Aristotle and Galileo: A Story of Two Ways of Knowing
The teacher heaved himself from his stone seat. “Enough sitting. My knees are aching. Let’s walk and talk together,” he said to his few disciples. Other teachers had more — some as many as thirty students — but Aristotle took his pleasure in selecting the six or seven students who could best understand his teachings.
Used to their teacher’s habit of wandering while he lectured, the students gathered together styli and wax tablets and a few closely spaced sheets of lecture notes painstakingly copied from their teacher’s own notes. They gathered in a close circle around their teacher as he walked, trying as best they could to prick out a few salient notes on their tablets. Walking, talking, and juggling the material of learning forced them to listen carefully to their teacher.
“An object falls through the air,” the teacher says. “Imagine two objects — a section of that column here,” he tapped it with his staff, “and a blade of grass dropped from a height. They fall toward the earth. Why?”
“Both contain Earth in their nature, and so are drawn to the greatest concentration of that element,” said Eudemus.
“And why does the column fall faster?” Aristotle asked.
“It is heavier,” blurted out Phanias.
“Which just means that it contains more Earth than the grass,” Eudemus put in.
“And Earth is another name of mass, so we can say that objects of greater weight fall faster than objects of lesser weight. Yes?”
The students tossed their heads back in agreement.
“But why do they fall at any speed at all? Why not simply contact the ground instantly as they leave the hand? What holds them back from their affinity with Earth?”
The students thought for a while, and finally Phanias ventured an answer, hoping to redeem himself from his earlier stupidity. “The element of Air pushes against them, and Air is inimical to Earth. Every falling object is a war between Air and Earth.”
“Exactly so. Now, reason this out. If there were no Air to push against falling objects, how fast would they fall?”
“Infinitely fast,” put in Eudemus. “Which is an absurdity.”
“Therefore?” Aristotle’s “therefore” was always devastating. It meant you hadn’t finished your chain of reasoning.
“Therefore there can be no place without air. There can be no void.”
“Because if there were?”
“It would lead to a logical absurdity, and the universe is rational.”
Aristotle smiled, pleased. “Exactly so. So now let us explore this idea of the rational . . . ” And the students walked with their wise teacher into two thousand years of fame.
* * *
Galileo huffed his way up the stairs of the tower, his secretary in tow lugging not only the necessary writing equipment but a heavy bag that made a low clunking noise with every step.
Galileo had done the arithmetic and it had all worked out, but for it to work out required something nearly unthinkable. Aristotle had to have been wrong. And not just Aristotle, but everyone else stretching back between that time and this — and that of course included the holy church.
Finally, at the top, he fished two cannon balls out of his bag. Aristotle was right about the air, at least partially — air resistance would slow down an object as it fell, which is why a feather did, indeed, fall slower than a cannon ball. But two cannon balls, one of a large caliber, another of a smaller caliber, should cut through the air at more or less the same speed, being spherical. He sent his secretary to the bottom to watch as he dropped the two objects, and call out whether they hit the earth at the same moment, or different moments.
He conducted the experiment over and over, with both him and his secretary watching on the ground, and in every instance, the two balls struck the ground at the same instant.
Rather than being elated, he found himself a bit disappointed. He felt cut adrift, like a boat whose rope has finally frayed beyond control. But no, that was the wrong analogy. He was more like a horse who has realized that the line that seemed to be securely tied was, in reality, merely draped over a twig. From here, he could go anywhere.
* * *
I’ve fictionalized these two incidents because they illustrate an important shift in the way that humans thought, and this story is one central to the history of science and — I wish to argue — magic. Because I wish to argue that contrary to magic being a science, magic and science are both two ways of knowing, compatible, but independent.
But the stories I’ve told are not stories of compatible ways of knowing, but two warring systems of knowledge.
Aristotle began with the commonly held assumption that our senses can be deceived. In fact, we know this to be not simply common sense, but quite true. A simple optical illusion can reveal that our eyes don’t always see what we think they do. Our ears can hear things that aren’t there, or mistake things that are; even our taste and touch can be confused. We can drink a soda and believe we’re tasting cherry, when really we’re drinking sugar and apple juice colored red and flavored with chemicals. Our senses are inadequate.
So Aristotle joined the tradition that, since senses are faulty, we must rely on reason. This idea led to mathematics, where senses are not only faulty but useless. One cannot see “two” — the best one can do is see symbols about twoness, or two of something. But arithmetic, not to mention the higher branches of mathematics, is abstract well beyond the range of sense. So we must rely on pure reason. We know that 2 + 2 = 4, to employ the hackneyed example, because if it doesn’t everything else we know about mathematics falls apart. In mathematics, we can have certain knowledge. Of course, that certain knowledge is of an abstract system, and as later mathematicians discovered, if you start with slightly different assumptions it’s easy to end up with a different system, in which 2 + 2 does not equal four but, perhaps, eight. Yet Aristotle would argue that the real world, while not the perfection of mathematics, clearly partook of it. After all, maybe the idea of right triangles is all just an abstraction, but just try to erect a house without it. The very concrete and sensory house is built of abstract numbers.
If pure reason led to truth in mathematics, Aristotle reasoned, and mathematics led to truth in matter, then surely we could come to truth about the physical world without relying on our senses at all. We could simply reason it out from first principles. Select the right set of first principles, apply rigorous reason, and knowledge would result like a nice buttery baklava. And if we avoid the engagement of the senses, we avoid the faults that senses are heir to.
Galileo began with a different set of assumptions. While accepting that senses could be deceived, he worked from the premise that this deception could be evened out by having multiple people observe at different times. In the fictionalized (and probably apocryphal) account above, both he and his secretary make observations, and they do not stop with just one but do it again and again. In addition to building up excellent calf muscles by lugging cannon balls up the leaning tower of Pisa, this method has the benefit of certainty. We know it works because we can see it working.
