NP Alabama Pi

[Terrance]

jporter wrote:
> 
> Here's a scoop from Johnson's 2/10/98 NY Times article"
> 
> "The ancient followers of the Greek mathematicin
> Pythagoras declared that numbers were the basic elements
> of the universe.Ever since, scientists have embraced a
> kind of mathematical creationism: God is a great
> mathematician, who declared, 'Let there be numbers!'
> before getting around to 'let there be light!'
> 
>  "Scientists usually use the notion of God metaphorically.
> But ultimately, most of them at least tacitly embrace the
> philosophy of Plato, who proposed, rather
> unscientifically, that numbers ansd mathematical laws are
> ethereal ideals, existing outside of space and time in a
> realm beyond the reach of human kind.

This story is way to simple, isn't it? Not quite the story
we find in Aristotle's Metaphysics, Plato, and the other
fragments.  Nevertheless, the author does identify two of
the principle positions in an important debate on BEING in
the culminating phase of Hellenic philosophy. Those two are
the Platonic and the Material, but he does not mention the
Atomists not the Philosopher's Philosopher, Aristotle. See
Metaphysica

"All men by nature desire to know....
  

"Down to the Italian school, then, and apart from it,
philosophers have
    treated these subjects rather obscurely, except that, as
we said, they have
    in fact used two kinds of cause, and one of these-the
source of
    movement-some treat as one and others as two. But the
Pythagoreans
    have said in the same way that there are two principles,
but added this
    much, which is peculiar to them, that they thought that
finitude and
    infinity were not attributes of certain other things,
e.g. of fire or earth or
    anything else of this kind, but that infinity itself and
unity itself were the
    substance of the things of which they are predicated.
This is why
    number was the substance of all things. On this subject,
then, they
    expressed themselves thus; and regarding the question of
essence they
    began to make statements and definitions, but treated
the matter too
    simply. For they both defined superficially and thought
that the first
    subject of which a given definition was predicable was
the substance of
    the thing defined, as if one supposed that 'double' and
'2' were the same,
    because 2 is the first thing of which 'double' is
predicable. But surely to
    be double and to be 2 are not the same; if they are, one
thing will be
    many-a consequence which they actually drew. From the
earlier
    philosophers, then, and from their successors we can
learn thus much. 

    Part 6 "



    "After the systems we have named came the philosophy of
Plato, which
    in most respects followed these thinkers, but had
pecullarities that
    distinguished it from the philosophy of the Italians.
For, having in his
    youth first become familiar with Cratylus and with the
Heraclitean
    doctrines (that all sensible things are ever in a state
of flux and there is no
    knowledge about them), these views he held even in later
years.
    Socrates, however, was busying himself about ethical
matters and
    neglecting the world of nature as a whole but seeking
the universal in
    these ethical matters, and fixed thought for the first
time on definitions;
    Plato accepted his teaching, but held that the problem
applied not to
    sensible things but to entities of another kind-for this
reason, that the
    common definition could not be a definition of any
sensible thing, as they
    were always changing. Things of this other sort, then,
he called Ideas,
    and sensible things, he said, were all named after
these, and in virtue of a
    relation to these; for the many existed by participation
in the Ideas that
    have the same name as they. Only the name
'participation' was new; for
    the Pythagoreans say that things exist by 'imitation' of
numbers, and
    Plato says they exist by participation, changing the
name. But what the
    participation or the imitation of the Forms could be
they left an open
    question. 

    "Further, besides sensible things and Forms he says
there are the objects
    of mathematics, which occupy an intermediate position,
differing from
    sensible things in being eternal and unchangeable, from
Forms in that
    there are many alike, while the Form itself is in each
case unique. 

    "Since the Forms were the causes of all other things, he
thought their
    elements were the elements of all things. As matter, the
great and the
    small were principles; as essential reality, the One;
for from the great and
    the small, by participation in the One, come the
Numbers. 

    "But he agreed with the Pythagoreans in saying that the
One is substance
    and not a predicate of something else; and in saying
that the Numbers
    are the causes of the reality of other things he agreed
with them; but
    positing a dyad and constructing the infinite out of
great and small,
    instead of treating the infinite as one, is peculiar to
him; and so is his
    view that the Numbers exist apart from sensible things,
while they say
    that the things themselves are Numbers, and do not place
the objects of
    mathematics between Forms and sensible things. His
divergence from
    the Pythagoreans in making the One and the Numbers
separate from
    things, and his introduction of the Forms, were due to
his inquiries in the
    region of definitions (for the earlier thinkers had no
tincture of dialectic),
    and his making the other entity besides the One a dyad
was due to the
    belief that the numbers, except those which were prime,
could be neatly
    produced out of the dyad as out of some plastic
material. Yet what
    happens is the contrary; the theory is not a reasonable
one. For they
    make many things out of the matter, and the form
generates only once,
    but what we observe is that one table is made from one
matter, while the
    man who applies the form, though he is one, makes many
tables. And
    the relation of the male to the female is similar; for
the latter is
    impregnated by one copulation, but the male impregnates
many females;
    yet these are analogues of those first principles. 

    "Plato, then, declared himself thus on the points in
question; it is evident
    from what has been said that he has used only two
causes, that of the
    essence and the material cause (for the Forms are the
causes of the
    essence of all other things, and the One is the cause of
the essence of the
    Forms); and it is evident what the underlying matter is,
of which the
    Forms are predicated in the case of sensible things, and
the One in the
    case of Forms, viz. that this is a dyad, the great and
the small. Further,
    he has assigned the cause of good and that of evil to
the elements, one to
    each of the two, as we say some of his predecessors
sought to do, e.g.
    Empedocles and Anaxagoras.