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essential attributes, starting from the common beliefs. Therefore to
investigate the essential attributes of one class of things,
starting from one set of beliefs, is the business of one science.
For the subject belongs to one science, and the premisses belong to
one, whether to the same or to another; so that the attributes do so
too, whether they are investigated by these sciences or by one
compounded out of them.
(5) Further, does our investigation deal with substances alone
or also with their attributes? I mean for instance, if the solid is
a substance and so are lines and planes, is it the business of the
same science to know these and to know the attributes of each of these
classes (the attributes about which the mathematical sciences offer
proofs), or of a different science? If of the same, the science of
substance also must be a demonstrative science, but it is thought that
there is no demonstration of the essence of things. And if of another,
what will be the science that investigates the attributes of
substance? This is a very difficult question.
(4) Further, must we say that sensible substances alone exist,
or that there are others besides these? And are substances of one kind
or are there in fact several kinds of substances, as those say who
assert the existence both of the Forms and of the intermediates,
with which they say the mathematical sciences deal?-The sense in which
we say the Forms are both causes and self-dependent substances has
been explained in our first remarks about them; while the theory
presents difficulties in many ways, the most paradoxical thing of
all is the statement that there are certain things besides those in
the material universe, and that these are the same as sensible
things except that they are eternal while the latter are perishable.
For they say there is a man-himself and a horse-itself and
health-itself, with no further qualification,-a procedure like that of
the people who said there are gods, but in human form. For they were
positing nothing but eternal men, nor are the Platonists making the
Forms anything other than eternal sensible things.
Further, if we are to posit besides the Forms and the sensibles
the intermediates between them, we shall have many difficulties. For
clearly on the same principle there will be lines besides the
lines-themselves and the sensible lines, and so with each of the other
classes of things; so that since astronomy is one of these
mathematical sciences there will also be a heaven besides the sensible
heaven, and a sun and a moon (and so with the other heavenly bodies)
besides the sensible. Yet how are we to believe in these things? It is
not reasonable even to suppose such a body immovable, but to suppose
it moving is quite impossible.-And similarly with the things of
which optics and mathematical harmonics treat; for these also cannot
exist apart from the sensible things, for the same reasons. For if
there are sensible things and sensations intermediate between Form and
individual, evidently there will also be animals intermediate
between animals-themselves and the perishable animals.-We might also
raise the question, with reference to which kind of existing things we
must look for these sciences of intermediates. If geometry is to
differ from mensuration only in this, that the latter deals with
things that we perceive, and the former with things that are not
perceptible, evidently there will also be a science other than
medicine, intermediate between medical-science-itself and this
individual medical science, and so with each of the other sciences.
Yet how is this possible? There would have to be also healthy things
besides the perceptible healthy things and the healthy-itself.--And at
the same time not even this is true, that mensuration deals with
perceptible and perishable magnitudes; for then it would have perished
when they perished.
But on the other hand astronomy cannot be dealing with perceptible
magnitudes nor with this heaven above us. For neither are
perceptible lines such lines as the geometer speaks of (for no
perceptible thing is straight or round in the way in which he

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