I’m not a philosopher, so what I’m attempting here is a bit arrogant of me, but we can summarize Aristotle’s underlying assumptions about knowledge and compare them to Galileo’s. For Aristotle, observation is secondary to reasoning. For Galileo, reasoning is secondary to observation. For Aristotle, we make a prediction based on reasoning from first principles. For Galileo, we define principles by reasoning from observation.
The scientific revolution was a war between these two ways of knowing the world. In the end, the latter system of reasoning conquered the former, usurping it to its own purposes. Pure reasoning still has a place in the sciences — mathematics, after all, is core to all sciences and still employs reasoning that Aristotle could understand, although he might not follow all the advanced concepts of modern mathematics. Now, scientists observe the physical world and create models of reasoning to explain and predict the behavior of that world. These models are called theories. It’s easy, therefore, to laugh at Aristotle’s naiveté. He simply had the incorrect method for gaining knowledge about the world, and now we have the correct method, and so we’re done. Give us enough time and observations, and we’ll figure it all out. And, in fact, we’ve come quite far in just a few hundred years after the scientific revolution. We know — with some certainty — more about the structure of reality than Aristotle could have imagined, and we even understand how to manipulate it to some degree. Aristotle’s explanation of a magnet from first principles was clumsy and inadequate. Scientific explanations of electromagnetism allow me to use this computer to write this essay, which some of you may be reading on an electric screen that would baffle Aristotle.
The problem is, the above isn’t entirely true. Aristotle didn’t have the wrong method, because Aristotle is still quite relevant. Virtue ethics as Aristotle described them, for example, are still relevant, and literary criticism classes still often begin with his works on the structure of tragedy. Obviously, those fields have advanced in volume of books if nothing else, but we still read Aristotle there not to ridicule him but to appreciate his insights. Yet physics classes rarely — if ever — begin with Aristotle’s Phusis. It seems he got some things right — in ethics, literary criticism, and other areas — and other things wrong. We cannot simplify then and say, “this system of knowledge is the right one, and his was the wrong one.”
The war between Aristotle and Galileo was misguided on all sides. On the side of Aristotle stood the church, which had long since reconciled that pagan philosopher with their understanding of the world. On the side of Galileo stood — at first — Galileo. Then the Royal Society of London and other groups of scientists who struggled mightily and won (the Church recently surrendered by apologizing to Galileo). The Church was wrong in that indeed Galileo had the right idea about gravity and the right notion about planetary motion (with some fuzzy details). But the church wasn’t arguing that — they were arguing about his method. If human observation could discover truth, what purpose remained for God? Their error was assuming that the truth of planetary motion is the same truth as the nature of the divine. Similarly, newly minted scientists made the same error, assuming that religion existed only to explain what science has not yet gotten around to on their grand to-do list.
The reality is more complicated.
The current state of this war is between two fronts: science and religion. Science, represented (or perhaps more accurately co-opted) by militant atheists like Richard Dawkins, argues that religion is inherently absurd and even deluded. Religion, on the other hand, argues that science cannot answer the questions that religion approaches. In this war of words, it is hard to tell who is winning, but the atheists are making some headway with the same sort of spurious and fallacious reasoning that they decry. It’s not my goal to enter this war in these pages; instead, I want to suggest another approach, as an inhabitant in that neutral country of magic. After all, we lost this war long ago — and yet a few of us still remain, quietly doing what the dominant culture no doubt regards as eccentric at best.
What magic offers is the model, not of war, but of a toolbox. Perhaps instead of imagining that one way of knowing the world is right and all the others are wrong, we could imagine that one way of knowing the world is very good at accomplishing a certain task, and other ways are good at accomplishing certain other tasks. The skeptic picks up magic and says “look at how empirical examination of astrology proves that it’s bunk. How can you still believe it?” This skeptic is like the do-it-yourselfer who picks up a wrench to pound in a nail. If you approach a system of knowledge, you must do so first by understanding its use.
Each system of knowledge begins with certain assumptions, axioms if you will, and has certain strengths. To understand and employ that system of knowledge you must understand its assumptions and strengths. Moreover, our toolbox must contain more than two means of knowledge about the world. In fact, magic teaches us a myriad of ways to understand the world. Most magicians pay their bills, do their taxes, and go to work like normal people living in an empirical world. But at the same time, they recognize that associational thinking — linking diverse symbols to create new ideas — can affect reality in a fundamental and concrete way.
If we imagine that associational thinking is the only tool in our box, we become superstitious and become paranoid at a world too fraught with meaning. On the other hand, if all we have is empiricism, we never examine our underlying assumptions about knowledge, our philosophical foundations, and so we can never move beyond a naive empirical view of the world into meaning. Meaning, if empiricism is the only tool in our toolbox, is reduced to data collection.
It’s clear, then, that different mental tools suit different life-tasks better. What is needed, in both science and magic, is cognitive flexibility and willingness to experiment meaningfully. I think that science can teach us something about magic, maybe even investigate some of its claims, just as magic can help us create meaning out of the discoveries of science. Yet science is not just magic that we’ve learned to understand, and magic is not just unexplained science. If that were the case, we would be the poorer for it. Our minds understand the world physically and metaphysically, and we need to honor both in order to make full use of our toolbox, and we must avoid the errors of both Aristotle and Galileo, while simultaneously respecting their unsurpassed contributions to human thought.
©2009 Patrick Dunn
Edited by Sheta Kaey
Patrick Dunn has written two books on the occult, Postmodern Magic: The Art of Magic in the Information Age and Magic Power Language Symbol: A Magician’s Exploration of Linguistics. He lives near Chicago, where he teaches and writes. You can find his blog here.