The Complete Aristotle (eng.)

in the Topics. The nature then of a premiss and the
difference between syllogistic, demonstrative, and dialectical
premisses, may be taken as sufficiently defined by us in relation
to our present need, but will be stated accurately in the
sequel.
    I call that a term into which the premiss is resolved, i.e. both
the predicate and that of which it is predicated, ‘being’ being
added and ‘not being’ removed, or vice versa.
    A syllogism is discourse in which, certain things being stated,
something other than what is stated follows of necessity from their
being so. I mean by the last phrase that they produce the
consequence, and by this, that no further term is required from
without in order to make the consequence necessary.
    I call that a perfect syllogism which needs nothing other than
what has been stated to make plain what necessarily follows; a
syllogism is imperfect, if it needs either one or more
propositions, which are indeed the necessary consequences of the
terms set down, but have not been expressly stated as
premisses.
    That one term should be included in another as in a whole is the
same as for the other to be predicated of all of the first. And we
say that one term is predicated of all of another, whenever no
instance of the subject can be found of which the other term cannot
be asserted: ‘to be predicated of none’ must be understood in the
same way.
2
    Every premiss states that something either is or must be or may
be the attribute of something else; of premisses of these three
kinds some are affirmative, others negative, in respect of each of
the three modes of attribution; again some affirmative and negative
premisses are universal, others particular, others indefinite. It
is necessary then that in universal attribution the terms of the
negative premiss should be convertible, e.g. if no pleasure is
good, then no good will be pleasure; the terms of the affirmative
must be convertible, not however, universally, but in part, e.g. if
every pleasure,is good, some good must be pleasure; the particular
affirmative must convert in part (for if some pleasure is good,
then some good will be pleasure); but the particular negative need
not convert, for if some animal is not man, it does not follow that
some man is not animal.
    First then take a universal negative with the terms A and B. If
no B is A, neither can any A be B. For if some A (say C) were B, it
would not be true that no B is A; for C is a B. But if every B is A
then some A is B. For if no A were B, then no B could be A. But we
assumed that every B is A. Similarly too, if the premiss is
particular. For if some B is A, then some of the As must be B. For
if none were, then no B would be A. But if some B is not A, there
is no necessity that some of the As should not be B; e.g. let B
stand for animal and A for man. Not every animal is a man; but
every man is an animal.
3
    The same manner of conversion will hold good also in respect of
necessary premisses. The universal negative converts universally;
each of the affirmatives converts into a particular. If it is
necessary that no B is A, it is necessary also that no A is B. For
if it is possible that some A is B, it would be possible also that
some B is A. If all or some B is A of necessity, it is necessary
also that some A is B: for if there were no necessity, neither
would some of the Bs be A necessarily. But the particular negative
does not convert, for the same reason which we have already
stated.
    In respect of possible premisses, since possibility is used in
several senses (for we say that what is necessary and what is not
necessary and what is potential is possible), affirmative
statements will all convert in a manner similar to those described.
For if it is possible that all or some B is A, it will be possible
that some A is B. For if that were not possible, then no B could
possibly be A. This has been already proved. But in negative
statements the case is different. Whatever is said to be possible,
either because B necessarily is A, or because B is not necessarily
A, admits of conversion like other negative statements, e.g. if one
should say, it is possible that man is not horse, or that no
garment is white. For in the former case the one term necessarily
does not belong to the other; in the latter there is no necessity
that it should: and the premiss converts like other negative
statements. For if it is possible for no man to be a horse, it is
also admissible for no horse to be a man; and