We have already had two distinct definitions of syllogism. According
to the first it is the application of class-attributes to individuals
known to belong to the class; according to the second it is the
comparison of two things or terms by reference to a third which both
resemble. When we arrive at the chapters in logic books devoted to the
exposition of the syllogism in detail, we find that the theorems there
discussed do not conform to either of those definitions. The only
sort of syllogism that can be 'converted' is one consisting of two
classifications, and a conclusion which predicates a classification,
as thus--
_All Englishmen are Europeans;
John Smith is an Englishman;
therefore John Smith is a European._
Observe the difference between this theorem and that adduced in
illustration of the Dictum (XXXVI). In the latter the first premise
is a categorical judgment and so therefore is the conclusion; in the
theorem just given the first premise is a classification, and the
conclusion is necessarily a classification.
We first remark that such an 'argument' is never met with in
real spontaneous thinking--it occurs only in logic books. It is
manufactured exclusively for Peripatetic consumption. The reason it
is not to be found is simple--the conclusion it yields is a
classification, and that is not enough for valid argument.
In reasoning we may introduce a classification as the _minor
premise_--that is, the proposition which brings the case under the
precedent--but the applicate is never a general or class idea. It is
one or more properties abstracted from the subject (whether the latter
be a single object or general idea), and applied to the case. Merely
to classify a case and so leave it would answer no rational purpose.
Logicians urge in recommendation of this syllogism that it gives a
certain conclusion. The premises being correct, the conclusion is
infallibly true.
No doubt it is, for in contemplating a thing we can mentally enter it
into all the classes to which it appears to belong, whatever be their
generality. Knowing the class European and the individual John Smith,
we see at once that the latter is contained in the former, and we can
do this without putting him first in the minor class English. It is
like saying, 'The pavilion is in the garden, John Smith is in the
pavilion, therefore he is in the garden.' Of course he is! The minor
premise of a double classification is superfluous. The fact that
such conclusions are certain, shows how nugatory they are. We are
not certain of anything till it has been experienced. In legitimate
reasoning the conclusion is never more than probable. The certainty of
these double classifications shows that we are stating what we already
know--not imagining an ideal addition to our positive knowledge.
_Doctrine of the Predicate._ So long as logicians are permitted to
fabricate their own examples, all is plain sailing with the syllogism.
But they are sometimes obliged to deal with genuine arguments. In
this case what they do is to assume that _for logical purposes_ every
predicate of the precedent--that is, the applicate--is a general or
class term. Even when an argument is good they spoil it with a bad
theory.
Sir William Hamilton states that up to his time logicians recognised
but one type of proposition--that called by him the proposition 'in
extension,' which means the classifying of the subject. He announced
that he intended to introduce a proposition 'in comprehension,'
meaning a judgment in the category of inherence--as for instance, 'man
is responsible.' He further said that he recognised a third type of
proposition, that concerning 'cause and effect.'
But in the course of working out these logical novelties he seems to
have discovered that they were irreconcilable with conversion, and so
he dropped them. The judgment in comprehension, he then declared, was
to all intents and purposes the same as one in extension, and as to
causation--why, a cause is a class, and an effect is an individual
belonging to that class![22]
Let us see what is the result of treating applicates as general ideas.
Take an example in each of the categories.
'The paper is white.' This means that the paper has the property or
attribute of whiteness. In logic it is interpreted to mean that paper
is an individual of the class _white_. This is wrong, for there is no
such class. No sane person would form a class out of salt, snow, milk,
china, silver, the moon, and other white things; for though they have
a common property it is not the sign of a common human utility.
The confusing a single property with a class is not always owing to
exigencies of syllogism. It pervades the writings of most Western
metaphysicians, and may be accounted for in this manner.
General ideas and abstract properties or ideas have in common that
they are _partial_ recognitions of what we perceive (XIV). The
partition in each is however made in a different way, and for a
different purpose. In generalisation the selection is done almost
mechanically. We see many things that have some common relation,
function, or utility for us, and we remember only so much of them
as appears to be necessary for the recognition of that relation or
utility--just so much of the Intellectual experience as has always
accompanied the Sentimental experience. The process is very like that
of putting a piece of wood or ivory in a turning-lathe, and whittling
off all that we do not want. A general idea is the useful core of
a multitude of superposed observations, each of which had something
irrelevant--something which it is better to forget. We whittle this
off and remember only the core.
Abstraction, on the other hand, is a conscious and deliberate
operation from beginning to end. It consists in distinguishing one by
one the properties of a thing, and even treating each property as if
it had an independent existence. For this exercise it is not
necessary to observe many things: we can analyse one alone, though an
acquaintance with other cognate objects is sometimes necessary to call
our attention to single properties. We need the shock of difference to
be able to distinguish well a fine abstraction--the difference between
shades of colours, for example. Abstraction is thus a minute
attention to individuals, and need not for a moment be confounded with
generalisation.
