From this survey we may sec that all the philosophers who forged and molded the Greek intellectual world stressed the study of nature for comprehension and appreciation of its underlying reality. From the timeof the Pythagoreans, practically all asserted that nature was designedmathematically. During the classical period, the doctrine of the mathematical design of nature was cstablished and the search for the mathematical lawsinstituted. Though this doctrine did not motivate all of the mathematics subsequently created, once established it was acccpted and consciously pursued by most of the great mathematicians. During the time that this
doctrine held sway, which was until the latter part of the nineteenth century, the search for the mathematical design was identified with the searchfor truth. Though a few Greeks-for example, Ptolemy-realized that mathematical theories were merely human attempts to provide a coherent account, the belief that mathematical laws were the truth about natureattracted some of the deepest and noblest thinkers to mathematics.
We should also note, in order to appreciate more readily what happened in the seventeenth century, thc Greek emphasis on the power of the mind. Because the Greek philosophers believed that the mind was the most powerful agent in comprehending nature, they adopted first principles that appealed to the mind. Thus the belief that circular motion was the basic type, defendedby Aristotle on the ground that the circle is complete whereas a rectilinearfigure, because it is bounded by many curves (line segments), is incomplete and therefore secondary in importance, appealed to the mind on aestheticgrounds. That the heavenly bodies should move with only constant or uniform velocity, was a conception which appealed to the mind perhaps because it was simplcer than nonuniform motion. The combination of uniform and circular motion seemed to befit heavenly bodies. That the sublunar bodies should be different from the planets, sun, and stars seemed reasonable also, because the heavenly bodies preserved a constant appearance whereas change on Earth was evident. Evn Aristotle, who stressed abstractions onlyinsofar as they helped to understand the observable world, said that we muststart from principles that are known and manifest to the mind and then proceed to analyze things found in nature. We proceed, he said, fromuniversals to particulars, from man to men, just as children call all men father and then learn to distinguish. Thus even the abstractions made from concrete objects presuppose some general principles emanating from themind. This doctrine, the power of the mind to yield first principles, was overthrown in the seventeenth century.
... carry on.
when I just read your post above lol. Please consider it.
