William Thomson (Abp. of York) William Thomson.

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to a supplementary one, which is called an episyl-
logism. Let us take the syllogism which a coroner's
jury might have to go through. The question is,
"Has A. B. been poisoned?" and the syllogism is,
" A man who has taken a large quantity of arsenic
has been poisoned, and A B. is found to have done
so, therefore he has been poisoned ; " with the addi-
tion of a prosyllogism and episyllogism the reasoning
would run — "A man who has taken arsenic has
been poisoned ; and A. B. has taken arsenic, for the
application of Marsh's and Reinsch's tests discover
it (Prosyl.) ; therefore A. B. has been poisoned, and



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LAWS OF THOUGHT. 241

therefore we cannot return a verdict of death from
natural causes." (Episyl.) A prosyllogism then is a
syllogism whose conclusion is a premiss in a given syl-
logism; an Episyllogism is one^ whose premiss is a
conclusion in a given syllogism. The Sorites, Pro-
syllogism and Episyllogism, deserve our attention as
the joints of thinking by which the various members,
the acts of immediate and mediate inference, are knit
together in an organic connection. Of them, how-
ever, the first can rarely be employed ; the two last
meet us continually.



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OUTLINE



LAWS OF THOUGHT.



PART IV.

APPLIED LOGIC.

'' Mais, paree que Tesprit se laisse qulequefois abuser par defausses
lueurs, lorsqu'il n'y apporte pas Tattention necessaire, et qu'il y a
bien des choses que Ton ne conn&it que par un long et difficile exa-
men, il est certain qu'il serait utile d'avoif des regies pour s'y con-
duire de telle sorte, que la recherche de la y^rit^ en fiit et plus &cile
et plus siire ; et ces regies, sans doute, nd sont pas impossibles." —
Abnaulb.



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APPLIED LOGIC.




§ 112. Province of Applied Logic.

N the foregoing pages the Laws of
Thought have been considered solely in
themselves; and their connection with
the objects they belong to has been
studiously kept out of view. It has been shown
that every conception consists of marks, without any
attempt to explain how the marks are to be obtained ;
that a judgment of a given quantity, quality, and re-
lation, can be converted or opposed, no matter whether
it is a true judgment with reference to the matter it
sets forth ; that a given form of syllogism is correct
and its proof cogent, whether or no the premisses it
draws from are frivolous, or even incorrect. In order
to understand aright the laws of thinking in them-
selves, this procedure was necessary; for we must
distinguish between faults in the forms themselves,
which we have the means of correcting without
travelling beyond them, and faults in the materials
of thinking, that cannot be corrected without a ref-
erence to the objects that supplied them. For ex-
ample, " some men are infallible," is a judgment cor-
rect in form, but false in matter, as our knowledge
of humanity teaches us ; again, to convert " some
men are philosophers," into " all philosophers are



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246 OUTLINE OF THE

men," is wrong in fonn, although it happens that
the latter judgment, erroneously produced, is mate-
rially correct.

Applied Logic teaches the application of the forms
of thinking to those objects about which men do
think. These objects arrange themselves under three
great divisions, Man, the Universe, and Absolute
Being. When the views we take of objects are
substantially correct, when our thoughts correspond
with facts, we are said to be in possession of the
truth ; and thus we return to a definition of Applied
Logic already proposed. It is the science of the
necessary laws of thought as employed in attaining
truth.

§ 113. Science.

These laws may be applied to the fragmentary
knowledge and scattered information gathered by
every one in his passage through the world ; they are
unconsciously applied in this way every instant. Bat
it would be a higher application of them to erect by
their means a complete structure of the truth that
related to one object or set of objects, as Zoology
contains all that relates to animals. Geology all we
know of the earth's structure, and Psychology all that
pertains to the human mind and soul. Such a sys-
tem of the truths that relate to one set of objects is
called a science, which has been defined (p. 26), a
system of principles and deductions, to explain some
object-matter. To fulfil its intention every science
must have attained to true statements concerning its
object-matter, so far as the nature of the case and
the present means of examination allow ; it must be



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LAWS OF THOUGHT. 247

able to define the object-matter, and its several sub-
ordinate parts, with clearness and precision ; and it
must be able to indicate the extent of the domain
the object-matter covers ; and lastly it must exhibit
these results in a systematic and harmonious shape.
For the first it must employ Induction and Deduc-
tion ; the second is the province of Definition ; the
third is provided for by Division ; and the fourth may
be referred to Method.



