Mathematics and the Real World: The Remarkable Role of Evolution in the Making of Mathematics (2014)

CHAPTER II. MATHEMATICS AND THE GREEKS’ VIEW OF THE WORLD

13. ON THE GREEK PERCEPTION OF SCIENCE

The chief architect of the mainstream Greek view of the model of the world was Aristotle. His rigorous philosophical approach, despite its many successes, also blocked original thought and led to the rejection of new ideas, ostensibly based on logic.

Aristotle's broad philosophical views fall outside our subject in this chapter, that is, the physical description of the world, and they encompass fields such as biology, zoology, and sociology. The philosophical approach of which Aristotle was a major proponent was that everything around us, including the laws of nature, has a purpose. Although the idea that the design of the world has a purpose arose many years before Aristotle and was presented by the school founded by Thales in Miletus, it was Aristotle who made the purpose underlying the laws of nature into a law of nature itself. The conclusions Aristotle drew from the principle of purposefulness (teleology) and how to use it to obtain a picture of the physical world had far-reaching implications.

The purpose as defined in Greek philosophy is nothing like the purpose that was and is still described by current monotheistic religions, that is, the need to satisfy the Creator. For Aristotle the purpose consisted of the search for sense and logic that were the basis of the physical laws. And as there is sense in formulating the laws of nature, according to Aristotle, they also satisfy the principles of beauty and aesthetics, and we must take that into account when searching for the laws of nature.

Aristotle based the principles of his theory on observations from nature. For example, he said, human beings grow teeth, the purpose of which is to chew food. Rain falls (or in Aristotle's words, the gods bring down rain), the purpose of which is to make grains grow, and similarly with other laws of nature. The purpose of the events that we see in nature enables us to discover the laws underlying the events, and vice versa, the purpose that we discover by virtue of our intelligence enables us to forecast those events. From a retrospective view it can be seen that although the cause and effect for Aristotle were totally different than those derived from the laws of evolution, the structure of Aristotelian thought is very similar to viewing nature via the evolutionary process. For Aristotle, the growth of teeth was a law of nature, and its purpose was to enable living beings to eat, while the evolutionary standpoint states that those living beings that grew teeth, enabling them to chew food, were the ones that developed. Likewise, Aristotle claimed that rain was a law of nature whose purpose was to enable grains to grow, whereas viewed from the evolutionary standpoint, grains developed in areas where there was rain. Either of these approaches helps us learn from the characteristics that we can observe how things developed. And vice versa, from the purpose, according to Aristotle, or from the conditions, according to evolution, we can predict the characteristics that we can see in nature.

Aristotle also expressed his views on the essence of space and motion in space. He saw bodies that fell to the ground, while other materials, such as flames or steam, rose. Whereas Plato tried to explain this by relating to the different weights of the various entities, Aristotle concluded that the purpose of pristine, pure elements such as steam or fire was to reach heaven, a pristine, pure place, while the purpose of materials such as ash or soil, which are clearly impure, was to reach the ground. His view was supported by the belief that the angels and gods, which are pure by definition, dwell in heaven. This led Aristotle to define a space that has directions, up and down. Upward is the direction toward the pure and the good, while downward is the spoiled and defective, toward the center of the Earth (even today, upward represents positive progress and downward signifies regression). This view of space answered the question about the antipodes, or specifically, what do up and down mean for people on opposite sides of the Earth. Downward for those on the other side of the Earth also means toward the center of the Earth, said Aristotle, hence they are not standing on their heads. This geometric view of the Earth as a sphere is of course consistent with ours. The purpose underlying Aristotle's directions up and down, relative to the Earth, firmly established the Earth as the center of the world for many years and predominated over other models, which in due course proved to be more correct.

With regard to the movement of various bodies, both earthly and heavenly, Aristotle observed that heavenly bodies moved in smooth, regular paths, a straight line or a circle, while earthly bodies moved along much more tortuous routes. The purpose that considered upward to represent purity while downward indicated inferiority led him to conclude that circular and straight paths were pure and other routes were defective. As it was geometry that served to describe the movement of the various bodies, Aristotle reasoned that the movements of heavenly bodies and earthly bodies were governed by different sets of rules. The gap between the different descriptions of earthly and heavenly motion persisted until the seventeenth century, when it was bridged by Newton. Aristotle also searched for a reason for the motion of the different bodies, and, by implication from the perception that the force exerted on a body causes it to move, he concluded that a force is responsible for all motion. Aristotle applied this conclusion to the heavenly bodies also. Hence, he claimed, the stars cannot move in a vacuum, and the world is filled with a substance he called ether. The ether also explained the source of the light and warmth of the Sun. The friction between the Sun and the ether creates heat. Aristotle went beyond that and rejected the model that described the world as consisting of atoms with a vacuum between them, as that would not allow for the exertion of the force required for motion. Hence, matter is continuous. The model of the atoms and the rejection of the assumption of the existence of the ether held until the nineteenth and twentieth centuries. Although many of the conclusions drawn from Aristotle's philosophy slowed the development of science, his philosophical principles nevertheless made an important contribution to scientific development.