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of a demonstration. And certainly the charge would be just, if we
could imagine the logician's object to be, to increase the certainty
of a conclusion which we are supposed to have already arrived at
by the clearest possible mode of proof. But it is very strange that
such an idea should ever have occurred to one who had even the
slightest tincture of Natural philosophy: for it might as well be
imagined that a natural philosopher's or a chemist's design is to
strengthen the testimony of our senses by a, priori reasoning, and
to convince us that a stone when thrown will fall to the ground, and
that gunpowder will explode when fired ; because they show that
according to their principles those phenomena must take place as
they do. But it would be reckoned a mark of the grossest ignorance
and stupidity not to be aware that their object is not to prove the
existence of an individual phenomenon, which our eyes have
witnessed, but (as the phrase is) to account for it: i.e. to show
according to what principle it takes place; — to refer, in short, the
individual case to a general law of nature. The object of Aristotle's
Dictum is precisely analogous; he had, doubtless, no thought of
adding to the force of any individual syllogism; his design was to
point out the general principle on which that process is conducted
which takes place in each syllogism. And as the Laws^* of nature
(as they are called) are in reality merely genera' ized facts, of which
all the phenomena coming under them are particular instances; so,
the proof drawn from Aristotle's Dictum is not a distinct demon-
stration brought to confirm another demonstration, but is merely a

^ AsDugald Stewart: Philosophy, vol. ii.: and Locke, vol. ii. ch. 17, f 4,
1* Appendix, No. 1, art. Law.


generalized and abstract statement of all demonstration whatever;
and is, therefore, in fact, the very demonstration which {mutatis
mutandis) accommodated to the various subject-matters, is actually
employed in each particular case.

In order to trace more distinctly the different steps of the Jst\?emeilt'
abstracting process, by which any particular argument may be of argument
brought into the most general form, we may first take a syllogism abstract.
[i.e. an argument stated accurately and at full length), such as the
example formerly given, " whatever exhibits marks of design, &c.,"
and then somewhat generalize the expression, by substituting (as in
algebra) arbitrary unmeaning symbols for the significant terms that
were originally used; the syllogism will then stand thus; ** every
B is A; C is B; therefore C is A." The reasoning, when thus
stated, is no less evidently valid, whatever terms. A, B, and C,
respectively, may be supposed to stand for. Such terms may
indeed be inserted as to make all or some of the assertions /aZse;
but it will still be no less impossible for any one who admits the
truth of the premises, in an argument thus constructed, to deny
the conclusion; and this it is that constitutes the conclusiveness of
an argument.

Viewing then the syllogism thus expressed, it appears clearly,
that " A stands for any thing whatever that is afiirmed of a certain
entire Class," {viz. of every B,) "which class comprehends or
contains in it something else,'' viz. C, (of which B is, in the second
premiss, affirmed) ; and that, consequently, the first term (A) is, in
the conclusion, predicated of the third C.

Now to assert the validity of this process, now before us, is to
state the very Dictum we are treating of, with hardly even a verbal
alteration: viz.:

1. Any thing whatever, predicated of a whole class,

2. Under which class something else is contained,

3. May be predicated of that which is so contained.

The three members into which the Maxim is here distributed,
correspond to the three propositions of the Syllogism to which they
are intended respectively to apply. ^^

The advantage of substituting for the terms in a regular syllogism, Utility of
arbitrary unmeaning symbols, such as letters of the alphabet, is crnt*'*^"* *
much the same as in Geometry: the Reasoning itself is then con- ^y^^^o^*
sidered, by itself, clearly, and without any risk of our being misled
by the truth or falsity of the conclusion; which is, in fact, accidental
and variable; the essential point being, as far as tbe argument is con-
cerned, the connection between the premises and the conclusion. We
are thus enabled to embrace the general principle of all reasoning,
and to perceive its applicabihty to an indefinite number of individual
cases. That Aristotle, therefore, should have been accused of

w See Book IV. Ch. m. § 1.


making use of these symbols for the purpose of darJcening his
demonstrations, and that too by persons not unacquainted with
Geometry and Algebra, is truly astonishing. If a geometer, instead
of designating the four angles of a square by four letters, were to
call them north, south, east, and west, he would not render the
demonstration of a theorem the easier; and the learner would be
much more likely to be perplexed in the application of it.