§ 114. Is a Philosophic Criterion of Truth possible.

The search after truth cannot long dispense with
any one of these instruments; and even with the
free use of them, the history of science shows how
slow has been the advance, how largely (to use Leib-
nitz's image) the sand and mud of error have been
mixed with the gold grains of truth. All of them
in their degree have to do with evidence, with the
proof of propositions ; Induction and Deduction
chiefly with the discovery and appreciation of evi-
dence, and Definition and Division chiefly with the
statement and arrangement of its results. Hence, if
we have to answer the question whether a Criterion
of Truth, L e. a standard for judging of the truth of
propositions, is possible,* we answer that evidence

* Phio speaks of " Experience, prudence, and reason," as affording
coiyointly a Kptnipiov of truth (Pol. 682 A.). This for the sense of
the word. For other proposed criteria, not mentioned in the text,
we have that of Wolff, determinabilitas prcBdicati per notionem subjecti
(hut it applies only to explicative judgments — see p. 175) ; that of
Descartes, " that is true which is clearly known and perceived," but
he admits that the test is somewhat vague; and lastly that of Plato,
" truth is confonnity with the ideas." Evidence is used by the Carte-
sians, sometimes in the sense of evidentness ; but we employ it to
mean *' the grounds which make evident."



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248 OUTLINE OF THE

is the sole means of establishing, and therefore the
sole standard for testing, the truth of any propo-
sition, and that all the operations connected with
evidence contribute their share to the criterion. But
such a maxim as that '^ a judgment must rest upon
sufficient evidence " is too abstract to be of use by
itself as a test of truth. In fact no shorter rule, no
more portable touchstone can be indicated, for the
examination of objective truth, than the whole sci-
ence and rules of evidence. And in the special
cases where other criteria appear to be applied, as in
the discussion whether religious truth is to be tried
by external testimony or internal conviction, whether
historical evidence or the religious sentiment is the
best criterion, the dispute is only as to the kind of
evidence that shall take precedence.

Four principal criteria of truth have been in dif-
ferent forms advocated by logicians ; the reader is
now in a position to estimate their value.

1st Criterion. The principle of Contradiction*
" The same attribute cannot be at the same time
affirmed and denied of the same subject." Or " the
same subject cannot have two contradictory attri-
butes." Or " the attribute cannot be contradictory
of the subject." * To illustrate this — at a particular
time facts were observed as to the motions of the
planets, which were inconsistent with the received
theory that these motions were circular. The theory
was consequently modified, first by the introduction
of epicycles, and finally by the substitution of the

* The first mode of statement is Aristotle^s, rd ydp airrd &fia indfh
Xeiv re kqI fi^ vndpxeiv &ivvaTov t€> ai)T(f> kcU Kara rb airro, Metaph. IV.
(r.) Hi. The second is Aristotelian ; the third is Kani*8.



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LAWS OF THOUGHT. 249^

theory of elliptic revolution ; because otherwise the
astronomer must have affirmed of the planets a cir-
cular and a non-circular motion, or in other words
must have assigned to a subject, to which he had
already given " circular motion," a predicate contra-
dictory of this.

2d Criterion. The principle of Identity. " Con-
ceptions which agree can be united in thought, or
affirmed of the same subject at the same time."
This principle is the complement of the former.

3d Criterion. The principle of the Middle being
excluded (lex exclusi medii). " Either a given judg-
ment must be true, or its contradictory ; there is no
middle course."* So that the proof of a judgment
forces us to abandon its contradictory entirely, as
would the disproof of it force us upon a fuU accept-
ance of the contradictory. This law, among other
uses, applies to the dialectical contrivance known to
logicians as redu^tio per impossibile.

