The great thinker Plato (427-347 BC) was from a wealthy Athenian family. In his youth he dreamed of a career in politics, and became a follower of Socrates. He abandoned political plans after Socrates' shocking execution, going abroad for a decade. He spent this time in Egypt and southern Italy, where he became familiar with Pythagorean thinking.
After he returned to Athens, Plato recruited a kind of brotherhood of talented pupils. They gathered outside of Athens in a sacred grove named after the mythical hero Akademos. In this peaceful place, Plato discussed philosophy and science with his pupils. It was here that Plato's Academy was born in 387 BC, the famous seat of learning which operated for nine centuries until the Emperor Justinian closed it in AD 529. Plato's team was very influential indeed. Among his pupils were the philosopher and scientist Aristotle, and the mathematicians Eudoxus, Callippus, and Theaetetos.
Instead of observations, the philosopher Plato emphasized the importance of thinking and reasoning when one attempts to understand what is behind the incomplete and muddy image of our world. For him true reality was the world of concepts. This may reflect the Pythagorean view of reality, number (also an abstract concept). Clearly, these two world views deviated from the material foundation of reality as seen by the Ionians and the atomists.
Plato's approach to the study of nature is revealed in astronomy. In the dialogue Republic he introduces an educational program suitable for the philosopher-rulers of his ideal city-state. The aim of the curriculum was to make it easier for the human mind to approach the only true subject of knowledge, the unchangeable world of ideas, not the ever changing phenomena of the world of the senses. In Plato's dialogue, Socrates regards mathematics (arithmetic, geometry) as a way to study unchanging truths. Another recommended field is astronomy, though in a sense that now seems quite alien to us.
Socrates' interlocutor Glaucon eagerly accepts astronomy as useful for farmers and sailors. However, Socrates bluntly condemns this aspect as useless for the philosopher. Glaucon then hopefully asserts that at all events astronomy compels the soul to look upward, away from the lower things. But again Socrates disagrees. For him "upward" is just toward the material heaven, not toward the realm of ideas, as expressed in clear words:... if any one attempts to learn anything that is perceivable, I do not care whether he looks upwards with mouth gaping or downwards with mouth closed: he will never, as I hold, learn - because no object of sense admits of knowledge - and I maintain that, in that case, his soul is not looking upwards but downwards, even though the learner float face upwards on land or in the sea.
Glaucon must again admit that he was wrong. But then "what is the way, different from the present method, in which astronomy should be studied for the purposes we have in view?" Socrates admits that "yonder embroideries in the heavens" are more beautiful and perfect than anything else that is visible, yet they are far inferior to that which is true, far inferior to the movements wherewith essential speed and essential slowness, in true number and in all true forms, move in relation to one another and cause that which is essentially in them to move: the true objects which are apprehended by reason and intelligence, not by sight. And Socrates goes on to clarify what he actually means:
Then we should use the embroideries in the heaven as illustrations to facilitate the study which aims at those higher objects, just as we might employ ...diagrams drawn and elaborated with exceptional skill by Daedalus or any other artist or draughtsman; for I take it that anyone acquainted with geometry who saw such diagrams would indeed think them most beautifully finished but would regard it as ridiculous to study them seriously in the hope of gathering from them true relations of equality, doubleness, or any other ratio. (Translations of Plato's texts from Heath: Aristarchus ofSamos.)
Socrates, and Plato, thought that the regular movements of celestial bodies roughly reflect the laws of the ideal world of motions just as hand-drawn geometric pictures offer hints about the mathematical laws governing true geometric figures. However, mere looking or making observations does not lead to genuine confident knowledge about geometry - these must be proved in derivations where visual impressions or measurements of even accurately made drawings do not appear as part of the argument. For example, one might make many scale drawings to approximately verify the theorem of Pythagoras, but one cannot be sure of its complete exactness without a geometric derivation (Fig. 2.1).
Fig. 2.1 Pythagorean Theorem. The area of the square drawn on the hypotenuse of a right-angled triangle is equal to the sum of the areas of the squares on the other two sides. You may try to prove this ancient theorem - there are many ways to do it
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