totle's dictum is precisely analogous : he had, to point out
doubtless, no thought of adding to the force of procestta
any individual syllogism ; his design was to point
out the general principle on which that process f " rms -
is conducted which takes place in each syllo-
gism. And as the Laws of nature (as they are Laws of
called) are in reality merely generalized facts, of erauzed rcu
which all the phenomena coming under them are
particular instances ; so, the proof drawn from
76 LOGIC. [UOOK 1
The Dictum Aristotle's dictum is not a distinct demonstration
brought to confirm another demonstration, but is
mere iy a generalized and abstract statement of
all demonstration whatever ; and is, therefore, in
fact, the very demonstration which, under proper
suppositions, accommodates itself to the various
subject-matters, and which is actually employed
in each particular case.
HOW to trace 56. In order to trace more distinctly the
u, g and different steps of the abstracting process, by
which any particular argument may be brought
into the most general form, we may first take a
syllogism, that is, an argument stated accurately
AU argument and at full length, such as the example formerly
Htalfil at full
length, given :
" Whatever exhibits marks of design had an intelligent author;
The world exhibits marks of design ;
Therefore, the world had an intelligent author :"
Propositions an< l tnen somewhat generalize the expression, by
S *atatra!!t by substituting (as in Algebra) arbitrary unmean-
terms - ing symbols for the significant terms that were
originally used. The syllogism will then stand
" Every B is A ; C is B ; therefore is A."
me reason- The reasoning, when thus stated, is no less evi-
ing no leas
valid, dently valid, whatever terms A, B, and C respect-
CHAP. III.] ANALYTICAL OUTLINE. 77
ively may be supposed to stand for ; such terms and
may indeed be inserted as to make all or some |M enL
of the assertions false; 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 con-
stitutes the conclusiveness of an argument.
Viewing, then, the syllogism thus expressed, syiiogismso
it appears clearly that " A stands for any thing affirms gen-
whatever that is affirmed 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 conclu-
sion, predicated of the third (C).
57. Now, to assert the validity of this pro- Another form
of stating the
cess now before us, is to state the very dictum dictum.
we are treating of, with hardly even a verbal
alteration, viz. :
1 . Any thing whatever, predicated of a whole The three
2. Under which class something else is con-
3. May be predicated of that which is so con-
The three members into which the maxim is correspond to
here distributed, correspond to the three propo- propositions.
78 LOGIC. [BOOK I.
sitions of the syllogism to which they are in-
tended respectively to apply.
The advantage of substituting for the terms,
* n a re g u ^ ar syllogism, arbitrary, unmeaning sym-
lymbois for b o ]s, suc fo as letters of the alphabet, is much the
same as in geometry : the reasoning itself is then
considered, 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
connection, t k e ar ^ umen f [ s concerned, the connection be-
point of the twecn the premises and the conclusion. We are
thus enabled to embrace the general principle of
deductive reasoning, and to perceive its applica-
bility to an indefinite number of individual cases.
That Aristotle, therefore, should have been ac-
Aristotie cuse( j o f making use of these symbols for the
right in using *
these sym- purpose of darkening his demonstrations, and
that too by persons not unacquainted with geom-
etry and algebra, is truly astonishing.
syllogism 58. It belongs, then, exclusively to a syllo-
whenab- gism, properly so called (that is, a valid argu-
re used, ment, so stated that its conclusiveness is evident
from the mere form of the expression), that if
letters, or any other unmeaning symbols, be sub-
stituted for the several terms, the validity of the
argument shall still be evident. Whenever this
CHAP. III.] ANALYTICAL OUTLINE. 79
is not the case, the supposed argument is either whevnotso,
unsound and sophistical, or else may be reduced ^"',^,1 '
(without any alteration of its meaning) into the wunsa ' Bd -
syllogistic form ; in which form, the test just
mentioned may be applied to it.