It belongs then exclusively to a Syllogism, properly so called
{i.e. a valid argument, so stated that its conclusiveness is evident
from the mere form of the expression), that if letters, or any other
unmeaning symbols, be substituted for the several terms, the
validity of the argument shall still be evident. Whenever this is
not the case, the supposed argument is either unsound and sophis-
tical, or else may be reduced (without any alteration of its meaning)
into the syllogistic form; in which form, the test just mentioned
may be applied to it.
chTr^acter Some persons have remarked of the ** Dictum" (meaning it as a

of the disparagement) that it is merely a somewhat circuitous explanation

ic um. ^y ^ji^f jg meant by a Class. It is, in truth, just such an explana-
tion of this as is needful to the student, and which must be kept
before his mind in reasoning. For we should recollect that
not only every Class [the Sign of which is a *' Common-term"]
comprehends under it an indefinite number of individuals, — and
often of other Classes, — differing in many respects from each other,
but also most of those individuals and classes may be referred,
each, to an indefinite number of classes according as we choose to
abstract this point or that, from each.

Now to remind one on each occasion, that so and so is referable
to such and such a Class, and that the class which happens to be
before us comprehends such and such things, — this is precisely all
that is ever accomplished by Reasoning.

For one may plainly perceive, on looking at any of the examples
above, that when we assert both the Premises taken in conjunction,
we have, virtually, implied the Conclusion. Else, indeed, it would
not be impossible (as it is) for any one to deny the Conclusion, wha
admits both Premises.^^
unsound" '^^ What is called an unsound or fallacious argument {i.e. an apparent
arguments, argument, which is, in reality, none) cannot, of course, be reduced
into this form; bst when stated in the form most nearly approaching
to this that is possible, its fallaciousness becomes more evident,
from its nonconformity to the foregoing rule: e.g. ** whoever is
capable of deliberate crime is responsible; an infant is not capable

18 Hence, some have considered it as a Since, however, a Syllogism is not a

disparagementtoa Syllogism (which they certain distinct kind of argument, but

imagine to be one kind of Argument) that any argument whatever, stated in a regur

you can gain no new truth from it; the lar form, tlie complaint, such as it is, Tiea

Conclusions it establishes being in fact against Reasoning altogether. In B. iv.

known already, by every one who bos cu. 2, this point is more fully explained,
admitted the Premises.


of deliberate crime; tlierefore, an infant is not responsible," (see
§ 3): here the term " responsible" is affirmed universallj of " those
capable of deliberate crime;" it might, therefore, according to
Aristotle's Dictum, have been affirmed of any thing contained mider
that class; but, in the instance before us, nothing is mentioned as
contained under that class; only, the term " infant" is excluded
from that class; and though what is affirmed of a whole class may
be affirmed of any thing that is contained under it, there is no
ground for supposing that it may be denied of whatever is not so
contained; for it is evidently possible that it may be applicable to a
whole class and to something else besides. To say, e.g. that all
trees are vegetables, does not imply that nothing else is a vegetable;
nor, when it is said, that '* all who are capable of deliberate crime
are responsible," does this imply, that *' no others are responsible;"
for though this may be very true, it has not been asserted in the
premiss before us; and in the analysis of an argument, we are to
discard all consideration of what might be asserted; contemplating
only what actually is laid down in the premises. It is evident,
therefore, that such an apparent argument as the above does not
comply with the rule laid down, nor can be so stated as to comply
with it; and is consequently invalid.

Again, in this instance, "food is necessary to life; com is food;
therefore, corn is necessary to life:" the term "necessary to life"
is affirmed of food, but not universally; for it is not said of every
hind of food: the meaning of the assertion being manifestly that
*' some food is necessary to life;" so that, expressed in symbols, the
apparent argument might stand thus; " Some X is Y; Z is X;
therefore Z is Y." Here again, therefore, the rule has not been
complied with, since that which has been predicated, [affiraied or
denied] not of the whole, but of a part only of a certain class,
cannot be, on that ground, predicated of whatever is contained
under that class.

