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Thus； as we maintain； to know a thing's nature is to know the reason
why it is； and this is equally true of things in so far as they are
said without qualification to he as opposed to being possessed of some
attribute； and in so far as they are said to be possessed of some
attribute such as equal to right angles； or greater or less。
3
It is clear； then； that all questions are a search for a 'middle'。
Let us now state how essential nature is revealed and in what way it
can be reduced to demonstration； what definition is； and what things
are definable。 And let us first discuss certain difficulties which
these questions raise； beginning what we have to say with a point most
intimately connected with our immediately preceding remarks； namely
the doubt that might be felt as to whether or not it is possible to
know the same thing in the same relation； both by definition and by
demonstration。 It might； I mean； be urged that definition is held to
concern essential nature and is in every case universal and
affirmative； whereas； on the other hand； some conclusions are negative
and some are not universal； e。g。 all in the second figure are
negative； none in the third are universal。 And again； not even all
affirmative conclusions in the first figure are definable； e。g。 'every
triangle has its angles equal to two right angles'。 An argument
proving this difference between demonstration and definition is that
to have scientific knowledge of the demonstrable is identical with
possessing a demonstration of it： hence if demonstration of such
conclusions as these is possible； there clearly cannot also be
definition of them。 If there could； one might know such a conclusion
also in virtue of its definition without possessing the
demonstration of it； for there is nothing to stop our having the one
without the other。
Induction too will sufficiently convince us of this difference；
for never yet by defining anything…essential attribute or accident…did
we get knowledge of it。 Again； if to define is to acquire knowledge of
a substance； at any rate such attributes are not substances。
It is evident； then； that not everything demonstrable can be
defined。 What then？ Can everything definable be demonstrated； or
not？ There is one of our previous arguments which covers this too。
Of a single thing qua single there is a single scientific knowledge。
Hence； since to know the demonstrable scientifically is to possess the
demonstration of it； an impossible consequence will follow：…possession
of its definition without its demonstration will give knowledge of the
demonstrable。
Moreover； the basic premisses of demonstrations are definitions； and
it has already been shown that these will be found indemonstrable；
either the basic premisses will be demonstrable and will depend on
prior premisses； and the regress will be endless； or the primary
truths will be indemonstrable definitions。
But if the definable and the demonstrable are not wholly the same；
may they yet be partially the same？ Or is that impossible； because
there can be no demonstration of the definable？ There can be none；
because definition is of the essential nature or being of something；
and all demonstrations evidently posit and assume the essential
nature…mathematical demonstrations； for example； the nature of unity
and the odd； and all the other sciences likewise。 Moreover； every
demonstration proves a predicate of a subject as attaching or as not
attaching to it； but in definition one thing is not predicated of
another； we do not； e。g。 predicate animal of biped nor biped of
animal； nor yet figure of plane…plane not being figure nor figure
plane。 Again； to prove essential nature is not the same as to prove
the fact of a connexion。 Now definition reveals essential nature；
demonstration reveals that a given attribute attaches or does not
attach to a given subject； but different things require different
demonstrations…unless the one demonstration is related to the other as
part to whole。 I add this because if all triangles have been proved to
possess angles equal to two right angles； then this attribute has been
proved to attach to isosceles； for isosceles is a part of which all
triangles constitute the whole。 But in the case before us the fact and
the essential nature are not so related to one another； since the
one is not a part of the other。
So it emerges that not all the definable is demonstrable nor all the
demonstrable definable； and we may draw the general conclusion that
there is no identical object of which it is possible to possess both a
definition and a demonstration。 It follows obviously that definition
and demonstration are neither identical nor contained either within
the other： if they were； their objects would be related either as
identical or as whole and part。
4
So much； then； for the first stage of our problem。 The next step
is to raise the question whether syllogism…i。e。 demonstration…of the
definable nature is possible or； as our recent argument assumed；
impossible。
We might argue it impossible on the following grounds：…（a） syllogism
proves an attribute of a subject through the middle term； on the other
hand （b） its definable nature is both 'peculiar' to a subject and
predicated of it as belonging to its essence。 But in that case （1） the
subject； its definition； and the middle term connecting them must be
reciprocally predicable of one another； for if A is to C； obviously
A is 'peculiar' to B and B to C…in fact all three terms are 'peculiar'
to one another： and further （2） if A inheres in the essence of all B
and B is predicated universally of all C as belonging to C's
essence； A also must be predicated of C as belonging to its essence。
If one does not take this relation as thus duplicated…if； that is； A
is predicated as being of the essence of B； but B is not of the
essence of the subjects of which it is predicated…A will not
necessarily be predicated of C as belonging to its essence。 So both
premisses will predicate essence； and consequently B also will be
predicated of C as its essence。 Since； therefore； both premisses do
predicate essence…i。e。 definable form…C's definable form will appear
in the middle term before the conclusion is drawn。
We may generalize by supposing that it is possible to prove the
essential nature of man。 Let C be man； A man's essential
naturetwo…footed animal； or aught else it may be。 Then； if we are to
syllogize； A must be predicated of all B。 But