Buridan copy Essay Example

objects of less attention. It still is not known, for example, whether Burundi was familiar with the concept of mail, similar to impetus, in Arab writers like as-Affair and Vaccine. Many of the particular features of Puritan's impetus hypothesis and several of the empirical observations he rings forward against Aristotle ideas on projectile motion and accelerated fall are found in earlier writings, all of which belong to a continuous tradition of critical commentary on Aristotle that stretches back almost to the Philosopher himself.

Which bothers authors Burundi had read is not known. What we find when we study this tradition is that certain points made by Philosophy, for example, recur in Burundi centuries later, just as many of the arguments brought against Aristotle by Burundi and Ores recur in the writings of subsequent authors, up to and beyond Galileo, their sources unacknowledged. Anonymous examples and arguments get passed from author to author, like well-polished stones. Impetus was certainly not a new idea with Burundi. Concepts of an intrinsic motive power had been introduced by Philosophy (6 the c.

CE) and other Greek commentators of late antiquity to improve Aristotle account of projectile motion. Arab commentators had also developed their own versions, several of which are reported and evaluated by Vaccine (d. 1 037) in his Book Of the Healing of the Soul. In the view Vaccine favored, projectile motion continues because an inclination (mail) is impressed on the projectile by the boning force.

This inclination was said to be permanent, so that the motion would continue in the absence of resistance, and to vary in strength with the weight of the body to which it

is communicated.

There is no direct textual evidence in Puritan's writings that he was acquainted with this hypothesis; the resemblances between the two are probably best seen as evidence that something like the impetus hypothesis is among the most reasonable ways to explain the relevant range of phenomena in an Aristotelian system. Another Arab commentator, ABA 'I-Barbara (d. 1164) had a similar theory, in which the impressed inclination was said to be self-expending rather than permanent.

Specific connections between the earlier Greek and Arab writers and medieval scholastics have not been the established, but several 13 c. Colleen discussed theories of impressed forces and inclinations in their commentaries. Roger Bacon and Thomas Aquinas, for example, in their commentaries on the Physics and De Scale, rejected the concept of an impressed force as contrary to the fundamental Aristotelian principle that violent motions of inanimate objects are extrinsically caused. They reasoned that positing an impressed force in the rejection would mean its continued motion resulted from an intrinsic principle, and this is contrary to the nature of violent motion.

Burundi and other writers of the 14th c. Were still tinkering within the Aristotelian system.

Some of their concepts anticipated later ones. Puritan's impetus resembles Galileo impetigo and Newton's momentum, since all three are defined as varying directly with mass and velocity. The relation is one of analogy, not homology, however.

The measure of Puritan's impetus is the same as the measure of Newton's momentum, but as theoretical concepts in two different systems, they are not entirely commensurate. Similarly, impetus is often considered an anticipation of Newtonian inertia, though the latter is independent of velocity, insofar as both

remove the need for an external cause of continuing uniform motion.

But again, the two concepts are only loosely analogous. What are still for Burundi puzzles in a basically Aristotelian physics would become in the following centuries full-scale anomalies, signaling the need for a new science.

L. Aristotle and the chemistry of motion The fundamental theoretical entities by which an Aristotelian like Burundi would attempt to explain such empirically observable phenomena as an iron joker getting hot in a fire, or an ox dying, are prime matter and substantial and accidental forms.

Substantial forms explain how the matter of a thing is organized so as to be the kind of thing it is and function in the way proper to it. Accidental forms explain the states, functions and effects of a thing that it can exist without. The process by which a certain form or state comes to be, however, requires an efficient cause. Every existence and occurrence, and thus every motion has an efficient cause.

Everything that is moved is moved by something. Living things can be self-moved, because they unite in themselves a mover (the soul) ND a moved (the body,) but in most cases, the mover and the thing moved are two different subjects.

The moving cause must be in contact with the thing moved-?there is no action at a spatial or temporal distance. A few accidental forms function as efficient causes or active principles for Aristotle, however. These are the elemental qualities. In what seems an older, more primitive, part of Aristotle thought, there is a kind of the chemistry Of motion based on the system Of Impedances (5 c.

BCC).

The elemental qualities are the intrinsic properties (hot, could, wet, dry,) of the 4 elements: Fire fiery: hot and dry reform: hot and moist Water liquid: cold and moist Earth solid: cold and dry Two other active qualities are gravity and levity.

