Not only did Descartes provide the first distinctly modern formulation of laws of nature and a conservation principle of motion, but he also constructed what would become the most popular theory of planetary motion of the late seventeenth century.
Principles of cartesian philosophy pdfs
Over the course of the next decade, Descartes worked on a large number of problems in both science and mathematics, with particular emphasis on the theory of light, mechanics including hydrostatics , and the free-fall of terrestrial bodies.
By the beginning of the s, however, Descartes embarked on a more ambitious plan to construct a systematic theory of knowledge, including physics. In the s, the publication of the Geometry, the Optics, and the Meteorology, along with a philosophical introduction, Discourse on the Method further presented Cartesian hypotheses on such topics as the law of refraction, vision, and the rainbow.
Yet, besides a brief sketch of his metaphysics and physics in the Discourse Parts IV and V , a comprehensive treatment of his physics had to await the publication of the Principles of Philosophy.
As an embodiment of his mature views, the Principles will thus form the basis of our examination of Cartesian physics.
A concise survey of Cartesian physics can be found in Garber b. The scientific career of Descartes, with special emphasis on his physics, is presented in Shea ; see also Gaukroger, Schuster, Sutton for the many aspects of his natural philosophy.
Gaukroger examines the Principles of Philosophy , especially the physics, whereas Slowik focuses primarily on Cartesian space and relational motion. Like many of his contemporaries e. A quantity of matter, for example, possesses weight, color, texture, and all of the other bodily properties, only in virtue of being conjoined with a determinate form of a billiard ball, chair, etc.
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:. This method of conducting science is quite contrary to the modern approach, needless to say, since modern scientists do not first engage in a metaphysical search for first principles on which to base their work.
As he argued in the Rules for the Direction of the Mind , pure mathematicians are only concerned with finding ratios and proportions, whereas natural philosophers are intent on understanding nature AT X — While some philosophers, such as Telesio, Campanella, and Bruno, held space to be always filled with matter i. Consequently, there cannot exist a space separate from body Pr II 16 , since all spatial extension simply is body and he rejects the possibility of a vacuum that is not extended.
If, for example, God removed the matter within a vessel such that nothing remained , then the sides of the vessel would immediately become contiguous but not through motion; Pr II Also like the Scholastics, Descartes rejects any form of atomism, which is the view that there exists a smallest indivisible particle of matter.
Rather, he holds that since any given spatially extended length is divisible in thought, thus God has the power to actually divide it Pr II Descartes notes that the vulgar concept of motion allows a body to simultaneously take part in many possibly contradictory motions, as when a sitting passenger on a ship views himself as at rest relative to the parts of the ship, but not at rest relative to the shore Pr II Yet, when motion is viewed as a translation of the contiguous neighborhood, a body can only partake in one motion, which dispels the apparent contradiction since the body must either be at rest, or in translation away from, its contiguous neighborhood.
Yet, as will be discussed in a later section, Descartes also holds that rest and motion are different bodily states, a view that is incompatible with a strict relationism as regards motion. Therefore, Cartesian reciprocity of transfer only satisfies relationism along with its ban on individual bodily states of motion for moving bodies i.
Many of the difficulties associated with Cartesian physics can be traced to the enormous ontological burden that Descartes places on his hypothesis of motion. The problem, of course, is that Descartes has defined motion as a change of contiguous bodies, and then proceeds to define body as that which moves translates, transports. Although this circularity threatens the entire edifice of Cartesian physics, it is possible that Descartes intended both motion and body to possess an equal ontological importance in his theory, such that neither is the more fundamental notion which serves as the basis for constructing or defining the other notion.
Yet, their intrinsic interrelationship entails that any attempted definition of one must inevitably incorporate the other. In addition, Descartes rejects any explanation of the solidity of a body that employs a bond among its particles since the bond itself would be either a substance or property, and thus the solidity of the bond would presumably need to be explained; Pr II A macroscopic material body is, essentially, held together just by the relative rest of its constituent material parts.
A History of Philosophy - 31 Descartes
This raises the obvious difficulty that the impact of such bodies should result in their dispersion or destruction for there is nothing to hold them together. If, as Descartes believes, substances are not dependent on other things in order to exist Pr I 51 , then any part of extension which is a body, via Pr II 10, as explained above would not qualify as a substance since it depend on its contiguous neighbors to delimit and define its boundary.
Yet, Descartes often declares that individual bodies are substances; e. The problem with this attempted solution, however, is that it lacks textual support, as is evident in the Pr I 51 quotation above. Along these same lines, some scholars e.
Whereas space is a genus or species concept for Descartes which is a universal; Pr I 59 , space is the individual for the supersubstantivalist, and thus ascribing supersubstantivalism to Descartes violates his nominalism Pr II 8. Indeed, the reason that Descartes seeks to equate bodily and spatial extension in this part of the Principles is that he strives to reject any view that treats space as a separate, usually incorporeal, entity that is independent of matter e.
By declaring that motion and rest are primitive states of material bodies without need of further explanation, and that bodies only change their state when acted upon by an external cause, it is not an exaggeration to claim that Descartes helped to lay the foundation for the modern theory of dynamics which studies the motion of bodies under the action of forces. Descartes, on the other hand, interpreted the phenomena of motion in an entirely new light, for he accepts the existence of inertial motion uniform or non-accelerating motion as a natural bodily state alongside, and on equal footing with, the notion of bodily rest.
That is, rest and motion are opposite or contrary states, and since opposite states cannot via the Scholastic principle transform into one another, it follows that a body at rest will remains at rest and a body in motion will remains in motion. In the following sections of the Principles , Descartes makes explicit the conserved quantity mentioned in this third law:.
As a consequence of his first law of motion, Descartes insists that the quantity conserved in collisions equals the combined sum of the products of size and speed of each impacting body. To give an example, if a body B of size 3 and speed 5 collides with a body C of size 2 and speed 4, then the total quantity of motion of the system is 23, a quantity which remains preserved after the collision even though the bodies may possess different speeds.
Moreover, Descartes envisions the conservation of quantity of motion as one of the fundamental governing principles of the entire cosmos.
When God created the universe, he reasons, a certain finite amount of motion quantity of motion was transmitted to its material occupants; a quantity, moreover, that God continuously preserves at each succeeding moment.
For example:. Astonishingly, Descartes claims that a smaller body, regardless of its speed, can never move a larger stationary body.
While obviously contradicting common experience, the fourth collision rule does nicely demonstrate the scalar nature of speed, as well as the primary importance of quantity of motion, in Cartesian dynamics.
Descartes conserves the joint quantity of motion by equipping the stationary object C with a resisting force sufficient to deflect the moving body B , a solution that does uphold the quantity of motion in cases where C is at rest. That is, since B merely changes its direction of inertial motion, and not its size or degree of speed and C equals zero throughout the interaction , the total quantity of motion of the system is preserved.
In the same way that a particular shape can be partitioned into diverse component figures, so a particular determination can be decomposed into various constituent directions. 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.
1. A Brief History of Descartes’ Scientific Work
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.
2. The Strategy of Cartesian Physics
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.
Spinoza’s Physical Theory
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.