Aristotle – A Way of Knowing -
By Patrick Dunn
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.
Aristotle 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 â€“ A Way of Knowing -
By Patrick Dunn
*** 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 â€” 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 â€” 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.
*** Aristotle vs. Galileo Aristotle reasoned that if we avoid the engagement of the senses, we avoid the faults that senses are heir to. He thus used reason and logic 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 account above, both he and his secretary make observations, and they do not stop with just one but do it again and again. This method has the benefit of certainty. We know it works because we can see it working.