4th Criterion. The principle of sufficient (or
determinant^^ reason* " Whatever exists, or is true,
must have a sufficient reason why the thing or prop-
osition should be as it is and not otherwise*" J
From this law are educed such applications as

* This is the iivri^ea/jg ^ ohK Jtari fiercL^ Ka^* airyv, of Aristotle,
(An. Post, I. i. /cai^ aiii^, " as appears per se from the nature of the
assertion." Trend.) Compare Metaph. IV. (r.) 7, and Alexander's
comment.

t C. A. Crusius, in a tract on this subject, finds fault with the
ambiguity of "sufficient," which might seem "sufficient for this
eflfect" without excluding it from the possibility of producing some
other. According to him, this principle involves absolute necessity,
and destroys morality.

X Leibnitz, Theod. I. J 44. Upon this principle, and those of
Contradiction and Identity, Leibnitz has based his Logic.



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250 OUTLINE OP THE

these : — 1. Granting the reason, we must grant what
follows from it. On this depends syllogistic infer-
ence. 2. If we reject the consequent, we must
reject the reason. If we admit the consequent, we
do not of necessity admit the reason.

Now the distinction between formal and material
truth, or in other words between self-consistency in
thinking, and conformity with facts, assists materi-
ally in forming an estimate of the worth of these
principles. A judgment may be formally true, and
materially false ; as in the inference " No men err,
Socrates is a man, therefore he cannot err," which is
correctly drawn, yet proves a falsehood from a false-
hood : or it may be materially true, yet formally
false, as, " Socrates is a man, Socrates erred, there-
fore all men err ; " where a true judgment has been
drawn from two true judgments, yet not correctly.
The four criteria in question are useful in securing
formal truth, that is, in keeping our thoughts in
harmony with each other ; but for the discovery of
material truth, for giving us thoughts that are true
representations of facts, they are either useless, or
only useful as principles subordinate to the higher
criterion of which all applied Logic is but the ex-
pansion, that every proposition must rest upon suffi-
cient evidence. The principle of contradiction has
been already implied in the doctrine of privative
conceptions in the theory of disjunctive judgments
and inferences and in other places. The principle
of the excluded middle is the canon of the inference
from contradictory opposition upon which the refuta-
tion of a false conclusion must rest. The principle
of the sufficient reason is implied in the syllogistic



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LAWS OF THOUGHT. 251

canon that every conclusion must follow from and
depend on sufficient premisses; it is employed in
other forms, in hypothetical reasonings in particular.
And in these purely formal applications the criteria
have their importance, but that not the highest.

Viewed as instruments for judging of material
truth, they sink into mere rules for the reception of
evidence. The first is a caution against receiving
into our notion of a subject any attribute that is
irreconcilable with some other, already proved upon
evidence we cannot doubt The second is a per-
mission to receive attributes that are not thus
mutually opposed, or a hint to seek for such only.
The third would compel us to reconsider the evi-
dence of any proposition, when other evidence
threatened to compel us to accept its contradictory.
The fourth commands that we seek the causes and
laws that have determined the existence of our sub-
ject, for the subject cannot be adequately known
except in these. So that the vaunted criteria of
truth are rules of evidence; and there is no one
means of judging of truth, except what the whole
science of Evidence affords.



A. Construction of Science.

§ 113. Induction and Deduction.
Induction * is usually defined to be the process of

* Opinions are somewhat divided both as to the meaning of
hrayoyif, the word of which Induction is the English equivalent,
and the nature of the argument that bears the name. i. It is sup-
posed to be a persuasive argument to which a person is induced



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252 OUTLINE OF THE

drawing a general law from a sufficient number of
particular cases ; Deduction is the converse process,
of proving that some property belongs to a particular
case, from the consideration that it comes under a
general law. More concisely. Induction is the pro-
cess of discovering laws from facts, and causes from
effects ; and Deduction that of deriving facts from
laws, and effects from their causes. E. g., that all
bodies tend to fall towards the earth is a truth
which has been obtained by considering a number
of bodies where that tendency has been displayed,
by induction ; if from this general principle we argue
that the stone we throw from our hands will show
the same tendency, we deduce. If it were always
possible duly to examine the whole of the cases to