There is an argument against miracles by the well-known Mr.
Hume, which has perplexed many persons, and which exactly corres-
ponds to the above. It may be stated thus : " Testimony is a kind
of evidence more likely to be false, than a miracle to be true;"
(or, as it may be expressed in other words, we have more reason
to expect that a witness should lie, than that a miracle should
occur) '* the evidence on which the Christian miracles are believed,
is testimony; therefore the evidence on which the Christian miracles
are believed is more likely to be false than a miracle to be true."

Here it is evident that what is spoken of in the first of these
Premises, is, "some testimony;" not "all testimony," [or any
whatever,'] and by " a witness" we understand " some witness, " not,
*' every witness:" so that this apparent argument has exactly the
B^me fault as the one above. ^^

15' See Appendix II. Example No. 26.



The fallacy in these last cases is, what is usually described in
logical language as consisting in the *' non-distribution of the
middle term:" i.e. its not being employed to denote all the objects
to which it is applicable. In order to understand this phrase, it is
necessary to observe that a Proposition being an expression in
which one thing is said, i.e. affirmed or denied of another, [e.g.
*' A is B,") both that of which something is said, and that which is
said of it {i.e. both A and B), are called '* terms;" from their being
(in their nature) the extremes or boundaries of the Proposition: and
there are, of course, two, and but two, terms in a proposition (though
it may so happen that either of them may consist either of one

Distribution word, or of Several); and a term is said to be " distributed," when
erms. -^ j^ taken universally, so as to stand for every thing it is capable
of being applied to; and consequently "undistributed," when it
stands for a portion only of the things signified by it: thus, " all
food," or every kind of food, are expressions which imply the
distribution of the term "food;" "some food" would imply its
non-distribution. And it is also to be observed that the term of
which, in one premiss, something is affirmed or denied, and to
which, in the other premiss, something else is referred as contained
in it, is called the " middle" term in the syllogism, as standing
between the other two {viz. the two terms of the conclusion), and
being the medium of proof. Now it is plain, that if in each premiss
a part only of this middle-term is employed, i.e. if it be not at all
distributed, no conclusion can be drawn. Hence, if, in the example
formerly adduced, it had been merely stated that " something" (not
" whatever/' or " everything'') " which exhibits marks of design is
the work of an intelligent author," it would not have followed, from
the world's exhibiting marks of design, that that is the work of
an intelligent author.

It is to be observed, also, that the words "all" and "every,"
which mark the distribution of a term, and " some," which marks
its non-distribution, are not always expressed: they are frequently
understood, and left to be supplied by the context; e.g. "food is
necessary;" viz. "some food;" "man is mortal;" w^. "every man.' ^

Propositfons Propositions thus expressed are called by logicians "indefinite,'^
because it is left undetermined by the form of the expression whether
the " subject " (the term of which something is affirmed or denied
being called the " subject " of the proposition, and that which is
said of it, the " predicate ") be distributed or not. Nevertheless it
is plain that in every proposition the Subject either is, or is not,
meant to be distributed; though it be not declared whether it is or
not. Consequently, every proposition, whether expressed indefinitely
or not, must be understood as either " universal " or "particular;'*
those being called Universal in which the predicate is said of the

and quality




whole of the subject (or, in other words, where the subject is distri-
buted); and those, Particular, in which it is said only of a part of
the subject: e.g. **A11 men are sinful," is universal; "some men
are sinful," particular. And this division of propositions is, in
logical language, said to be according to their ** quantity. ^^

