This idea became the foundation for his way of thinking, and was to form the basis for all his works. Comparatively little is known of Descartes' life between and He spent a while in Paris, apparently keeping very much to himself, and some have speculated that he might have suffered some sort of a breakdown at this time.
Then he studied at the University of Poitiers, receiving a law degree from Poitiers in He took the law degree to comply with his father's wishes but he quickly decided that this was not the path he wanted to follow. He wrote in Discourse on the Method :- I entirely abandoned the study of letters, resolving to seek no knowledge other than that which could be found in myself or else in the great book of the world.
I spent the rest of my youth travelling, visiting courts and armies, mixing with people of diverse temperaments and ranks, gathering various experiences, testing myself in the situations which fortune offered me, and at all times reflecting on whatever came my way so as to derive some profit from it. He may have returned to Paris before he enlisted in the military school at Breda in , becoming a volunteer in the army of Maurice of Nassau.
While in Breda his formal study was of military engineering but he started studying mathematics and mechanics under the Dutch scientist Isaac Beeckman, and began to seek a unified science of nature. Advised by Beeckman, he began considering mechanical problems. While in Holland, he wrote to Beeckman in March about his new ideas:- [ I want to promote a ] completely new science by which all questions in general may be solved that can be proposed about any kind of quantity, continuous as well as discrete.
But each according to its own nature. In arithmetic, for instance, some questions can be solved by rational numbers, some by surd numbers, and others can be imagined but not solved. For continuous quantity I hope to prove that, similarly, certain problems can be solved by using only straight or circular lines, that some problems require other curves for their solution, but still curves which arise from one single motion and which therefore can be traced by the new compasses, which I consider to be no less certain and geometrical than the usual compasses by which circles are traced; and, finally, that other problems can be solved by curved lines generated by separate motions not subordinate to one another.
After this time in Holland he left the service of Maurice of Nassau and travelled through Europe with the plan to join the army of Maximilian of Bavaria. In he joined the Bavarian army and was stationed in Ulm. An important event in his life was three dreams he had in November These he believed were sent by a divine spirit with the intention of revealing to him a new approach to philosophy.
The ideas from these dreams would dominate much of his work from that time on. After this he left the army but since the plague was ravaging in Paris he could not return there but instead began a period of travel. From to Descartes travelled through Europe, spending time in Bohemia , Hungary , Germany, Holland and France - He spent time in in Paris where he made contact with Marin Mersenne , an important contact which kept him in touch with the scientific world for many years, and with Claude Mydorge.
From Paris he travelled through Switzerland to Italy where he spent some time in Venice and in Rome, then he returned to France again He renewed his acquaintance with Mersenne and Mydorge , and met Girard Desargues. His Paris home became a meeting place for philosophers and mathematicians and steadily became more and more busy.
By Descartes, tired of the bustle of Paris, the house full of people, and of the life of travelling he had before, decided to settle down where he could work in solitude. He gave much thought to choosing a country suited to his nature and he chose Holland. What he longed for was somewhere peaceful where he could work away from the distractions of a city such as Paris yet still have access to the facilities of a city. It was a good decision which he did not seem to regret over the next twenty years.
He told Mersenne where he was living so that he might keep in touch with the mathematical world, but otherwise he kept his place of residence a secret.
He wrote to Mersenne in October :- [ The foundations of physics ] is the topic which I have studied more than any other and in which, thank God, I have not altogether wasted my time.
At least I think that I have found how to prove metaphysical truths in a manner which is more evident than the proofs of geometry - in my opinion, that is: I do not know if I shall be able to convince others of it.
During my first nine months in this country I worked on nothing else. This work was near completion when news that Galileo was condemned to house arrest reached him. He, perhaps wisely, decided not to risk publication and the work was published, only in part, after his death.
He explained later his change of direction saying In Holland, Descartes had a number of scientific friends as well as continued contact with Mersenne. His friendship with Beeckman continued and he also had contact with Mydorge , Hortensius, Huygens and Frans van Schooten the elder. Langer [ ] describes Descartes' life in Holland:- As throughout his life he continued to do his work abed in the mornings.
His evenings he generally devoted to the consideration of his correspondence, which was mainly scientific, rarely personal, and of which he was painstakingly careful, while the intermediate part of the day he gave to relaxation. In matters of money he was neither extravagant nor parsimonious, showing himself in this respect a true philosopher. He always did some entertaining, now more, now less, professing to find considerable enjoyment in conversation, though he was himself rather taciturn.
The work describes what Descartes considers is a more satisfactory means of acquiring knowledge than that presented by Aristotle's logic. Only mathematics, Descartes feels, is certain, so all must be based on mathematics. However his approach through experiment was an important contribution. However many of Descartes' claims are not only wrong but could have easily been seen to be wrong if he had done some easy experiments.
For example Roger Bacon had demonstrated the error in the commonly held belief that water which has been boiled freezes more quickly. However Descartes claims In [ 22 ] Scott summarises the importance of this work in four points:- He makes the first step towards a theory of invariants, which at later stages derelativises the system of reference and removes arbitrariness.