Another cause of the confusion in question can be traced to the use of
the verb 'is' to represent both the relation of a thing to the general
idea it has contributed to form, and the relation of a single property
to the thing in which it inheres. We say 'The man _is_ a British
subject'--classifying him; we say also 'The man _is_ cold'--mentioning
one of his attributes. There is no class of cold men, and the two
relations have nothing in common. A class does not inhere in a man as
cold inheres in him. There is no _object_ corresponding to class--it
is a conceptual creation.
The ambiguity of 'is' favours the syllogistic doctrine of predication,
and there is a rule to the effect that in syllogising propositions,
all verbs are to be converted into 'is' (or its conjugates) with a
participle or noun, so that if they were not before statements
of classification they now become such. 'He walks' is clearly no
classification; but 'he is walking' is assimilated by false analogy
to such a classification as 'he is human,' and so is treated as a
classification by those who reason according to the Letter.
The substantive verb has no positive and uniform meaning. As an
auxiliary it is a mere sign of tense, and in other positions it is an
indefinite mark of relationship, the precise meaning of which must
be determined by the subject and the context. It may sometimes be
dispensed with in classification, as 'Victoria Regina'--'Phillips,
Dentist.'
In the second category we have such propositions as 'the book lies on
the table.' In syllogistic this is first altered to 'the book is lying
on the table,' and it is feigned that 'lying on the table' is a class
or general idea, and 'book' an individual of that class. To interpret
'the groom stands by the horse' a class has to be created, composed of
the persons who happen to be standing by horses.
'The mountain is ten miles off' is a judgment in perspection.
Syllogistically we are asked to believe that a class of things exists
having the common property of being ten miles off, and that the
mountain is entered in that class. The absurdity of this doctrine is
self-evident.
In the remaining categories the reduction to 'is' has, if possible, a
worse effect. In changing 'Canada lies west of Ireland' into
'Canada is a country lying west of Ireland,' we lose the relation
in concretion, and express instead a verbal definition. Instead of
affirming a position we explain a name. In such a proposition as 'the
town of A lies 100 miles due north of B,' it is plain the predicate
cannot be a class, for only one place has the quality expressed.
In the fifth category we have such a proposition as 'water freezes
when the temperature falls to zero Centigrade.' This is turned into a
substantive sentence by saying 'water is that liquid which freezes,'
&c., which is a verbal or identical proposition.
'Cecrops founded Athens' is a judgment in causation. In turning it
into 'Cecrops was (or is) the founder of Athens,' we emphasise the
man's name, but the relation signified by 'founded' is slurred over
or lost sight of. Boole converts 'Caesar conquered the Gauls' into
'Caesar is he who conquered the Gauls,'[23] and this he interpreted
as classification. We need not be surprised that he should suppose
a class could be formed by one individual, for he elsewhere tells us
that _Nothing_ is a class.[24]
Classification is not judgment of any sort--it is a variety of
recollection. Logicians imagine it is the only judgment, and so far as
they can they degrade true judgments to that spurious form.
_Moods of the Syllogism._ Having persuaded themselves that
classification is the beginning, middle, and end of reasoning,
logicians next proceed to divide the matter of their science.
Modern logicians who have some acquaintance with real thinking as
exemplified in works of physical science, can, if acting according
to their natural intelligence, lay down correct rules for dividing a
subject. These are simple and obvious: divide according to fundamental
resemblance--let each division correspond to some definite human
utility--let the more important properties take precedence of the less
important, and so forth: the merest common sense.
But in the division of their own subject they follow Aristotle, and so
lose their way.
It is plain that an act of reasoning is a mental thing in the first
place, and only when uttered, and thus in a secondary sense, is it
a material object. The classification of arguments should therefore
follow mental characteristics. Logicians make it follow the material
characteristics of the terms in which the arguments are uttered. Their
moods of the syllogism are mere varieties of expression, not varieties
of reason.
The number of these moods is accidental, depending on flexibility
of language and ingenuity in inventing varieties of syntax. Mere
transposition of premises constitutes a difference of mood. Logicians
however pretend to base their numeration on a more general necessity.
They calculate from the distinctive parts of the three propositions
forming a syllogism, varied by negation, &c., that there _ought to be_
sixty-four moods. Experience proves that in spite of their free and
easy method of multiplying syllogistic varieties they cannot produce
anything like that number. One logician has thirty-six moods, another
thirty-two, a third eleven; the more orthodox fix the number at
nineteen. But they all admit that every argument can be reduced to
one of four fundamental types--the moods of the First Figure. Why then
have more classes than these four? Because, says Whately, it would be
'occasionally tedious' to reduce every argument to the first figure.
If the 11, 19, 32, or 36 classes were natural arguments taken
down untouched from men's lips, and it was found to be useless and
troublesome to reduce them to four artificial forms, the plea might
be admitted. But the so-called valid syllogisms are themselves
artificial, and just as tedious to make as the moods of the first
figure. Not only so, but an elaborate system of mnemonic rules is
provided for reducing the valid moods to the fundamental moods, thus
admitting that the former are only intermediate halting places between
the natural speech and the fundamental moods. It is _expected_ that
the intermediates should be reduced to the first figure.
