational things such as willing, desiring or judging. There had to be a ‘likeness’ between an idea and what it was of, and Sorell’s summary on p74 of Descartes’ account on the ‘ideas’ of God or of number is far from clear. Even less clear is how the ‘rational soul’ does not depend for its operation on the sense-organs and can exist without a body. It is impossible to summarize here all the ins and outs of Descartes’ thinking on these topics, but it is worth recording that the notion that the mind (or brain) has innate capacities and ideas has turned out to be fruitful in contemporary linguistics.

Chapter 15 is ‘The Mind’.
Descartes claimed that many of our ideas are independent of sense-experience, and that the mind ‘can be conceived of as quite complete even when it lacks a faculty of sense-perception’. ‘The only capacities a mind must possess are purely intellectual ones and the ability to perform the kind of willing involved in judgment’. In the ‘Objections’ which readers raised to the Meditations and which Descartes published as an Appendix to them, a major query was ‘the sharp distinction between mind and body in which the mind is one sort of substance and the body another’. This is called Cartesian Dualism.

Curiously, Sorell does not seem to mention the most penetrating objection to Cartesian Dualism which is that if body and mind are sharply different things, indeed different kinds of things, how can they causally interact with each other? How can a non-physical mind exert a causal influence on a physical body, such as a decision in your mind to raise your arm or whistle a tune? Both criticism and endorsement of Cartesian Dualism have gone on for centuries, and the debate continues to this day. In The Concept of Mind (1949) British philosopher Gilbert Ryle criticized what he called ‘the dogma of the ghost in the machine’ with its ‘theoretical shuttlecocks which are forever being bandied from the physiologist to the psychologist and from the psychologist back to the physiologist’. Quite apart from the puzzle of causal interaction, what about predicates such as ‘clever’? If we call a schoolboy clever, are we describing his mind or his behaviour?

Chapter 16 is ‘Body’.
Just as Descartes conceived of mind as being complete in itself and separate from the body, likewise he thought of body leaving out all properties that depend on a mind. His concept of body presupposes the existence of material objects, but how is this known by the non-material mind? The answer is that as a ‘thinking substance’ the mind has a faculty for receiving ideas or perceptions from some external source. But how do we know that this source is indeed external? The answer (as before) is that if the causes of these ideas or perceptions were not bodies, we would be deceived in our thinking. But ‘God does not constitute us to be liable to this kind of error’ – so bodies exist. Q.E.D.

I think that puts it in a nutshell, but once again Descartes is using the same sort of circular argument as before. There are of course conundrums that are unanswered, such as how events in the body’s nervous system are translated into the mind’s experiences of colour, smell, taste and so on. In fairness to Descartes, these questions are still outstanding on any other theory of body and mind, such as behaviourism or physicalism.

Chapter 17 is ‘The Physics made Public’.
This relates to Descartes’ Principles of Philosophy published in Latin in 1644 and in French in 1647. Sorell spends some time relating how Descartes had to deal with various critics from years gone by, and how he placated and obtained support from some Jesuits who had previously opposed him.

His book outlined his philosophy as a whole, not just physics where he deals with the laws of nature, motion and impact. It seems however that much of what he said is more metaphysics than physics, for example if one starts with a conception of mind or of body and subtracts the non-essential attributes, will the substance ‘left over’ be the same as the original one? I am inclined to doubt whether this sort of question is studied by present-day students of physics. His physics was, according to Sorell, ‘hard to perform calculations with, made no mention of mass and had striking drawbacks as a theory of gravity’. In the event it was entirely overtaken by Newton’s theories later in the 17th century.

Sorell notes (p92) ‘that the failings of Descartes’ science were bound to be acute, because it was founded on armchair speculation that he rarely bothered to test experimentally’. On the other hand he says that ‘much fruitful scientific theorizing has been conducted a priori – by thought experiment’. He should have added that this is, or should be, always followed up by real experiment. But a further criticism he makes of Descartes is that his vague use of the term ‘deduction’ seems to refer to a train of thought that is free of doubt or unclarity – which is very different from its exact meaning in formal logic. We noted earlier that his rejection of Aristotle’s logic seemed to be based more on misunderstanding than anything else. This was a very discouraging chapter.

Chapter 18 is ‘The Other Sciences’.
Descartes compared philosophy to a tree whose roots are metaphysics, whose trunk is physics and whose branches are the other sciences. The three principal ones are medicine, mechanics and morals. His work on these subjects in the 1630’s and 1640’s was never completed, however.

By mechanics he meant not machinery but how matter composes particular types of bodies including plants, animals and the human body. Medicine was concerned with the causes of and means of conserving life in the human body. Morals was the study of the passions, strategies for controlling them and ways of directing the will towards good or evil. One interesting point worth recording is that ethics, in his view, was not only concerned with controlling the passions, ‘it embraced the idea of the public good’ – which sounds very much like a forerunner to 19th century utilitarianism.

Chapter 19, ‘Last Days’, is really rather sad.
Evidently Descartes left for Sweden in 1649 to become Tutor to Queen Christina who was very keen to learn philosophy from such a distinguished thinker. Unfortunately Queen Christina liked to take her lessons at five o’clock in the morning (whilst Descartes’ preferred habit was to remain in bed, thinking, until noon). The Swedish winter disagreed with him too and he contracted pneumonia, dying in February 1650 at the age of 53.

In Chapter 20, ‘Descartes’ Ghost’, Sorell summarizes Descartes’ intellectual legacy.
It seems that criticism and condemnation of his ideas continued for some years after his death. Decades later Newton’s physics superseded Descartes’, and ‘revisionary interpretations’ of his philosophy were put forward. In the long term, however, his principal legacy has been to have identified a series of major questions which remain at the centre of philosophy such as the mind/body problem. A major achievement is how he showed that ‘a mathematical understanding of the physical world is more objective than the one suggested by the senses’. His contributions to mathematics were major and beyond dispute.

In my own view his contribution to science may have been even greater if, instead of seeking to back up his physics with metaphysics, he had turned instead to the idea of probability. With his first class intellect, who knows, he might have become one of the originators of present day probability theory. On the other hand, his quest was always for certainty, so it is likelier that he would have rejected the notion of probability out of hand – if it had ever occurred to him.

RHS, 2013.