Sometimes these are considered derivative from the four elemental qualities; elsewhere they are treated as equally primary. All naturally occurring bodies are believed to be mixtures of the four elements, so "pure earth" and "pure fire" function more as theoretical entities in models of motion than as descriptive terms. Pure fire is said to have levity absolutely, and pure earth to have weight or gravity absolutely. The two intermediate elements (air and water) are said to have pity or gravity relatively, depending on their locations.

Water when found in the clouds has gravity and a natural tendency to fall to its natural place above the earth. Subterranean water has levity and a natural tendency to rise. ) The general idea is that internal tendencies to motion are caused by differences in the composition of bodies out of the elements. To the question "Why does body X move naturally to place P? " Aristotle answers as follows: X is composed of the elements earth, air, fire, and water in the proportions The natural place of a body composed of the elements in proportions :q:r:s is Bodies realize their natures most fully when they are in their natural places.

Bodies in natural motion strive to realize their natures most fully. Hence, In natural motion, X moves to P.

Local movements of terrestrial bodies, composed of the four elements and their compounds, are governed by the

natural tendencies of the elements to arrange themselves concentrically around the center of the world, with earth at the center and water, air and fire in successive layers outward. There is constant change as the elements are transformed into one another and different compounds are formed.

The tartar place of a body is determined by the element that predominates in its composition. When a body is away from its natural place, its form is a motive principle. In this way the elemental qualities become inorganic forces that cause motion.

For example: the downward motion of a stone falling from the airy regions will have as its substantial efficient cause whatever generated it by giving it the substantial form of a stone; the accidental efficient cause of its motion will be its accidental form, gravity or weight; and the final cause specifies the direction of the movement.

Other active accidental forms are aid to cause motion indirectly; heat and cold, for example, can cause motion through condensation and rarefaction. Substantial forms are active through their accidents. So if we ask what kinds of forces are available to explain motions in an Aristotelian account, there are organic forces (the muscle power of human beings and animals, and all the external instruments by which these are extended) and inorganic forces consist ting Of the six active or elemental qualities.

Typical cases Of motion are instances of pushing and pulling, like Socrates pushing a cart.

But inorganic forces can cause motion, too. The heat of fire can make something else hot, cause it to expand, or cause a change in its magnitude and location. The dryness of air can

dry wet clothes or shrink a plant by desiccation. Local motion is always against a resistance.

Since causes act instantaneously, a motive force not opposed by some resistance would cause, not locomotion, which is successive by nature, but instantaneous change of place. (Aristotle argues further that since the concept of instantaneous motion is incoherent, all motive forces must meet some resistance, and therefore no vacuum exists in nature. Hicks IV. 8. 21 b. 12-22) The basic principle relating motion to boning force and resistance is that the ratio of distance traveled to time elapsed varies directly with the motive force and inversely with the resistance.

Aristotle spells this out in BC. VII, Chi. 5 of the Physics: If mover A moves an object B through a distance C in the time period D, then the same force will move half of B in the time period D through twice the distance C, or it will move half of B in half of D through the whole distance C. Doubling the motive force or halving the resistance results in twice the velocity, sisters Paramus. But as Aristotle recognizes in this passage, it is not always the case that halving the force or bubbling the resistance will result in half the velocity. Motion only occurs if the force continues to be greater than the resistance after such changes have been made.

) This Aristotelian law Of motion is Often expressed as V FIR where V = velocity, F = motive force, R = resistance, and the proportion symbol means "varies directly as. " How will projectile motion be treated in such a theory? An Aristotelian model of

the motion of a projectile will make some abstractions, as all models must.

It will treat the projectile simply as a heavy body, (although pure earth does not exist in nature,) thus abstracting from any levity it might have as a suture. And it will lump together, additively, the resistance of the medium with resistance from the contrary inclination to downward motion of the moved object. While these particular abstractions could be regarded as damaging for the theory, the most serious problem has to do with the motive force.

Since projectile motion is violent motion, its efficient cause is not some natural accident of the movable object itself, like weight.

It must be moved by a separate subject acting as an external mover, in constant contact with the moved. So, what exactly keeps the projectile moving after it leaves the projector? Without an external push, a stone should either remain at rest or move in a straight line toward the center of the earth. If a man holds a stone in his hand and moves it forward slowly, then lets go, it drops to the ground.

Why should its trajectory be different when he moves it forward more rapidly? Aristotle explanation was one of the weakest parts of his theory of motion.