59. What is called an unsound or fallacious Deflation of
argument, that is, an apparent argument, which argument
is, in reality, none, cannot, of course, be reduced
into this form ; but when stated in the form most
nearly approaching to this that is possible, its whenr*-
. duced to the
lallaciousness becomes more evident, from its form, the fat
nonconformity to the foregoing rule. For ex- evide'nT"'
" Whoever is capable of deliberate crime is responsible ; Example.
An infant is not capable of deliberate crime ;
Therefore, an infant is not responsible."
Here the term "responsible" is affirmed uni- Anaiysisof
versally of " those capable of deliberate crime ;"
it might, therefore, according to Aristotle's dic-
tum, have been affirmed of any thing contained
under that class ; but, in the instance before us,
nothing is mentioned as contained under that its defective
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 sup-
posing that it may be denied of whatever is not
80 LOGIC. [BOOK i.
so contained ; for it is evidently possible that it
, may be applicable to a whole class and to some-
the iirguineut J
is not good, thing else besides. To say, for example, that all
trees are vegetables, does not imply that nothing
else is a vegetable. Nor, when it is said, that
what the a j] wno are capable of -deliberate crime are re-
implies, sponsible, does this imply that no others are
responsible; for though this may be very true,
what is to it has not been asserted in the premise before us ;
be done in 1-1 i /
the analysis and in the analysis ot an argument, we are to
argument, discard a ^ consideration of what might be as-
serted ; contemplating only what actually is laid
down in the premises. It is evident, therefore,
The one that such an apparent argument as the above
comply with ^ oes no * com ply with the rule laid down, nor
the rule. can ^e so stated as to comply with it, and is
60. Again, in this instance :
Another " Food is necessary to life ;
example. Corn is food ;
Therefore corn is necessary to life :"
in what the tne term "necessary to life" is affirmed of food,
defective, but not universally; for it is not said of every
kind of food <he meaning of the assertion be-
ing manifestly that some food is necessary to
life : here again, therefore, the rule has not been
complied with, since that which has been predi-
CHAP. III.] ANALYTICAL OUTLINE. 81
cated (that is, affirmed or denied), not of the why we
whole, but of apart only of a cerlain class, can-
not be, on that ground, predicated of whatever
is contained under that class. food -
DISTRIBUTION AND NON-DISTRIBUTION OF TERMS.
61. The fallacy in this last case is, what is Fallacy in the
usually described in logical language as consist-
ing in the " non-distribution of the middle term ;"
tion of the
that is, its not being employed to denote all the middle term
objects to which it is applicable. In order to
understand this phrase, it is necessary to observe,
that a term is said to be " distributed," when it is
taken universally, that is, so as to stand for all
its significates ; and consequently "undistribu-
ted," when it stands for only a portion of its sig-
nificates.* Thus, "all food," or every kind of what dutn-
. , . , . , , ,. ., button means
food, are expressions which imply the distribu-
tion of the term " food ;" " some food" would Non-distribu-
imply its non-distribution.
-\o\v, it is plain, that if in each premiss a. part
only of the middle term is employed, that is, if
it be not at all distributed, no conclusion can
How the ex-
be drawn. Hence, if in the example formerly ample might
adduced, it had been merely stated that " some- Tarie<1 .
* Section 15.
82 LOGIC. [BOOK i.
thing" (not " whatever" or " every thing")
" which exhibits marks of design, is the work of
an intelligent author," it would not have fol-
what it | OW ed, from the world's exhibiting marks of de-
haveimpiied. sign, that that is the work of an intelligent author
words mark- 62. It is to be observed also, that the words
ing distribu- . . . . . ..
tion or non- " all and " every, which mark the distribution
distribution / j ,, i_ i i ,
not always " a term > an " SOme, which marks Its non-
expressed, distribution, are not always expressed : they are
frequently understood, and left to be supplied by
the context ; as, for example, " food is neces-
sary ;" viz. " some food ;" " man is mortal ;" viz.