But the distribution or non-distribution of the predicate is entirely Quantity
independent of the quantity of the proposition; nor are the signs
*'all" and "some" ever affixed to the predicate; because its
distribution depends upon, and is indicated by, the ''quality'' of the
proposition; i.e. its being affirmative or negative; it being a uni-
versal rule, that the predicate of a negative proposition is distribu-
ted, and of an affirmative, undistributed. The reason of this may
easily be understood, by considering that a term which stands for a
whole Class may be applied to {i.e. affirmed of) any thing that is
comprehended under that class, though the term of which it is thus
affirmed may be of much narrower extent than that other, and may,
therefore, be far from coinciding with the whole of it. Thus it may
be said with truth, that *' the Negroes are uncivilized," though the
term uncivilized be of much wider extent than " Negroes," compre-
hending, besides them, Hottentots, &c.; so that it would not be
allowable to assert, that '' all who are uncivilized are Negroes;"
it is evident, therefore, that it is a part only of the term "uncivi-
lized " that has been affirmed of " Negroes;" and the same reason-
ing applies to every affirmative proposition; for though it may so
happen that the subject and predicate coincide; i.e. are of equal
extent, as, e.g. "all men are rational animals;" "all equilateral
triangles are equiangular;" (it being equally true, that "all rational
animals are men," and that "all equiangular triangles are equi-
lateral;) yet this is not implied by the form of the expression; since
it would be no less true, that " all men are rational animals, " even
if there were other rational animals besides Man.

It is plain, therefore, that if any part of the predicate is appli-
cable to the subject, it may be affirmed, and, of course, cannot be
denied, of that subject; and consequently, when the predicate is
denied of the subject, this implies that no part of that predicate is
applicable to that subject; i.e. that the whole of the predicate is
denied of the subject; for to say, e.g. that "no beasts of prey
ruminate," implies that beasts of prey are excluded from the whole
class of ruminant animals, and consequently that "no ruminant
animals are beasts of prey." And hence esults the above-mentioned
rule, that the distribution of the predicate is implied in negative
propositions, and its non-distribution, in affirmatives.

The learner may perhaps be startled at being told that the Non-
predicate of an affirmative is never distributed; especially as Aldrich qJ-^*^?"*'*^
has admitted that accidentally this mm/ take place: as in such a Predicate in
proposition as "all equilateral triangles are equiangular; but this
is not accurate; he might have said that in such a proposition as


tlie above tlie predicate is distributable, but not that it is actually
distributed: i.e. it so happens that "all equiangular triangles oro
equilateral;" but this is not implied in the previous assertion; and
the point to be considered is, not what might be said with truth, but
what actually has been said. And accordingly mathematicians give
distinct demonstrations of the above two propositions.

If it happen to be my object to assert that the Predicate as well
as the Subject of a certain affirmative proposition is to be understood
as distributed — and if I say, for instance, " all equilateral triangles,
and no others, are equiangular," — I am asserting, in reality, not
one proposition, merely, but two. And this is the case whenever
the proposition I state is understood (whether from the meaning of the
words employed, or from the general drift of the discourse) to imply
that the whole of the Predicate is meant to be affirmed of the

Thus, if I say of one number — suppose 100 — that it is the Square
of another, as 10, then, this is understood by every one, from his
knowledge of the nature of numbers, to imply, what are, in reality,
the two propositions, that 100 is "the Square of 10," and also that
*' the Square of 10 is 100." So also, if I say that " Romulus was
the first king of Rome," this implies, from the peculiar signifcor-
tion of the words, that '* the first king of Rome was Romulus."

Terms thus related to each other are called in technical language,
"convertible" [or *' equivalent "] terms. But then, you are to
observe that when you not only affirm one term of another, but also
affirm (or imply) that these are " convertible " terms, you are making
not merely one assertion, but two.
i^'stribution It is to be remembered, then, that it is not sufficient for the middle
terms. term to occur in a Universal-proposition; since if that proposition
be an affirmative, and the middle-term be the predicate of it, it will
not be distributed; e.g. if in the example formerly given, it had been
merely asserted, that " all the works of an intelligent author show
marks of design," and that ** the universe shows marks of design,'*
nothing could have been proved; since, though both these proposi-
tions are universal, the middle-term is made the predicate in each,
and both are affirmative; and accordingly, the rule of Aristotle is
not here complied with, since the term '* work of an intelligent
author," which is to be proved applicable to "the universe," would '=
not have been affirmed of the middle-term ("what shows marks of
design") under which "universe" is contained; but the middle-
term, on the contrary, would have been affirmed of it.

