James Welton.

A manual of logic, Volume 2 online

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" energy is translational. The only other gas which has been compound.
" found to behave similarly is mercury gas, at a high tem-
" perature " (p. 352 b), " In the case of mercury the absence
" of interatomic energy is regarded as a proof of the mon-
" atomic character of the vapour, and the conclusion holds
"equally good for argon. . . . Now a monatomic gas can
" only be an element, or a mixture of elements ; and hence
" it follows that argon is not of a compound nature " (p. 353).

But whether it is an element or a mixture of elements is ?^?S*\"®
still doubtful. " There is evidence both for and against the whether
" hypothesis that argon is a mixture : for, owing to Mr. Sfmrfe^as
" Crookes' observations of the dual character of its spectrum ; or a Jiiix-
" against, because of Prof. Olszewski's statement that it has
"a definite melting point, a definite boiling point, and a
" definite critical temperature and pressure ; and because on
"compressing the gas in presence of its liquid, pressure
" remains sensibly constant until all gas has condensed to
" liquid. The latter experiments are the well-known criteria
"of a pure substance ; the former is not known with cer-
"tainty to be characteristic of a mixture. . . . For the
" present, however, the balance of evidence seems to point
" to simplicity » (p. 353 h).

If argon is an element its atomic weight is 40, for its The atoinio
molecule is identical with its atom, and the molecular weight a^on. ^


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140 iNDUCTIOtr.

Book V. of a gas is doable its density, which in the case of argon ia
^^•^ - approximately 20.
Argon is ex- Many attempts were made to induce argon to combine
io^rt! ^ with other snbstances, bat they all proved abortive. Since
the pablication of the paper we are quoting from, however,
M. Berthelot claims to have established that nnder the
inflnence of electricity argon enters into chemical action
with benzene vapour. If this is the case, it is the first
chemical action in which argon has been observed to take
part, and the gas is, therefore, of an extremely inert character.
Its Inertness Finally, the determination of the nature of argon as
its late dis- far as it has gone answers the objection to the hypo-
cov«y. thesis of the existence of argon drawn from previous
non-observation. ''It need excite no astonishment that
'* argon is so indifferent to reagents. For mercury, although
'^ a monatomic element, forms compounds which are by no
" means stable at a high temperature in the gaseous state ;
"and attempts to produce compounds of argon may be
" likened to attempts to cause combination between mercury
" gas at 800** and other elements " (p. 353 b), " Its inertness,
'^ which has suggested its name, sufi&ciently explains why it
*' has not previously been discovered as a constituent of com-
'* pound bodies" (p. 354 a). Since the publication of the
paper, however. Professor Bamsay and Mr. Crookes have
found that a gas obtained from a mineral called deveite
is a mixture of argon and helium, a most interesting dis-
covery, as helium was hitherto only known as abundant in
the surroundings of the sun. On the other hand, it has
been ascertained that there is no argon in mice or peas —
these being chosen as representatives of the animal and
vegetable kingdoms respectively.
The above Even Buch an imperfect outline as the above makes
tions iUiu- abundantly manifest that induction is by no means an easy
SedocWno P^^^^s, or one that can be reduced to mechanical rules ;
of indue- that the procedure starts from, and is guided throughout by
hypotheses ; that number of experiments is appealed to only
as a guarantee that only known conditions a^e operative ;
that the procedure of perceptual analysis is to establish a


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podtive connexion, to purge this of exceptions and to limit Book V.
and corroborate it by negative instances ; and that one in- ^•^ '
ductive enquiry gives rise to others. In brief, this discovery
of first-rate scientific importance illustrates in every point
the doctrine of induction set forth in this and the preceding

^155. Mill's 'Experimental' or 'Inductive ' Methods.

Although we regard the preceding exposition as a complete As Mill's
statement of the logical principles which guide all qualitative have ob-
analysis of the given, and of the general character of the ^^«raa cur-
method adopted, yet a discussion of this subject in an rency they
English treatise on Logic would probably be considered in- eomeexami-
complete if it did not embrace a consideration of the " Four i^*^®^-
"Methods of Experimental Enquiry" or "Methods of
" Direct Induction," as they are indifferently called, to which
Mill's Logic has given currency and authority. To this, then,
we will now briefly address ourselves.

(i.) Statement of the Methods.

