- THE EARLIEST GREEK GEOMETRY 293
and less philosophical. It is likely that even Plato realized that his attempt to un-
derstand the universe through his Forms was not going to work. His late dialogue
Parmenides gives evidence of a serious rethinking of this doctrine. In any case, it
is clear that Plato could not completely dominate the intellectual life of his day.
1.9. Aristotle. Plato died in 347 BCE, and his place as the pre-eminent scholar
of Athens was taken a decade after his death by his former pupil Aristotle (384-322
BCE). Aristotle became a student at the Academy at the age of 18 and remained
there for 20 years. After the death of Plato he left Athens, traveled, got married,
and in 343 became tutor to the future Macedonian King Alexander (the Great),
who was 13 years old when Aristotle began to teach him and 16 when he became
king on the death of his father. In 335 Aristotle set up his own school, located
in the Lyceum, over the hill from the Academy. For the next 12 years he lived
and wrote there, producing an enormous volume of speculation on a wide variety
of subjects, scientific, literary, and philosophical. In 322 Alexander died, and the
Athenians he had conquered turned against his friends. Unlike Socrates, Aristotle
felt no obligation to be a martyr to the laws of the polis. He fled to escape the
persecution, but died the following year. Aristotle's writing style resembles very
much that of a modern scholar, except for the absence of footnotes. Like Plato, in
mathematics he seems more like a well-informed generalist than a specialist.
The drive toward the logical organization of science reached its full extent in
the treatises of Aristotle. He analyzed reason itself and gave a very thorough and
rigorous discussion of formal inference and the validity of various kinds of arguments
in his treatise Prior Analytics, which was written near the end of his time at the
Academy, around 350 BCE. It is easy to picture debates at the Academy, with the
mathematicians providing examples of their reasoning, which the logician Aristotle
examined and criticized in order to distill his rules for making inferences. In this
treatise Aristotle discusses subjects, predicates, and syllogisms connecting the two,
occasionally giving a glimpse of some mathematics that may indicate what the
mathematicians were doing at the time.• Academy
* Lyceum
Athens in the fourth century BCE: the waterfront (Piraeus),
Academy, and Lyceum.