Burundi describes it as follows: Along with the projectile the projector moves the adjacent air, and that swiftly moved air has the power of moving the projectile... The air joined to the projector is moved by the projector, and that Ovid air moves another next to it and that other, up to a certain distance.

Thus the first air moves the projectile to

the second air and the second to the third and so on. Hence Aristotle says there is not one mover, but many, one after another. Hence he also says that the motion is not continuous, but is Of contiguous beings.

The projectile is borne along by successive contiguous motions in the medium.

Notice that the air is both moved, itself, and caused to have the power to act as a mover of the projectile and the neighboring air. II. Burundi on projectile motion In Book Ill Question 7 of his commentary on Aristotle Physics, Burundi rings four objections against the Aristotelian account: 1) A turning millstone would continue to turn, once the hand is removed from it, even if by covering the millstone with a cloth the adjacent air were kept from contact with it. ) However rapidly the air is moved, it is easily divisible; thus it is not obvious how it would sustain a stone weighing a thousand pounds projected from a sling or mechanical device. 3) One could move the adjacent air just as swiftly or more swiftly with his hand if he held nothing in the hand than if he held the stone in his hand which he wished to hurl.

Therefore, if that air from the speed of its motion were of such a force that it could move the stone swiftly, it would seem that if one person should push the air against another equally swiftly, that air ought to push him forcefully and truly noticeably, and we do not perceive this. ) If the continued motion of a projectile after it leaves the mover were sustained by the

moved air adjacent to the projectile, it would follow that a feather would be projected farther than a stone, the less heavy object farther than the more heavy object of the same size and shape. But this is not what we observe. Something interesting is going on in these objections to the Aristotelian explanation. The first objection is straightforward: the motion of a turning millstone does not seem to depend on the action of the surrounding medium.

But the last three reject the air-as-motive-force explanation for reasons that have to do with force as a product of quantity-of-matter and velocity. They share an implicit assumption that when analyzing motions, moving force and resistance can be treated interchangeably, since the measure of both will vary with the weight and the velocity. In Puritan's day there were few precise measures of force. The muscular energy of an animal and the intensity of an elemental quality like wetness do not lend themselves to quantitative analysis.

In the paradigm example of natural motion, the relevant force (F) is the specific weight of the falling body, measured in terms of (total or average) velocity (V) and resistance (R) of the medium. This can be expressed in the simple formula, V FIR.

Heavier objects of the same size and shape fall faster in the same medium. In violent motion forces are measured indirectly according to the principle that equal forces will cause equal weights (or equal quantities of matter) to move equal distances n equal times. (Physics VII. . Bibb. 30-AAA.

28) Thus, F WAD/T or FEW , where D is distance, W is weight or quantity of matter, and T

is time. Weight functions both as the internal force of natural motions and as resistance to force, in violent motions. Weight is also a variable that could be measured independently of the Aristotelian laws of motion in which it functioned. In objection #2, Burundi reasons that if the air is to be the cause of the projectile's continuing motion, it must act with a force greater than the total resistance.

The resistance, in the case of a thousand-pound stone, will be the assistance of the medium, (however that would play out under the hypothesis in question,) and the weight of the stone. Puritan's intuition is that the air WOUld have to act with a force greater than a thousand pounds to overcome the resistance of the stone's natural downward movement, and that this amounts to saying the air would have to offer resistance greater than the downward force of the stone's gravity. The terms force and resistance are interchangeable; what matters are the relative magnitudes.

And since the resistance of a medium varies directly with its density, the air would not offer efficient resistance to the stone's fall. Puritan's argument in objection #3 is as follows: Assume ex hypothesis that in throwing a stone a man moves the stone and the surrounding air.

Assume also that the force of impact of a moved object is determined by its velocity alone. Then, since by Aristotelian principles a man can move a lighter object faster than a heavy one, sisters Paramus, he should be able to produce a noticeable force of impact by throwing the air alone.

But this is not what we observe. The larger argument

is a reduction. If force of impact is determined by velocity lone, then the most damaging projectiles are the lightest, since they can be thrown the fastest. But this is absurd.

Again, Burundi is working with the role Of quantity of matter in both force and resistance. He doesn't deny that, in principle, a man can move a light object faster than a heavy one, according to the Aristotelian law that in violent motion weight acts as resistance. But quantity of matter is also a factor in force.

Air is less dense than rock, so air moving at the same velocity as the stone has less force than the stone does.