"every man." Propositions thus expressed are.
called called by logicians " indefinite" because it is left
undetermined by the form of the expression
whether the subject be distributed or not. Nev-
ertheless it is plain that in every proposition
the subject either is or is not meant to be dis-
tributed, though it be not declared whether
But every }t is or not ; consequently, every proposition,
must be whether expressed indefinitely or not, must be
understood as either "universal" or "particu-
Particular. Jar ;" those being called universal, in which the
predicate is said of the whole of the subject
(or, in other words, where all the significates
are included) ; and those particular, in which
each. only a part of them is included. For example :
CHAP. III.] ANALYTICAL OUTLINE. 83
"All men are sinful," is universal: "some men This division
are sinful," particular ; and this division of prop-
ositions, having reference to the distribution of
the subject, is, in logical language, said to be ac-
cording to their " quantity."
63. But the distribution or non-distribution Distribution
of the predi-
of the predicate is entirely independent of the catebasno
, . reference to
quantity of the proposition ; nor are the signs quan tit y .
" all" and " some" ever affixed to the predicate ;
because its distribution depends upon, and is HasrefereIIC "
indicated by, the " quality'' of the proposition ;
that is, its being affirmative or negative ; it being
a universal rule, that the predicate of a negative
proposition is distributed, and of an affirmative, ^ henitis
undistributed. The reason of this may easily
be understood, by considering that a term which The reason
stands for a whole class may be applied to (that
is, 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 ma y bea P-
coinciding with the whole of it. Thus it may the subject,
. and yet of
be said with truth, that " the Negroes are unciv- muc h wider
ilized," though the term " uncivilized" be of much
wider extent than " Negroes," comprehending,
besides them, Patagonians, Esquimaux, &c. ;
so that it would not be allowable to assert, that
84 LOGIC. [BOOK i.
oniya all who are uncivilized are Negroes." It is ev-
ident, therefore, that it is a part only of the
term "uncivilized" that has been affirmed of
" Negroes ;" and the same reasoning applies to
every affirmative proposition.
But it may It may indeed so happen, that the " subject
'tent'with an( ^ predicate coincide, that is, are of equal
the subject: exten t . a s, for example: "all men are rational
animals ;" " all equilateral triangles are equian-
gular ;" (it being equally true, that " all rational
uiis not im- animals are men," and that " all equiangular tri-
piied in the M ... ... .
form of the angles are equilateral ; ) yet this is not implied
uon ' by the form of the expression ; since it would
be no less true that "all men are rational ani-
mals," even if there were other rational animals
if any part of It is plain, therefore, that if any part of the
islp P p iicaWe predicate is applicable to the subject, it may be
to the sub- affirmed, and of course cannot be denied, of that
ject, it may
be affirmed subject ; and consequently, when the predicate
of the sub-
ject, is denied of the subject, this implies that no
part of that predicate is applicable to that sub-
ject ; that is, that the whole of the predicate is
if a predicate denied of the subject : for to say, for example,
Is denied of a , .
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
CHAP. III. j ANALYTICAL OUTLINE. 80
hence results the above-mentioned rule, that the Distribution
distribution of the predicate is implied in nega- jjjjj^^
tive propositions, and its non-distribution in af- ne ^ lllve
64. It is to be remembered, therefore, that Not sufficient
for the mid-
It is not sufficient for the middle term to occur die term to
. . . .- , occur in a
in a universal proposition ; since if that propo- universa i
sition be an affirmative, and the middle term be P* ? " 11011 *
the predicate of it, it will not be distributed.
For example : 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," It mus t be M
nothing could have been proved ; since, though ^^j^
both these propositions are universal, the middle term8 of tbe
term is made the predicate in each, and both are that those
. terms may be
affirmative ; and accordingly, the rule of Ans- compared to-
totle 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 con-
trary, would have been affirmed of it.