The exposition of these "methods" occupies a foremost Mill regards
place in Mill's system, and follows his discussion of the pre- methods as
liminary doctrines of the uniformity of nature and causation. JJ^^^
The methods themselves are based upon the popular idea of general laws
causation, as an invariable sequence between phenomena, with r^m- ^
which Mill sets out. " Cause" is at first regarded as a phy- JJ^^ ^"
sical thing, though it is afterwards confined to some particular phenomena.
property of a thing. The inductive problem takes the form
of BO analysing the conrse of observed events that it becomes
possible to gather from an examination of them universal pro-
positions about their succession. Throughout runs the funda-
mental assumption of empiricism, that all inference is based
upon perceptible resemblance [c/. § § 138 (i.)^; 145 (v.)], and that,
consequently, all instances of the same causal sequence will
have points of resemblance both in the antecedent and in twomaiu*
the consequent phenomena. Hence, there are two " obvious ^^^ "*
" modes of singling out from among the circumstances which Agreement
" precede or f oUow a phenomenon, those with which it is Sice,^^*^'
1 First Edition, § 155 (i).


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Book V.

Ch. V.

of which all
others are


from Hers-
cbel, but
them more

Canons : —

"really coDneoted by an invariable law. . . • One iB, by
'* comparing together different instances in which the
*^ phenomenon occurs. The other is, by comparing instances
"in which the phenomenon does occur, with instances in
"other respects similar in which it does not. These two
" methods may be respectively denominated, the Method of
" Agreement, and the Method of Difference " (Mill, Logic, IIL,
viii., § 1). The other two methods given by Mill as in-
dependent — those of "Kesidnes" and of "Concomitant
"Variations'* — are really but particular cases of these.
Mill gives, moreover, a fifth method, though he does not
recognize it as independent, but as merely a double applica-
tion of the method of agreement, which he styles the " Joint
" Method of Agreement and Difference " or the " Indirect
" Method of Difference,"

All these methods are gathered from HerschePs Pre-
liminary Discourse on the Study of Natural Philosophy " in
" which alone," says Mill, " of all books which I have met
" with, the four methods of induction are distinctly recog-
" nized, though not so clearly characterized and defined, nor
" their correlation so fully shown, as has appeared to me desir-
**able" (Logic, III., ix., § 3). Mill, therefore, to repair this
imperfection, formulated the four [or five] methods with con-
siderable show of precision in the following five " Canons of
" Induction " (ibid,, viii.), and, denoting " antecedents by the
" large letters of the alphabet, and the consequents corre-
"sponding to them by the small" (ibid., § 1), also gave
symbolic formulae to express the chief methods : —

(1) Agree-

First Canon (Method of Agreement).

"If two or more instances of the phenomenon under
" investigation have only one circumstance in common,
"the circumstance in which alone all the instances
" agree, is the cause (or effect) of the given pheno-
" menon."

Symbolic formula : ABC — abc; ADE — ade .; A — a is causal


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Second Canon (Method of Difference). Book V.

Ch. V

* If an instance in which the phenomenon under invest!- -*- '
" gation occurs, and an instance in which it does not enc?-^^^
" occur, have every circumstance in common save one,
'^ that one occurring only in the former ; the circnm-
'^ stance in which alone the two instances differ, is the
" effect, or the cause, or an indispensahle part of the
" cause, of the phenomenon."

Symbolic formula: ABC — abo ; BC—bc .*. A— a is causal

Third Canon (Joint Method).

** If two or more instances in which the phenomenon (3) Joint
" occurs have only one circumstance in common, while andl^er-
"two or more instances in which it does not occur ^^^*
^* have nothing in common save the absence of that
"circumstance ; the circumstance in which alone the
**two sets of instances differ, is the effect, or the
" cause, or an indispensable part of the cause, of the
" phenomenon."

Symbolic formula. Mill gives no formula for this method,
and several have been suggested which more or less
fail to fulfil the conditions of the canon. Bearing in
mind that, as Dr. Fowler puts it {Ind. Log,, p. 160),
" the positive and negative instances must be in pari
" materia,^ the formula might, on the lines of those
already given, be thus expressed :

ABC— abo, ADE^ade; BDM—bdm, CEO— ceo .•, ^— a is a
causal sequence.

Fourth Canon (Method of Residues).
*' Subduct from any phenomenon such part as is known (^) Resi-

"by previous inductions to be the effect of certain "°^'

" antecedents, and the residue of the phenomenon is

" the effect of the remaining antecedents.*'
Symbolic formula : If A — a, B — b are known to be causal

sequences, then, given ABC — abo, it can be inferred

that — is also a causal sequence.


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Book V. Fifth Canon (Method of Ooncomitant Variations).

Ch. V.

— " Whatever phenomenon varies in any manner whenever

xxatva^ ' " another phenomenon varies in some particular

**°'"' " manner, is either a cause or an effect of that pheno-

" menon, or is connected with it through some fact of

" cansation.*'

The 83rmbolic formula would appear to be AiBC — aibo;

A^BC — a^bc; A^jBC — aJ)OS /. A — a is a causal sequence.

