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. I have tried to give myself
some grounding in ancient mathematics, but can only do so
much. I wanted to have some sense of what it might be like
to be thinking in the ways open to such people as Theaetetus
that Plato knew. I am not sure if this idea even makes sense
to mathematicians.
As philosophers, we have to ask questions about the role of
mathematics in philosophy, and time does not allow all of us
to be experts in everything. The result may be that views of
mathematics that would never be accepted by 'real'
mathematicians become used in the pursuit of philosophical
dogma. I believe that it is important to gain some idea of
the way that mathematics has been regarded by philosophers
in history, as this has clearly influenced the way that they
presented and understood the philosophical remarks that they
made (the same seems to be true today, as ideas drawn from
decision theory are increasingly used in thinking about
moral and political philosophy, as in modern Contract
theory). It might then seem that one should not do
philosophy without a degree in mathematics, but this is
demanding: one might not realize until much too late that
this was required. There is no easy answer, but the question
merits discussion. There is a need for philosophers to bring
such questions into the discussion of the texts, and so we
need material which is available to non-mathematicians (as
provided currently by Ian Mueller for Greek philosophy). It
seems true that (some) mathematicians need to let the rest
of us know what is -or has been- going on.
For instance, one should be cautious of the assertions of
those who dogmatically present methods as mathematical.
Worse, along with this goes an attitude: as mathematics is
often conceived by non-mathematicians as attaining dogmatic
certainty, so this supports a view of philosophy as capable
of attaining equally dogmatic results. Did not some writers
who tried to present the 'mathematics necessary for the
study of Plato' misconceive the role of mathematics, as well
as not understanding mathematics? Should I defer to them?
Can I legitimately use the views of people like Lakatos to
suggest that while Plato saw mathematicians achieving
results, his real philosophical interests should (and in my
view did)
lie in the fact that they were prepared and able to canvass,
develop and reject ideas in a communal way, not that they
reached some otherwise unattainable certainty? Most of all,
can I do any of these things without being a mathematician?
and how otherwise can I argue against dogmatic
interpretations? And I mean doing more than reading the
excellent works of people like Ian Mueller, although this
has helped immensely.
I am only too well aware that I am trying to do something
which may well be beyond my powers: my excuse is that I
think there are some interesting questions about method to
be examined, that go deep into the heart of philosophy, and
I do not think that one can simply leave them to the
mathematicians, but we must try to discuss them in more
accessible ways.
Greetings from Calgary, where the snow has melted.
Janet Sisson