If, however, one of the premises be negative, the middle-term
may then be made the predicate of that, and will thus, according to
the above remark, be distributed; e.g. "no ruminant animals are
predacious; the lion is predacious; therefore the lion is not ruminant:'*
this is a valid syllogism; and the middle -term (predacious) is
distributed by being made the predicate of a negative proposition.


The form, indeed, of the syllogism is not that prescribed by the
Dictum, but it may easily be reduced to that form, by stating the
first proposition thus: **no predacious animals are ruminant;" which
is manifestly implied (as was above remarked) in the assertion that
**no ruminant animals are predacious." The syllogism will thus
appear in the form to which the Dictum applies.

It is not every argument, indeed, that can be reduced to this The DJctnm
form by so short and simple an alteration as in the case before us: applicable^
a longer and more complex process wiU often be required; and rules
will hereafter be laid down to facilitate this process in certain cases:
but there is no sound argument but what can be reduced into this
form, without at all departing from the real meaning and drift of it;
and the form will be found (though more prolix than is needed for
ordinary use) the most perspicuous in which an argument can be

All Reasoning whatever, then, rests on the one simple Principle
laid down by Aristotle, that "what is predicated, either affirmatively
or negatively, of a term distributed, may be predicated in like
manner {i.e. affirmatively or negatively) of any thing contained
under that term." So that when our object is to prove any proposi-
tion, i.e. to show that one tenn may rightly be affirmed or denied of
another, the process which really takes place in our minds is, that
we refer that term (of which the other is to be thus predicated) to
some class ^® [i.e. middle term) of which that other may be affirmed,
or denied, as the case may be.

Whatever the subject-matter of an argument may be, the Reason-
ing itself, considered by itself, is in every case the same process;
and if the writers against Logic had kept this in mind, they would
have been cautious of expressing their contempt of what they call
*' syllogistic reasoning," which is in truth a/^ reasoning; and instead •

of ridiculing Aristotle's Principle for its obviousness and simplicity,
would have perceived that these are, in fact, its highest praise: the
easiest, shortest, and most evident theory, provided it answer the
purpose of explanation, being ever the best.

§ 6.

If we conceive an inquirer to have reached, in his Investigation of
the theory of Reasoning, the point to which we have now arrived, a
question which would be likely next to engage his attention, is that
of Predication; i.e. since in reasoning we are to find a middle-term
which may be predicated affirmatively of the Subject in question, we
are led to inquire what terms may be affirmed, and what denied, of
what others.

It is evident that a proper-name, or any other term which denotes Common H
but a single individual, as "Caesar," "the Thames," "the Con- ?eS^

W That is, either an actual^ or a potential class. See above, § 3.



queror of Pompey," **tliis river " (hence called in Logic a ** Singular-
term") cannot be affirmed of any thing besides that individual, and
may therefore be denied of any thing else; we may say, "this
river is the Thames," or ** Caesar was the conqueror of Pompey;'*
but we cannot say of any thing else that it is the Thames, &c.

On the other hand, those terms which are called " Common,^ ^ as
denoting anyone individual of a whole class, as "river," "con-
queror," may of course be affirmed of any, or all that belong to that
class: [of anything answering to a certain description] as, "the
Thames is a river;" "the Rhine and the Danube are rivers."

Common-terms, therefore, are called " predicables " {vis.ajirma-
tively-'pYedicahle), from their capability of being affirmed of others:
a Singular-term, on the contrary, may be the Subject of a proposi-
tion, but never the Predicate, unless it be of a negative proposition;
(as e.g. the first-born of Isaac was not Jacob;) or, unless the Subject
and Predicate be only two expressions for the same individual
object; as in some of the above instances.
Abstraction The process by which the mind arrives at the notions expressed
^eneraiiza- ^J ^hcse " common " (or in popular language, " general ") terms, is
iion. properly called "Generalization;" though it is usually (and truly)

said to be the business of abstraction; for Generalization is one of

Online LibraryRichard WhatelyElements of logic → online text (page 6 of 34)