MiU'a Ex^ As examples of the Method of Agreement^ Mill gives : -
(1) of Agree- ** Let the antecedents be the contact of an alkaline substance
mont; "and an oil This combination being tried under several
** varieties of circumstances, resembling each other in nothing
'^ else, the results agree in the production of a greasy and
'^ detersive or saponaceous substance : it is therefore con-
'* eluded that the combination of an oil and an alkali causes
" the production of soap. It is thus we enquire, by the
*^ Method of Agreement, into the effect of a given cause. In
'* a similar manner we may enquire into the cause of a given
" effect. . . . For example, let the effect a be crystaUization.
'^ We compare instances in which bodies are known to assume
'* crystalline structure, but which have no other point of agree-
*^ ment ; and we find them to have one, and as far as we can
** observe, only one, antecedent in common : the deposition
'' of a solid matter from a liquid state, either a state of
''fusion or of solution. We conclude, therefore, that the
''solidification of a substance from a liquid state is an
" invariable antecedent of its crystallization '' (ihid,, § 1).
(2)of Diff«r. Of the Method of Difference Mill says : "It is scarcely
" necessary to give examples of a logical process to which we
'^ owe almost all the inductive conclusions we draw in early
" life. When a man is shot through the heart, it is by this
"method that we know that it was the gun-shot which
" killed him : for he was in the fulness of life immediately
" before, all circumstances being the same, except the wound"
{iUd., § 2).
(8) of Joint As an example of the Joint Method of Agreeing and
' Difference^ Mill takes one of the steps in Dr. Wells' investi-

cnce ;


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gation into the formation of dew : " It appears that the Book V.

"instances in which much dew is deposited, which are very ^^•^ '

" various, agree in this, and, so far as we are able to observe,

** in this only, that they either radiate heat rapidly or conduct

" it slowly : qualities between which there is no other cir-

" cumstance of agreement, than that by virtue of either, the

" body tends to lose heat from the surface more rapidly than

*' it can be restored from within. The instances, on the con-

" trary, in which no dew, or but a small quantity of it, is

" formed, and which are also extremely various, agree (so far

" as we can observe) in nothing except in not having this

" same property. We seem, therefore, to have detected the

" characteristic difference between the substances on which

" dew is produced, and those on which it is not produced.

" And thus have been realized the requisitions of what we

"have termed the Indirect Method of Difference, or the

" Joint Method of Agreement and Difference " (III., ix., § 3).

In illustration of the Method of Residues Mill quotes from (4) of Resi-
Herschel several instances from various sciences. For *
example : " Many of the new elements of chemistry have
" been detected in the investigation of residual phenomena.
" Thus Arf wedson discovered lithia by perceiving an excess
" of weight in the sulphate produced from a small portion of
" what he considered as magnesia present in a mineral he
"had analysed" (quoted from Nat, Phil., § 161). "* Almost
"all the greatest discoveries in Astronomy,' says the same
" author, * have resulted from the consideration of residual
" phenomena of a quantitative or numerical kind. ... It
" was thus that the grand discovery of the precession of the
"equinoxes resulted as a residual phenomenon, from the
" imperfect explanation of the return of the seasons by the
" return of the sun to the same apparent place among the
" fixed stars'" {Outlines of Astronomy, § 856, quoted by Mill,
III., ix., § 6).

Amongst examples of the Method of Concomitant Variations (5) of Con-
Mill takes the doctrine of inertia : "The simple oscillation of y^iationa.
" a weight suspended from a fixed point, and moved a little
" out of the perpendicular, which in ordinary circumstances

LOG. II, 10


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Book V. " lasts but a few minutes, was prolonged in Borda's experi-
^^•^ ' " ments to more than thirty hours, by diminishing as much
" as possible the friction at the point of suspension, and by
" making the body oscillate in a space exhausted as nearly as
'* possible of its air. There could therefore be no hesitation
^* in assigning the whole of the retardation of motion to the
*^ influence of the obstacles ; and since, after subducting this
" retardation from the total phenomenon, the remainder was
** an uniform velocity, the result was the proposition known
**as the first law of motion" (III., viii., § 7).

Mill discusses other and more complex examples, in which
he finds several of the methods exemplified, but the above
are sufficient to show the kind of investigation of nature he

(ii.) Examination of the Hetliods.