(kndyeTcu) to assent. Comp. Upoaexe firj ae TjTTrjtrg rh irpoar}vlc oOtov
Kol Ti6i> Kol tirayuyov {Epictetus, Ench. 84), where the last word
means persuasive, alluring. Compare Cicero (de In v. I. 31.). "Induc-
tio est oratio, quae rebus non dubiis capiat assensiones ejus quicum
instituta est; quibus assensionibus facit, ut illi dubia quaedam res,
propter similitudinem earum rerum, quibus assentit, probetur." 2.
It is the bringing in (rd kirdyeiv) examples or comparisons, Td ev rile
elKovag kTTdv€(r^ai—{Xenophon, CEcon. 17, J 15.) This latter deriva-
tion finds most favour. Then the process itself is sometimes
described as if it were a way of proving particular unknown fiicts
from particular known facts. " Cum plura interrogasset [Socrates],
quae £iteri adversario necesse esset, novissime id de quo quaerebatur,
inferebat, cui simile concessisset." (Quinctilian, V. 11.) The logi-
cian will see that this comes close to the logical Argument from
Example. Both in Induction and Example, however, there is an
appeal to a general law, expressed or implied. Our definition is
that of Aristotle (Top. I. 12.), "Induction is the process from par-
ticulars to universals." In using the phrase " the syllogism from
induction," A. hints at that wider view of syllogism, as the simple
element of all reasoning whatever, which it is one main object of
this book to develop. See Heyder, Darstellung, pp. 60, 219 ; Emesti,
Lex. Techn. ; Trendelenburg, Excerpta, § 20 ; but chiefly Reinhardi,
Opuscula, I. 212.



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LAWS OF THOUGHT. 253

which a law applies, and to see by intuition the
significant and important parts of each, the process
of Induction would be simple enough. But a com-
plete inspection of all the cases is very seldom pos-
sible ; even the laws on whose invariable operation
the strongest reliance is placed, must have been laid
down upon the evidence of a number of cases very
limited when compared with the whole ; that men
must all die, and that heavy bodies tend to fall
towards the earth, are statements which no one can
boast of having verified by enumeration. The per-
fect certainty with which they are believed, rests
upon far less than the millionth part of the cases
that might be brought to bear witness about them.
Nor again are the significant and essential circum-
stances easy to observe, in the few cases that lie
within the reach. Either they escape notice alto-
gether, as did the fact of the earth's revolution in
the early days of Astronomy; or they are so en-
tangled or overlaid with a mass of other facts that
their importance does not at first appear, like the
action of cold in the production of dew, before Dr.
Wells's observations, or the influence of an open
drain in producing and sustaining fever, till within
the last few years. It appears then that the pure
inductive syllogism, that argument by which a law
is laid down as the exact sum of all the single cases,
will not suffice for scientific research. To take an
example —

Gold, silver, copper and the rest will combine with oxygen,
Grold, silver, copper and the rest are the only metals ;
Therefore all metals combine with oxygen.

(A syllogism in A U A, Fig. iii. p. 227.)



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254 OUTLINE OF THE

This argument could not be formed until people
discovered what at first no one suspected, that oxy-
gen was the cause of the rusting and tarnishing of
metals ; and it still stands open to dispute if a metal
should be hereafter discovered that refuses to com-
bine with oxygen. Yet it might be selected as one
of the inductions that approach most near to perfect
enumeration. The logic of science then must em-
ploy other instruments than this syllogism, so very
limited in its application, so very liable to question.
Four principal questions require to be answered by
Applied Logic.

1. How are the causes of facts to be distinguished, amidst a multi-
tude of other &ct8, all open to observation ?

2. How are causes discovered which are less open to observation
than the effects?

3. When should an incomplete enumeration (or induction) of £EU!ts
be deemed sufficient, and on what principle ?

4. How should new laws be expressed and recorded ?

The following sections contain an indication of
the answers to these four inquiries, but by no means
a full exposition of them.



§ 114 Search for Causes. Inductive Methods.

All men are apt to notice likenesses in the facts
that come before them, and to group similar facts
together. The similarities are sometimes so obvious
that the most careless observer is arrested by them ;
the rise of the tide to-day and yesterday, the tenden-
cy to fall which a stone firom the hand, an acorn from
an oak, and a hailstone from a cloud exhibit alike,
and the power of growth exhibited by a grain of corn



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LAWS OF THOUGHT. 255

and a tulip root, afford groups of cases which seem
so to classify themselves as to leave the mind little
room for inquiry. The faculty by which such
similarities are apprehended is called observation ; the
act of grouping them together under a general state-
ment, as when we say " All seeds grow — all bodies
fall,'! has been already described as generalization.