If, however, one of the premises be negative, if O ne P rem
the middle term may then be made the predicate L
86 LOGIC. [BOOK i.
tive. the mid- of that, and will thus, according to the above
teme thT remark, be distributed. For example :
" No ruminant animals are predacious :
uted. 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
The form of predicate of a negative proposition. The form,
thissyiio- j n( j ee( j O f tn e syllogism is not that prescribed
gum will not
be that pre- by the dictum of Aristotle, but it may easily be
the dictum, reduced to that form, by stating the first prop-
but may be ... _ T . . .
reduced to it osition thus : " JMo predacious animals are ru-
minant;" which is manifestly implied (as was
above remarked) in the assertion that "no ru
minant animals are predacious." The syllogism
will thus appear in the form to which the dictum
AH argu- 65. It is not every argument, indeed, that
menta cannot .
be reduced can be reduced to this form by so short and sim-
* a pie an alteration as in the case before us. A
longer and more complex process will often be
required, and rules may be laid down to facilitate
this process in certain cases ; but there is no
sound argument but what can be reduced into
But an argu- this form, without at all departing from the real
' meaning and drift of it ; and the form will be
CHAP. 111.] ANALYTICAL OUTLINE. 87
found (though more prolix than is needed for be reduced
... to the pre-
ordmary use) the most perspicuous in which an KTiboA form
argument can be exhibited.
66. All deductive reasoning whatever, then, AII deductive
, i i j j i_ reasoning
rests on the one simple principle laid down by re8tsont he
A i ii . u dictum.
" What is predicated, either affirmatively or
negatively, of a term distributed, may be predi-
cated in like manner (that is, affirmatively or neg-
atively) of any thing contained under that term."
So that, whtn our object is to prove any prop- what ore ih
osition, that is, f.o show that one term may rightly F
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 (that is, middle term)
of which that other may be affirmed, or denied,
as the case may be. Whatever the subject-mat- The reason-
ter of an argument may be, the reasoning itself, the same.
considered by itself, is in every case the same
process; and if the writers against Logic had Mistakes or
. . writers on
kept this m mmd, they would have been cautious Logic,
of expressing their contempt of what they call
"syllogistic reasoning," which embraces all de-
ductive reasoning; and instead of ridiculing Aris-
totle's principle for its obviousness and simplicity, Aristotle*
\vould have perceived that these are, in fact, its
simple and highest praise: the easiest, shortest, and most
evident theory, provided it answer the purpose
of explanation, being ever the best.
RULES FOR EXAMINING SYLLOGISMS.
Tests of the 67. The following axioms or canons serve
JMtfL ! as tests of the validity of that class of syllo-
gisms which we have considered.
1st test. 1 st - If two terms agree with one and the same.
third, they agree with each other.
ad test. 2d. If one term agrees and another disagrees
with one and the same third, these two disagree
with each other.
The first the On the former of these canons rests the va-
affirmative lidity of affirmative conclusions ; on the latter,
f2Td of negative: for, no syllogism can be faulty
of negative. wm ' c h <j O es not violate these canons ; none cor-
rect which does ; hence, on these two canons
are built the following rules or cautions, which
are to be observed with respect to syllogisms,
for the purpose of ascertaining whether those
canons have been strictly observed or not.
Every syiio- 1st. Every syllogism has three and only three
am* ami t erms > VIZ - the middle term and the two terms
<miy three Q f t h e Conclusion : the terms of the Conclusion
are sometimes called extremes.
Every gyiio- 2d. Every syllogism his three and only three
CHAP. III.] ANALYTICAL OUTLINE. 89
propositions; viz. the major premise ; the minor gismhas
. . three and
premise; and the conclusion. oniytim-e
3d. If the middle term is ambiguous, there P? 031
are in reality two middle terms, in sense, though m ust not iw
but one in sound.
There are two cases of ambiguity: 1st. Where TWO cases
the middle term is equivocal ; that is, when used lst ^^
in different senses in the two premises. For
" Light is contrary to darkness ;
Feathers are light ; therefore,
Feathers are contrary to darkness."