Thus air cannot be the moving force for the stone's continued motion. Notice the ambiguity at this point of the concept of the force the stone has while in motion. Puritan's argument is that because of its greater density, the stone has more of it than the air, which is supposed to be moving it, does. In Aristotelian categories he can say that the force (understood as weight or inclination to downward motion) of the stone is greater than the moving force of the air.

Then this argument is the same as #2. But he is working toward another concept of a force internal to the projectile but different from weight.

This line of thought continues in objection #4. The fourth objection brings to the surface a very deep problem in the Aristotelian theory of motion. Aristotle fundamental theorem, that the ratio of distance traveled to time elapsed varies directly with the motive force and inversely with the resistance, describes and unifies a wide

range of empirical phenomena. In the large domain of violent motions, I. E. Actions caused by external movers, the law that the same force moves a light object farther than a heavy one seems Obvious: Socrates can carry a light load farther than a heavy one.

Yet as Burundi points out, the attempt to fit the motion of a projectile into the Aristotelian model of violent motion would require that the moving force should be able to move a light body farther than a heavy one of the same size and shape. "It would follow that you would project a feather farther than a stone, the less heavy farther than the more heavy, with the sizes and shapes the same; and this is observed to be false. But for a certain range of phenomena, just the reverse is true. We can throw a baseball farther than a safety pin. Air resistance is not the explanation, Burundi reasons, since we can generally throw a heavy object farther than a light one of the same size and shape. What is the explanation, then? It is not easy to fit the phenomena of projectile motion into a single, Aristotelian model.

If we move an object slowly, then let go, it falls to the ground. If we move it rapidly, then let go, it contain uses its motion in the same direction. Why is that?

What relationship, between what variables, determines the critical velocity for 'takeoff' in such cases? In the same way, while can throw a stone farther than a feather, as Burundi says, I cannot throw a 1 00-b. Stone farther than a 5-b.

One. Why does

the Aristotelian model for violent motion hold for part of the range of phenomena but not the rest? Why is it that while I can in general move a light object farther or faster than a heavy one, an object already in motion seems to move farther or faster if it is heavy? Burundi had at his fingertips two models of motion from the Aristotelian theory.

In the model for violent motion weight acts as a resistance, lowering velocity or distance traveled, or increasing time, sisters Paramus. But in the model for natural motion, accidents like weight act as motive forces, not resistances. In the paradigm case of natural motion, weight increases the speed of a falling body, sisters Paramus.

I suggest that Burundi away that the simplest way to save all the phenomena, without contradicting fundamental Aristotelian principles, was to consider the motion of the projectile after it leaves the projector as a case of natural, rather than violent, motion.

In the passages which follow, he does not explicitly refer to projectile motion as 'natural motion,' but by making impetus an accident that moves the subject in which it inheres, he accomplishes the same thing. Impetus joins weight, levity, heat, cold and the other active qualities included among the efficient causes of motion. And so it seems to me that what should be said is that the mover in moving hat is moved impresses upon it a certain impetus or force that moves the moved thing in the direction the mover moved it...

And the more swiftly the mover moves the moved thing, the stronger the impetus it impresses on it.

The stone is

moved by that impetus after the projector ceases to move it, but the impetus is continuously diminished by the resisting air and by the gravity of the stone inclining it against the direction the impetus inherently moves it. Hence the motion of that stone is made continuously slower, and finally the impetus is so diminished or corrupted that the gravity of the stone prevails ever it and moves the stone down to its natural place. [commentary on Aristotle Physics,BC. Evil, IQ 2] The impressed force varies directly with the velocity of the initial motion.

And since weight is understood to function as it does in natural motion, rather than as it does in violent motion, the impetus will vary directly with the weight of the moved body as well. If someone should ask how it is that hurl a stone farther than a feather, and a hand-sized iron ball farther than the same sized wooden one, I reply that the reception of all natural forms and dispositions is in matter and by reason f the matter. Hence, hovercraft more there is of matter, by that much more can a body take on the impetus more intensely.

Now other things being equal, there is more prime matter in a dense and heavy body than in a rarefied and light one; hence the dense and heavy one receives more from that impetus and more intensely, just as iron can receive more from heat than wood or water of the same quantity.

A feather, however, receives such an impetus so sparsely that such an impetus is at once corrupted by the resisting air. And so even if a

light piece of wood and a heavy piece of iron of he same size and shape should be moved equally swiftly by the projector, the iron would be moved farther because the impetus would be impressed more intensely it.