Algebra makes it possible to recognise the typical problems in geometry and to bring together problems which in geometrical dress would not appear to be related at all. Algebra imports into geometry the most natural principles of division and the most natural hierarchy of method. Not only can questions of solvability and geometrical possibility be decided elegantly, quickly and fully from the parallel algebra, without it they cannot be decided at all.
Wallis writes There seems little to justify Wallis 's claim, which was probably made partly through patriotism but also through his just desires to give Harriot more credit for his work. Harriot 's work on equations, however, may indeed have influenced Descartes who always claimed, clearly falsely, that nothing in his work was influenced by the work of others. Descartes' Meditations on First Philosophy , was published in , designed for the philosopher and for the theologian.
However many scientists were opposed to Descartes' ideas including Arnauld , Hobbes and Gassendi. This is an important point of view and was to point the way forward.
Descartes did not believe in action at a distance. Therefore, given this, there could be no vacuum around the Earth otherwise there was no way that forces could be transferred. In many ways Descartes' theory, where forces work through contact, is more satisfactory than the mysterious effect of gravity acting at a distance. However Descartes' mechanics leaves much to be desired.
He assumes that the universe is filled with matter which, due to some initial motion, has settled down into a system of vortices which carry the sun, the stars, the planets and comets in their paths. Despite the problems with the vortex theory it was championed in France for nearly one hundred years even after Newton showed it was impossible as a dynamical system. As Brewster, one of Newton 's 19 th century biographers, puts it:- Thus entrenched as the Cartesian system was The uninstructed mind could not readily admit the idea that the great masses of the planets were suspended in empty space, and retained their orbits by an invisible influence If a ball is propelled downwards from left to right at a 45 degree angle, and then pierces a thin linen sheet, it will continue to move to the right after piercing the sheet but now at an angle nearly parallel with the horizon.
In a letter to Clerselier February 17th, , Descartes explains:. This principle can be illustrated with respect to our previous example involving the fourth collision rule.
If both B and C were to depart at the same speed and in the same direction after impact, it would be necessary for the smaller body B to transfer at least half of its quantity of motion to the larger stationary body C.
Yet, Descartes reasons that it is easier for B in this situation to merely reverse it direction than to transfer its motion:. One of the most problematic instances involves the relational compatibility of the fourth and fifth collision rules. From a relational standpoint, however, rules four and five constitute the same type of collision, since they both involve the interaction of a small and large body with the same relative motion or speed difference between them.
One might be tempted to appeal to the basic Cartesian tenet that motion and rest are different intrinsic states of bodies, or the reciprocity of transfer thesis, to circumvent this difficulty see section 3 : i.
The problem with this line of reasoning, however, is that it only works if one presupposes that the two bodies are approaching one another, and this is not a feature of the system that can be captured by sole reference to the contiguous neighborhood of each individual body. Even if there is reciprocity of transfer between a body and its neighborhood, it is still not possible to determine which collision rule the impact will fall under, or if the bodies will even collide at all, unless some reference frame is referred to that can compute the motion of both bodies relative to one another.
Suppose, for instance, that a certain spatial distance separates two bodies, and that one of the bodies is, and the other is not, undergoing a translation relative to its neighboring bodies. Given this scenario, it is not possible to determine if; i the translating body is approaching the non-translating body, or ii the spatial interval between them remains fixed and the translating body simply undergoes a change of neighborhood i.
The context of the collision rules also supports the view that the motions of the impacting bodies are determined from an external reference frame, rather than from the local translation of their contiguous neighborhoods. In order to better grasp the specific role of Cartesian force, it would be useful to closely examine his theory of centrifugal effects, which is closely associated with the second law of nature.
Yet, as stated in his second law, Descartes contends wrongly that the body tends to follow a straight line away from the center of its circular trajectory. By his reckoning, the tendency to follow a tangential path exhibited by a circling body, such as the flight of the stone upon release from the sling, can be constructed from two more basic or primary inclinations: first, the tendency of the object to continue along its circular path; and second, the tendency of the object to travel along the radial line away from the center.
Hence, while determinations necessitate a span of several instants, tendencies towards motion are manifest only at single instants. This is a crucial distinction, for it partitions Cartesian dynamics into two ontological camps: forces that exist at moments of time, and motions that can only subsist over the course of several temporal moments.
In many parts of the Principles , moreover, Descartes suggests that quantity of motion is the measure of these bodily tendencies, and thus quantity of motion has a dual role as the measure of non-instantaneous bodily motion as well as the instantaneous bodily tendencies see Pr III In a letter, six years before the Principles , he concludes:.
On the other hand, he is willing to acknowledge the commonly observed fact that larger objects are much harder to set in motion than smaller objects. Since inertial forces are a consequence or a by-product of motion, as the product of the size times speed of bodies, Descartes apparently did not object to incorporating these phenomena within the discussion of the modes of material substance.
