Posterior Analytics   

triangles'.
When, then, does our knowledge fail of commensurate universality,
and when it is unqualified knowledge? If triangle be identical in
essence with equilateral, i.e. with each or all equilaterals, then
clearly we have unqualified knowledge: if on the other hand it be not,
and the attribute belongs to equilateral qua triangle; then our
knowledge fails of commensurate universality. 'But', it will be asked,
'does this attribute belong to the subject of which it has been
demonstrated qua triangle or qua isosceles? What is the point at which
the subject. to which it belongs is primary? (i.e. to what subject can
it be demonstrated as belonging commensurately and universally?)'
Clearly this point is the first term in which it is found to inhere as
the elimination of inferior differentiae proceeds. Thus the angles
of a brazen isosceles triangle are equal to two right angles: but
eliminate brazen and isosceles and the attribute remains. 'But'-you
may say-'eliminate figure or limit, and the attribute vanishes.' True,
but figure and limit are not the first differentiae whose
elimination destroys the attribute. 'Then what is the first?' If it is
triangle, it will be in virtue of triangle that the attribute
belongs to all the other subjects of which it is predicable, and
triangle is the subject to which it can be demonstrated as belonging
commensurately and universally.

6

Demonstrative knowledge must rest on necessary basic truths; for the
object of scientific knowledge cannot be other than it is. Now
attributes attaching essentially to their subjects attach
necessarily to them: for essential attributes are either elements in
the essential nature of their subjects, or contain their subjects as
elements in their own essential nature. (The pairs of opposites
which the latter class includes are necessary because one member or
the other necessarily inheres.) It follows from this that premisses of
the demonstrative syllogism must be connexions essential in the
sense explained: for all attributes must inhere essentially or else be
accidental, and accidental attributes are not necessary to their
subjects.
We must either state the case thus, or else premise that the
conclusion of demonstration is necessary and that a demonstrated
conclusion cannot be other than it is, and then infer that the
conclusion must be developed from necessary premisses. For though
you may reason from true premisses without demonstrating, yet if
your premisses are necessary you will assuredly demonstrate-in such
necessity you have at once a distinctive character of demonstration.
That demonstration proceeds from necessary premisses is also indicated
by the fact that the objection we raise against a professed
demonstration is that a premiss of it is not a necessary truth-whether
we think it altogether devoid of necessity, or at any rate so far as
our opponent's previous argument goes. This shows how naive it is to
suppose one's basic truths rightly chosen if one starts with a
proposition which is (1) popularly accepted and (2) true, such as
the sophists' assumption that to know is the same as to possess
knowledge. For (1) popular acceptance or rejection is no criterion
of a basic truth, which can only be the primary law of the genus
constituting the subject matter of the demonstration; and (2) not
all truth is 'appropriate'.
A further proof that the conclusion must be the development of
necessary premisses is as follows. Where demonstration is possible,
one who can give no account which includes the cause has no scientific
knowledge. If, then, we suppose a syllogism in which, though A
necessarily inheres in C, yet B, the middle term of the demonstration,
is not necessarily connected with A and C, then the man who argues
thus has no reasoned knowledge of the conclusion, since this
conclusion does not owe its necessity to the middle term; for though