Is there anything analogous to this sort of division in any science or
branch of practical thought? Would logicians themselves sanction such
a classification in a natural science? If a zoologist, for example,
were to determine beforehand how many classes of animals there
ought to be, would they not say he was acting improperly? If, after
discovering that he had five times as many classes as he could find
animals to put into them, he still retained his classification and
required his pupils to write out the names or symbols of all the
useless classes--would not logicians be apt to call him a pedant? Yet
in a modern work on logic such a task is prescribed for students:--
'Write out the sixty-four moods of the syllogism, _and strike
out the fifty-three invalid ones_.'
We might have excused the existence of a merely verbal classification
in logic, if it were accompanied by and subordinated to a
classification of theorems considered as mental facts. But in
syllogistic the verbal is the dominant classification, and we have
seen from the procedure of Sir William Hamilton--in dropping his
categorical judgments--that when the two principles of division
conflict, it is the mental which has to give way. The Letter is
allowed to kill the Spirit.
_All the Moods reducible to One._ Syllogists appear not to know their
own schematism very well. They say there are four ultimate moods,
which it is impossible to reduce to any lower number. But since each
of the four is, mentally, a double classification, it must be possible
to reflect this common property in the mode of expression. The
difference between them can only be verbal. Let us adopt another than
the ordinary symbolism.
Cut a card into three triangular pieces of unequal size, and call
them by the letters A, B, C, beginning with the largest. These are the
terms of the syllogism.
A A
/\B /\ B
/ /\C / \ /\C
/ / /\ / \ / /\
/ / / \ / \ / / \
/ / / \ / \ / / \
/ / / \ / \ / / \
+------------+ +------------+ +----------+
_Barbara._ _Celarent._
A A
/\B /\ B
/ /\ C / \ /\ C
/ / \ : / \ / \ :
/ / \: : / \ / \: :
/ / /\ : / \ / /\ :
/ / / \ : / \ / / \ :
+------------+... +------------+ +----------+...
_Darii._ _Ferio._
The first mood _Barbara_ is formed by placing the cards on top of each
other, so that B is within the margin of A, and C within the margin of
B. This is the syllogism, 'All B is A, all C is B, therefore all C is
A.'
Next let B and C be as above, but let A be wholly apart from both.
This is _Celarent_: 'No B is A, all C is B, therefore no C is A.'
In _Darii_ the whole of B is in A, but only a part of C coincides with
B. The syllogism is: 'All B is A, some C is B, therefore some C is A.'
In _Ferio_ A is again wholly separated from the others, and C is only
partially in B. Argument: 'No B is A, some C is B, therefore some C is
not A.'
It is to be remembered that all the other figures and moods are
reducible to the above figure of four moods, so that the reduction
applicable to the latter is equally applicable to the former.
To reduce _Darii_ to _Barbara_ all that is necessary is to ignore the
dotted part of C. That is suggested by the use of the word 'some,'
which has a correlative 'all' or 'others.' But the correlative
quantity does not enter into the syllogism, and we know nothing about
it. It may not even exist. We are therefore at liberty to substitute
for 'some C' the name D, and consider it an integer instead of a
fraction. Then we have the _Barbara_ syllogism: 'All B is A, all D (=
some C) is B, therefore all D is A.' The phrase 'all of some' is quite
allowable: 'I met some firemen, all of whom wore brass helmets.'
_Ferio_ in the same manner is reduced to _Celarent_. The dotted part
of C is cut away, and the part really significant in the syllogism is
called E. Then 'No B is A, all E is B, no E is A.'
Finally _Celarent_ can be reduced to _Barbara_. B cannot indeed be
enclosed in A, but we assume the existence of a whole having all the
characters which A has _not_, or having none of the characters which
A has. This is the whole F = Not-A. Then _Celarent_ becomes _Barbara_
thus: 'All B is F, all C is B, therefore all C is F.'
This demonstrates that there is only one fundamental operation where
syllogists suppose there are at least four. The difference is wholly a
matter of language, and disappears on changing the names of the terms
and ignoring irrelevant suggestions. But the syllogism, I repeat, does
not represent the act of reasoning, and its moods and figures are fit
only to be a game for children.
[Footnote 20: _Logic_, Book I. § 3.]
[Footnote 21: _Logic_, Book II. c. 3. § 2.]
[Footnote 22: _Lectures_, iii. pp. 287 and 356. The
impossibility of reconciling their definitions and rules to
real thinking and argument is the despair of logicians. Most
of them take to symbols, which are more accommodating than
real experience, having just such properties as their makers
choose to put in them. Sir William Hamilton had the courage to
declare that a logician might use arguments of a concrete or
real form, but that it is not necessary they should agree with
real fact. 'The logician has a right to suppose any material
impossibility, any material falsity; he takes no account of
what is objectively impossible or false, he has a right to
assume what premises he please, provided that they do not
involve a contradiction in terms.'--_Id._ 322. That means
in plain English that a logician may misrepresent matters of
fact, if he cannot otherwise establish his theory!]
[Footnote 23: _Laws of Thought_, p. 35.]
[Footnote 24: _Ibid._ p. 47.]