The Complete Aristotle (eng.)

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 the conclusion is necessary, the mediating link is
a contingent fact. Or again, if a man is without knowledge now,
though he still retains the steps of the argument, though there is
no change in himself or in the fact and no lapse of memory on his
part; then neither had he knowledge previously. But the mediating
link, not being necessary, may have perished in the interval; and
if so, though there be no change in him nor in the fact, and though
he will still retain the steps of the argument, yet he has not
knowledge, and therefore had not knowledge before. Even if the link
has not actually perished but is liable to perish, this situation
is possible and might occur. But such a condition cannot be
knowledge.
    When the