2d. Where the middle term is not distrib- MCM*
uted ; for as it is then used to stand for a part
only of its significates, it may happen that one
of the extremes is compared with one part of
the whole term, and the other with another part
of it. For example :
" White is a color ;
Black is a color ; therefore,
Black is white."
" Some animals are beasts ;
Some animals are birds ; therefore,
Some birds are beasts."
3d. The middle term, therefore, must be dis- termmustb*
tributed, once, at least, in the premises; that is, n ted:
90 LOGIC. [BOOK i
and once is by being the subject of a universal,* or predi-
cate of a negative ;f and once is sufficient ;
since if one extreme has been compared with a
part of the middle term, and another to the
whole of it, they must have been compared with
Notennmust 4th. No term must be distributed in the con-
tedinthe elusion which was not distributed in one of the
premises; for, that would be to employ the
which was f r J
ootdistnbu- w hole of a term in the conclusion, when you
ted in a
premise, had employed only a part of it in the premise ;
thus, in reality, to introduce a fourth term.
This is called an illicit process either of the
major or minor term. J For example :
gjanj D]e " All quadrupeds are animals,
A bird is not a quadruped ; therefore,
It is not an animal." Illicit process of the major.
5th. From negative premises you can infer
prove noth- nothing. For, m them the Middle is pronounced
to disagree with both extremes; therefore they
cannot be compared together : for, the extremes
can only be compared when the middle agrees
with both; or, agrees with one, and disagrees
with the other. For example :
Example. " A fish is not a quadruped ;"
" A bird is not a quadruped," proves nothing.
* Section 62. f Section 63. J Section 40.
CHAP. III.] ANALYTICAL OUTLINE. 91
6th. If one premise be negative, the conclu- ir
sion must be negative; for, in that premise the
middle term is pronounced to disagree with one
will be negar
of the extremes, and in the other premise (which live ;
of course is affirmative by the preceding rule),
to agree with the other extreme ; therefore, the
extremes disagreeing with each other, the con-
clusion is negative. In the same manner it may and recipro.
be shown, that to prove a negative conclusion,
one of the premises must be a negative.
By these six rules all Syllogisms are to be whatfoi-
tried ; and from them it will be evident, 1st, these six
that nothing can be proved from two particular
premises,- (since you will then have either the
middle term undistributed, or an illicit process.
For example :
" Some animals are sagacious ;
Some beasts are not sagacious ;
Some beasts are not animals.")
And, for the same reason, 2dly, that if one of 2d inference
the premises be particular, the conclusion must
be particular. For example :
" All who fight bravely deserve reward ;
" Some soldiers fight bravely ;" you can only infer that
" Some soldiers deserve reward :"
for to infer a universal conclusion would be
an illicit process of the minor. But from two
92 LOGIC. [BOOK i.
rwouniver- universal Premises you cannot always infer a
jTnS'S universal Conclusion. For example :
(rive a uni-
>. -i-.il con- " All gold is precious ;
du6ion - All gold is a mineral ; therefore,
Some mineral is precious.'
And even when we can infer a universal, we
are always at liberty to infer a particular ; since
what is predicated of all may of course be pre
dicated of some.
Definition of Q8. By a fallacy is commonly understood
" any unsound mode of arguing, which appears
to demand our conviction, and to be decisive
of the question in hand, when in fairness it is
Detection of, not." In the practical detection of each indi-
depends on .
Bcuteness. vidual fallacy, much must depend on natural
and acquired acuteness ; nor can any rules be
given, the mere learning of which will enable
us to apply them with mechanical certainty and
Hints and readiness ; but still we may give some hints that
will lead to correct general views of the subject,
and tend to engender such a habit of mind, as
will lead to critical examinations.
same of IA>- Indeed, the case is the same with respect to
Logic in general ; scarcely any one would, in
ordinary practice, state to himself either his