<< I have been following this thread with some interest, and
wish to present a somewhat different viewpoint on the
discussion. How far can one appreciate the history of
mathematics without being a mathematician? In particular how
does this affect what philosophers can legitimately do?
I do read Greek (ancient) but I am a philosopher, not a
mathematician, by training. I am wondering if I can
legitimately pursue my research, which concerns the
influence of mathematics on Plato's thought, specifically
his views on moral theory. Most people remember that in the
_Republic_ mathematics is a required step for the study of
dialectic or philosophy. In later dialogues, mathematics
does not have this role, but Plato often uses examples drawn
from mathematics and claims in the Laws that a knowledge of
the paradoxical fact of incommensurability should be
required of every schoolchild. >>
Thinking that Plato was right about this, I teach incommensurability to
schoolchildren. In fact, I just completed teaching it to my sixth grade
ancient history class, followed by Zeno of Elea and Democritus. They were
fascinated. The Apology of Socrates followed without fuss.
Don't you think this argument is not about what to teach but when and to whom
to teach it?
-Bill Everdell, Brooklyn
Who, alas, has less Greek than Latin or math