_Of Mediate Inferences or Syllogisms._
§ 540. A Mediate Inference, or Syllogism, consists of two
propositions, which are called the Premisses, and a third proposition
known as the Conclusion, which flows from the two conjointly.
§ 541. In every syllogism two terms are compared with one another by
means of a third, which is called the Middle Term. In the premisses
each of the two terms is compared separately with the middle term; and
in the conclusion they are compared with one another.
§ 542. Hence every syllogism consists of three terms, one of which
occurs twice in the premisses and does not appear at all in the
conclusion. This term is called the Middle Term. The predicate of the
conclusion is called the Major Term and its subject the Minor Term.
§ 543. The major and minor terms are called the Extremes, as opposed
to the Mean or Middle Term.
§ 544. The premiss in which the major term is compared with the middle
is called the Major Premiss.
§ 545. The other premiss, in which the minor term is compared with the
middle, is called the Minor Premiss.
§ 546. The order in which the premisses occur in a syllogism is
indifferent, but it is usual, for convenience, to place the major
premiss first.
§ 547. The following will serve as a typical instance of a syllogism--
Middle term Major term \
Major Premiss. All mammals are warm-blooded | Antecedent
> or
Minor term Middle term | Premisses
Minor Premiss. All whales are mammals /
Minor term Major term \ Consequent or
.'. All whales are warm-blooded > Conclusion.
§ 548. The reason why the names 'major, 'middle' and 'minor' terms
were originally employed is that in an affirmative syllogism such as
the above, which was regarded as the perfect type of syllogism, these
names express the relative quantity in extension of the three terms.
[Illustration]
§ 549. It must be noticed however that, though the middle term cannot
be of larger extent than the major nor of smaller extent than the
minor, if the latter be distributed, there is nothing to prevent all
three, or any two of them, from being coextensive.
§ 550. Further, when the minor term is undistributed, we either have a
case of the intersection of two classes, from which it cannot be told
which of them is the larger, or the minor term is actually larger than
the middle, when it stands to it in the relation of genus to species,
as in the following syllogism--
All Negroes have woolly hair.
Some Africans are Negroes.
.'. Some Africans have woolly hair.
[Illustration]
§ 551. Hence the names are not applied with strict accuracy even in
the case of the affirmative syllogism; and when the syllogism is
negative, they are not applicable at all: since in negative
propositions we have no means of comparing the relative extension of
the terms employed. Had we said in the major premiss of our typical
syllogism, 'No mammals are cold-blooded,' and drawn the conclusion 'No
whales are cold-blooded,' we could not have compared the relative
extent of the terms 'mammal' and 'cold-blooded,' since one has been
simply excluded from the other.
[Illustration]
§ 552. So far we have rather described than defined the syllogism. All
the products of thought, it will be remembered, are the results of
comparison. The syllogism, which is one of them, may be so regarded in
two ways--
(1) As the comparison of two propositions by means of a third.
(2) As the comparison of two terms by means of a third or middle
term.
§ 553. The two propositions which are compared with one another are
the major premiss and the conclusion, which are brought into
connection by means of the minor premiss. Thus in the syllogism above
given we compare the conclusion 'All whales are warm-blooded' with the
major premiss 'All mammals are warm-blooded,' and find that the former
is contained under the latter, as soon as we become acquainted with
the intermediate proposition 'All whales are mammals.'
§ 554. The two terms which are compared with one another are of course
the major and minor.
§ 555. The syllogism is merely a form into which our deductive
inferences may be thrown for the sake of exhibiting their
conclusiveness. It is not the form which they naturally assume in
speech or writing. Practically the conclusion is generally stated
first and the premisses introduced by some causative particle as
'because,' 'since,' 'for,' &c. We start with our conclusion, and then
give the reason for it by supplying the premisses.
§ 556. The conclusion, as thus stated first, was called by logicians
the Problema or Quaestio, being regarded as a problem or question, to
which a solution or answer was to be found by supplying the premisses.
§ 557. In common discourse and writing the syllogism is usually stated
defectively, one of the premisses or, in some cases, the conclusion
itself being omitted. Thus instead of arguing at full length
All men are fallible,
The Pope is a man,
.'. The Pope is fallible,
we content ourselves with saying 'The Pope is fallible, for he is a
man,' or 'The Pope is fallible, because all men are so'; or perhaps we
should merely say 'All men are fallible, and the Pope is a man,'
leaving it to the sagacity of our hearers to supply the desired
conclusion. A syllogism, as thus elliptically stated, is commonly,
though incorrectly, called an Enthymeme. When the major premiss is
omitted, it is called an Enthymeme of the First Order; when the minor
is omitted, an Enthymeme of the Second Order; and when the conclusion
is omitted an Enthymeme of the Third Order.