Now if any obvious generalization be examined,
as for example " bodies tend to fall," we see that this
only furnishes us with the sum of several distinct
facts ; that " bodies fall " is only a shorter form of
stating that this body falls, and that body, and that
other, and so on till every single body has been men-
tioned. Why all bodies tend to fall has not been
stated. In other words a law has been laid down ;
but the cause of its operation remains to be ascer-
tained. A law or rule is a general principle em-
bodying a class of facts ; when it is regarded in its
connection with theory it usually has the former
name, and when it is concerned with practice, the
latter. The formation of such general propositions
is the first procedure in the formation of science ; at
the same time they are of little service unless accom-
panied by the ascertainment of causes.

What then do we understand by the cause of any
given fact or thing ? We mean the sum of the fficts
or things to which it owes its being. We know that
the various phenomena that engage us are not so
many beginnings or new creations, but are parts of
a long sequence of events, brought about by many
facts that have passed already, and destined in their
turn to bring about other phenomena. In this se-
quence, no new force is gained or lost ; there is corn-



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256 OUTLINE OF THE

mutation of forces, but, so far at least as we can see,
neither increase nor diminution. When we inquire
into causes, we are only seeking one step higher up
in the sequence for the forces now combined in the
new phenomenon under examination; we wish to
know what concurring agencies they were, which
brought this fact about. Now the older writers
attempted not merely to find out these antecedent
phenomena, but to assign the kind of share which
each took in producing the result, by dividing causes
into efficient, formal, material, concomitant, and the
like. This is partly founded on a wrong view of
causation, and it is partly beyond our reach. If we
attempt with them to pronounce that the producing
or efficient cause of any thing {ca/usa principalis,
Kvpujv (UTiov) is to be sought in one particular ante-
cedent fact, whilst the other facts whose concurrence
was no less required for the result, must take subor-
dinate places as instrumental or impelling causes,
we are in danger of the double mistake of elevating
almost into a personal agent one of our phenomena,
and of slighting others which have equally conduced
to the end. All we know for certain is, that there
are certain antecedents, the want of any one of which
would have made the phenomenon wholly, or in its
present shape, impossible. We must therefore apply
universally, what the scholastic writers admitted in
some cases, the principle that all the facts or ele-
ments from which a new fact or thing draws its
existence, f. e. all the associate causes {causce essen^
tialUer sociatce) of it, make up what we term its
cause, on the scholastic maxim that " several partial
causes concurring for one effect, must be regarded as



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LAWS OF THOUGHT. 257

one " (causce partiales in toto concursu statU pro tma).
The cause of an explosion of coal-gas is not the
lighted candle alone, nor the gas which it kindles,
nor the admixture of common air which makes the
gas explosive, but it is the concurrence of all three.

The cause of any phenomenon is only then truly
assigned when account has been taken of all the
precedent phenomena. It remains to observe that
common language is not always framed upon this
complete view. If 1 shake an apple-tree and an
apple fall, I am spoken of as the cause of the fall ;
yet all that I did was to give an opportunity for the
law of gravitation to act. In fact my action is
selected as the cause, where a little thought would
have shown that several causes concurred. This arises
partly from the obvious sequence, in point of time, of
the fall to my action. But although we say that the
cause is antecedent to its effect, we must not under-
stand this as implying invariable antecedence in
point of time. The vices of the court and govern-
ment concurred to cause the French Revolution, and
were antecedent to it in time ; the law of gravitation
causes the fall of the apple, and the oscillations of a
pendulum, but it is not antecedent to tbese ia point
of time, but actually present in them. The antece-
dence of the cause is one of relation, rather than of
time ; if it were otherwise, that act alone which
preceded in time a given phenomenon must be
reckoned as its cause, where perhaps it only gave
the occasion for the chief and constant cause to
operate. He who applied the match to the powder
would be the one cause of all the destruction that
followed the explosion of the mine.

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Where it is proposed to inquire for the cause of a
phenomenon, it is not implied that one cause can


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