A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. I
John Stuart Mill · en
Applying this view of propositions to the two premises of a syllogism,
we obtain the following results. The major premise, which, as already
remarked, is always universal, asserts, that all things which have a
certain attribute (or attributes) have or have not along with it, a
certain other attribute (or attributes). The minor premise asserts that
the thing or set of things which are the subject of that premise, have
the first-mentioned attribute; and the conclusion is, that they have (or
that they have not) the second. Thus in our former example,
All men are mortal,
Socrates is a man,
therefore
Socrates is mortal,
the subject and predicate of the major premise are connotative terms,
denoting objects and connoting attributes. The assertion in the major
premise is, that along with one of the two sets of attributes, we always
find the other: that the attributes connoted by "man" never exist unless
conjoined with the attribute called mortality. The assertion in the
minor premise is that the individual named Socrates possesses the former
attributes; and it is concluded that he possesses also the attribute
mortality. Or if both the premises are general propositions, as
All men are mortal,
All kings are men,
therefore
All kings are mortal,
the minor premise asserts that the attributes denoted by kingship only
exist in conjunction with those signified by the word man. The major
asserts as before, that the last-mentioned attributes are never found
without the attribute of mortality. The conclusion is, that wherever the
attributes of kingship are found, that of mortality is found also.
If the major premise were negative, as, No men are omnipotent, it would
assert, not that the attributes connoted by "man" never exist without,
but that they never exist with, those connoted by "omnipotent:" from
which, together with the minor premise, it is concluded, that the same
incompatibility exists between the attribute omnipotence and those
constituting a king. In a similar manner we might analyse any other
example of the syllogism.