Yet, even if Descartes described force as an intrinsic fact of material interactions, the exact nature of the relationship between force and matter remains rather unclear. In particular, is force a property actually contained or present within bodies? Or, is it some sort of derivative phenomenal effect of the action of speed and size, and thus not present within extension? All that can be safely concluded is that Descartes envisioned the forces linked with bodily inertial states as basic, possibly primitive, facts of the existence of material bodies—a broad judgment that, by refusing to take sides, opts out of this difficult ontological dispute.
A vortex, for Descartes, is a large circling band of material particles. The entire Cartesian plenum, consequently, is comprised of a network or series of separate, interlocking vortices.
In our solar system, for example, the matter within the vortex has formed itself into a set of stratified bands, each lodging a planet, that circle the sun at varying speeds. As described in Pr III , a planet or comet comes to rest in a vortex band when its radially-directed, outward tendency to flee the center of rotation i. More specifically, Descartes holds that the minute particles that surround the earth account for terrestrial gravity in this same manner Pr IV 21— As for the creation of the vortex system, Descartes reasons that the conserved quantity of motion imparted to the plenum eventually resulted in the present vortex configuration Pr III God first partitioned the plenum into equal-sized portions, and then placed these bodies into various circular motions that, ultimately, formed the three elements of matter and the vortex systems see Figure 3.
Figure 3. Circular motion is therefore necessary for Descartes because there are no empty spaces for a moving object to occupy. Returning to the vortex theory, Descartes allots a considerable portion of the Principles to explicating various celestial phenomena, all the while adopting and adapting numerous sub-hypotheses that apply his overall mechanical system to specific celestial events.
One of the more famous of these explanations is the Cartesian theory of vortex collapse, which also provides an hypothesis on the origins of comets Pr III — Briefly, Descartes reckons that a significant amount of first element matter constantly flows between adjacent vortices: as the matter travels out of the equator of one vortex, it passes into the poles of its neighbor.
Under normal conditions, primary matter flows from the poles of a vortex into its center, i. Since the adjacent vortices also possess the same tendency to swell in size, a balance of expansion forces prevents the encroachment of neighboring vortices.
Once the vortex is engulfed by its expanding neighbors, the encrusted sun may become either a planet in a new vortex, or end up as a comet passing through many vortices. On the whole, the vortex theory offered the natural philosopher a highly intuitive model of celestial phenomena that was compatible with the mechanical philosophy. The vortex theory likewise provided a built-in explanation for the common direction of all planetary orbits.
Additionally, the vortex theory allowed Descartes to endorse a form of Copernicanism i. Through this ingenious maneuver, Descartes could then claim that the earth does not move—via his definition of place and motion—and yet maintain the Copernican hypothesis that the earth orbits the sun. The Strategy of Cartesian Physics 3. Space, Body, and Motion 4. The Problem of Relational Motion 6.
The Strategy of Cartesian Physics Like many of his contemporaries e. In a revealing passage from The World , Descartes declares the Scholastic hypothesis to be both an unintelligible and inadequate methodological approach to explaining natural phenomena: If you find it strange that I make no use of the qualities one calls heat, cold, moistness, and dryness…, as the philosophers [of the schools] do, I tell you that these qualities appear to me to be in need of explanation, and if I am not mistaken, not only these four qualities, but also all the others, and even all of the forms of inanimate bodies can be explained without having to assume anything else for this in their matter but motion, size, shape, and the arrangement of their parts AT XI 25— In the following sections of the Principles , Descartes makes explicit the conserved quantity mentioned in this third law: We must however notice carefully at this time in what the force of each body to act against another or resist the action of that other consists: namely, in the single fact that each thing strives, as far as in its power, to remain in the same state, in accordance with the first law stated above….
This force must be measured not only by the size of the body in which it is, and by the [area of the] surface which separates this body from those around it; but also by the speed and nature of its movement, and by the different ways in which bodies come in contact with one another. An ill person can hallucinate. An amputee can feel phantom limb pain. People are regularly deceived by their own eyes, dreams, and imaginations.
Descartes, however, realized that his argument opened a door for "radical doubt": That is, what was stopping people from doubting the existence of, well, everything? The cogito argument is his remedy: Even if you doubt the existence of everything, you cannot doubt the existence of your own mind—because doubting indicates thinking, and thinking indicates existing.
Descartes argued that self-evident truths like this—and not the senses—must be the foundation of philosophical investigations. Descartes was obsessed with certainty. His advice included this classic chestnut: To solve a big problem, break it up into small, easy-to-understand parts—and check each step often. Some say it's because he simply desired privacy for his philosophical work, or that he was avoiding his disapproving family.
In his book titled Descartes , philosopher A. Grayling makes another suggestion: "Descartes was a spy. He collected seven objections and published them in the work. Descartes, of course, had the last word: He responded to each criticism.
Which, put briefly, posits that the material body and immaterial mind are separate and distinct. He believed no such thing. According to the Stanford Encyclopedia of Philosophy , Descartes denied that animals were even conscious, let alone capable of speech.
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