### Aristotle - The Organon ANALYTICA PRIORIA Book 1 Part 24

## One premiss must be affirmative, one universal

1.
Further in every syllogism one of the premisses must be
affirmative,
and universality must be present:
unless one of the premisses is
universal either a syllogism will not be possible, or it will not
refer to the subject proposed, or the original position will be
begged. Suppose we have to prove that pleasure in music is good. If
one should claim as a premiss that pleasure is good without adding
'all', no syllogism will be possible; if one should claim that some
pleasure is good, then if it is different from pleasure in music, it
is not relevant to the subject proposed; if it is this very
pleasure, one is assuming that which was proposed at the outset to
be proved. This is more obvious in geometrical proofs, e.g. that the
angles at the base of an isosceles triangle are equal. Suppose the
lines A and B have been drawn to the centre. If then one
should assume
that the angle AC is equal to the angle BD, without claiming
generally
that angles of semicircles are equal; and again if one should assume
that the angle C is equal to the angle D, without the additional
assumption that every angle of a segment is equal to every
other angle
of the same segment; and further if one should assume that when
equal angles are taken from the whole angles, which are themselves
equal, the remainders E and F are equal, he will beg the thing to be
proved, unless he also states that when equals are taken from equals
the remainders are equal.

2.
It is clear then that in every syllogism there must be a universal
premiss, and that a universal statement is proved only when all the
premisses are universal, while a particular statement is proved both
from two universal premisses and from one only:
consequently if the
conclusion is universal, the premisses also must be universal, but
if the premisses are universal it is possible that the conclusion
may not be universal. And it is clear also that in every syllogism
either both or one of the premisses must be like the conclusion. I
mean not only in being affirmative or negative, but also in being
necessary, pure, problematic. We must consider also the
other forms of
predication.

3.
It is clear also when a syllogism in general can be made
and when it
cannot;
and when a valid, when a perfect syllogism can be formed;
and that if a syllogism is formed the terms must be arranged
in one of
the ways that have been mentioned.

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