Discuss the way in which Greek art and science reflected Greek values and philosophies.

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Answer: Greeks believed in reasonable design of the world. At least in philosophy, science and arts Greeks believe that there are laws that rule the world and these laws are rational. In arts they apply principle of proportion and harmony. It does not mean there are no irrationalist philosophies but laws of reason have a prominence. At the very beginning of Greek philosophy tradition, philosophy is permeated by mythology but even then Greeks believe in reasoanable design of the world that is possible to discover and they try to formulate and verbalize these laws.

Explanation: Nietzsche in his "Birth of Tragedy" criticized Socrates and the way of reasoning Socrates introduced became for him Socrates' philosophy introduces dominance of "Apolinean" principle (reason, rationality, proportions, harmony) in detriment of "Dionisian" (intoxication, irrational, chaotic, instinctual). For him fertility and success of Greeks resulted from inner conflict between Apolinean and Dionysian which now (with Socrates) was "resolved" in favour of the former. But irrational never left Greeks completely which is visible in various derivates of Platonism. But irrationalist philosophies of Greek origin always worked rather as subterranean streams whereas rationalism usually assumed dominant role. This can be said about renaissance ... it re-discovers ancient Greek philosophy but especially (not only of course) its rational aspect. European philosophy still draws its main scientific paradigms (Aristotelian, neo-Platonic and mechanistic) from ancient Greece.