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I was studying Aristotle's laws of motion and comparing them to Newton's. He states that heavier bodies fall faster than lighter ones. I really can't understand how he could have committed such a mistake. It seems obvious that two stones with different weights would reach the ground at the same time.

Furthermore, he believed that after applying a force to an object that object will move with a constant speed. But in the falling experiment we see that the speed will increase for normal objects like stones (not something like leather whose speed is influenced by air resistance).

How did Aristotle make these mistakes?

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    $\begingroup$ I don't think it's accurate to refer to "Aristotle's laws of motion." Aristotle never conceived of universal, mathematical laws that in theory would predict the outcome of any set of initial conditions. $\endgroup$
    – user466
    Commented Jun 23, 2015 at 22:58
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    $\begingroup$ @Ben Crowell I agree that "Aristotle's laws of motion" is a modernism, but I am not sure why laws are supposed to be universal or mathematical, some are qualitative and all have a range of applicability. Ironically, Newton's formulation of his laws is quite Aristotelian, he even distinguishes rest and motion as qualitatively different states, just like Aristotle. Predicting from a set of initial conditions is even more of a modernism that comes from working with differential equations. $\endgroup$
    – Conifold
    Commented Jun 24, 2015 at 20:59
  • $\begingroup$ Formerly on Physics. $\endgroup$
    – HDE 226868
    Commented Jun 26, 2015 at 22:36

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Air or more generally medium resistance was not yet treated as a separate effect in Aristotle's time. Nor was there a clear idea of motion in a vacuum, in fact most ancient Greek philosophers, including Aristotle, did not believe that vacuum exists. So he had to explain phenomena as they are observed, resistance and all, and without the benefit of experiments where different factors can be controlled for. His prototypical example was a rock and a feather, which do not fall at the same speed. That different weights would fall simultaneously if effects of resistance can be neglected is not obvious at all unless you perform an experiment, and that did not become common practice in science until 17th century, two millennia after Aristotle.

In Aristotle’s Physics: a Physicist’s Look Rovelli explains that in a resisting medium the steady speed attained by a body after a transient phase is indeed proportional to the force causing the motion, so his "law of motion" does hold in the limit of high friction/resistance. As for the free fall, it is not that easy to notice the increase in speed over the short periods of time that everyday objects take to fall from small heights (people did not deliberately drop stones from tall towers in his time). Aside from that, Aristotle distinguished between violent motions, caused by a force, and natural motions, that do not require a force, free fall is one of the natural ones. Another one is the circular motion of stars in the heaven. Aristotle's "law" therefore applies to neither.

This being said, Aristotle's theories of free fall and projectile motion were criticized already in late antiquity, e.g. by John Philoponus (c. 490 – 570 AD), who anticipated modern empirical approach:"But this [view of Aristotle] is completely erroneous, and our view may be completely corroborated by actual observation more effectively than by any sort of verbal argument. For if you let fall from the same height two weights, one many times heavier than the other you will see that the ratio of the times required for the motion does not depend [solely] on the weights, but that the difference in time is very small".

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    $\begingroup$ Galileo was first to disprove that heavier object fall faster: with mental experiment: would bag of rocks fall faster than a single rock? $\endgroup$ Commented Oct 27, 2016 at 22:39
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Everyone makes mistakes. Look at Newton, even though he knew perfectly well that action at a distance was philosophically speaking, nonsense, he still went with it because he could see no way past this impasse. It was only after Einstein we see where the mistake is.

Neverthless, we don't belittle Newton for not inventing general relativity, and celebrate what he did get right: his three laws of motion, his gravitational theory and the calculus.

Likewise, rather than belittling Aristotle for what he got wrong, we should celebrate what he got right. Carlo Rovelli, in his book, Quantum Gravity, stated that it was Descartes that should be honoured for forcefully enunciating the principle of locality in physics.

He's right on that this notion is central to physics, but wrong about who should get credit for this notion. Aristotle, long before Descartes, stated that change only occurs on the application of a force, and only then if the substance on which the force is applied has the potential to change and actually does change. His careful language around this principle has all the hallmarks of careful scientific thinking.

This, by the way, is more or less the essence of Newtons first law of motion: that an object will carry on in straight line motion unless a force is applied.

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How did Aristotle make these mistakes? Probably the resason is the same in most if not all cases: There was not a single experiment performed before Archimed. From atomism of Leukippos to Aristotle's laws of motion there was always only pure imagination or philosophy (except explanations based on observation, for instance the wrong life cycle of bees or the not reproducing eels). Aristoteles stated for instance acoustic dispersion: signals of different pitch should spread out with different velocities. Small wonder that many errors arose.

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Yes, Aristotle got it wrong. And he could not do it otherwise. Why do we blame Aristotle and not Archimedes and Heron, who were closer than Aristotle to this subject? Not everything said by Aristotle or his followers is wrong. In the "pseudo-mechanics," we have a kind of vector addition of speeds.

Despite the fact that archers throwing arrows from moving horses toward moving enemies should have some knowledge of vector addition, we do not have any record of research about this subject despite its importance for warfare at that time. I am puzzled why people do not understand the gigantic step made by Galileo.

Strato of Lampsacus made the observation that the fact that rain (and in general any falling liquid) separates into drops is an indication of acceleration. We have to wait for Domingo de Soto, whom Galileo read, to make this remark. But they associate only a change in speed and not the rules of this change. Nobody relates it to Oresme’s definition: "uniformly non-uniform."

Immediately prior to Galileo, Leonardo had the correct facts both for the static composition of forces and free fall but did not draw the correct conclusions. Galileo, first of all, invented the pendulum to measure time more accurately. Next, he slowed down the process to make it more manageable. He then eliminated factors that may have influenced motion, showing that the amount of mass does not affect the speed of fall.

At this stage, all that remains to be done is to find the relation between speed v(t), time t, and distance s(t). Galileo first thought that v(t) = k s(t), but he could not confirm that, and it took him 10 years until he found that v(t) = k t. But he did not stop there. He experimented with the inclined plane and concluded that if we have two inclined planes at different angles, then a ball dropped on one will reach the same height on the second, i.e., the first manifestation of the law of the conservation of energy.

From this, Galileo reached the conclusion that when the second plane is at an angle of 0, the ball will move to infinity to get back to the same height.

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