HUi clainiB For these methods Mill makes very high claims. They

meUi^ are " the only possible modes of experimental enquiry — of

m Th nl " ^^''®®* induction d posteriori, as distinguished from deduc-

meansof ex- " tiou" (III., viii., § 7). " In saying that no discoveries were

g^"!*^ " ever made by the Four Methods, he [Whewell] affirms

" that none were ever made by observation and experiment ;

" for assuredly if any were, it was by processes reducible

" to one or other of those methods " (III., ix., § 6). But

(2) Methods this is not all. *^ Induction is proof ; it is inferring some-

" thing unobserved from something observed : it requires,

*' therefore, an appropriate test of proof ; and to provide

"that test, is the special purpose of inductive logic''

(III., ii., § 6). " The business of Inductive Logic is to pro-

*^ vide rules and models (such as the Syllogism and its rules

"are for ratiocination), to which if inductive arguments

"conform, those arguments are conclusive, and not other-

" wise. This is what the Four Methods profess to be "


These claims are by no means universally granted by
logicians. As Mr. Bradley says : " The balance of authority
" among modern logicians is, I think, against the claims of
" the inductive proofs, and is not on their side " (Prin, </

of Froot


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Log.^ p. 331). Indeed, as will appear in the sequel, Mill Book V«
himself does not consistently maintain these high claims, .1.*
and abundantly shows that the canons both demand the
unattainable^andfail to give conclusive proofs of fchobe general
propositions which he held it to be the business of induction
to discover and prove {cf. III., i., § 2).

In considering the methods, and their claims to be indue- Mill's sym-
tive proofs, it is well at the outset to draw attention to the mi^f^dhig.
unfortunate character of Mill's symbolism. The use of A, a ;
Bj b; Cj ; &c., suggests that the causal connexions sought
are already obtained ; and this suggestion is strengthened by
Mill's speaking of a,^, o as " the consequents corresponding
" to " the antecedents A, B, 0, This would be an open
begging of the question. Mill probably does not mean
this, but intends his symbols as mere empty forms. They
are, however, undoubtedly confusing; if the correspond-
ence between large and small letters means nothing, it
should not be employed ; whilst if it has meaning, it begs
the whole question.

It must next be noticed that the methods bear a strong All the
family likeness to each other. They are all based on the based ou the
same principle. Both Agreement and Difference, Mill tells ^j^J^H® °^
us, *' are methods of elimination. . . . The Method of Agree-
^ ment stands on the ground that whatever can be eliminated,
" is not connected with the phenomenon by any law. The
*' Method of Difference has for its foundation, that what-
*' ever cannot be eliminated, is connected with the pheno-
" meuon by a law " (III., viii., § 3). The Joint Method is
"a double employment of the Method of Agreement''
{ihid,, § 4). " The Method of Residues is ... a peculiar
" modification of the Method of Difference ^ (ibid., § 5).
The Method of Concomitant Variations is '* but a modifica-
" tion either of the Method of Agreement or of the Method
«of Difference" (III., xxii., §4). The methods might,,
indeed, all be expressed by the formula AB — xy, AC — xz^
which avoids the objection just urged to Mill's symbolio
statements. Here, as B can be removed without affecting x^
it is assumed that B and x are not causally connected ; whilst


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148 iNDuonoH.

PooK v. as the removal of B is attended by the removal of /, it is

^'^ ' assumed that B— j' is a causal sequence. This represents

the mode of proceeding by each method. Each, by removing

parts of a complex whole, seeks to establish a relation between

the remaining parts, llius the methods are at bottom, as

Mr. Bradley points out, " all of them Methods of Residues

"or Methods of Difference" (op. ct«., p. 337).

The We must now examine the claims of the methods to be

not***^du^ called " inductive." By induction Mill continually tells us

fecMeofS? he means inference from particulars. It is needless to

ferencefrom multiply quotations : two or three will suffice as examples.

particulars, u ^jj processes of thought in which the ultimate premises

"are particulars . . . are . . . Induction" (11., iii., § 7).

"Induction ... is that operation of the mind, by which

" we infer that what we know to be true in a particular case

"or cases, will be true in all cases which resemble the former

"in certain assignable respects" (III., ii., § 1). " The experi*

" mental method . . . makes its experiments directly upon the

for they all «* complex oase" (III., X., § 8). But, if we examine the canons

univer^ of the methods we find they do not even profess to start

from particular complex facts. They demand that the

"instances" "have only one circumstance in common,"

** have every circumstance in common save one," " have

" nothing in common save the absence of that circumstance."

Yery little consideration is needed to show that the complex

t particular facts of experience can never fulfil such conditions

as these. Such facts never agree, still less do they differ, in

one point only. The canons assume that many circumstances

are first dismissed from consideration as " already known to

"be immaterial to the result" (III., viii., § 3). That is, they

assume that the complex particulars of experience have

already been analysed, and that limited groups of antecedents

and consequents, known to be causally connected, have been

separated out for the purpose of the " inductive " enquiry,

whose task is only to obtain simpler causal connexions by

eliminating some of the elements still left. Thus, as Mr.

Laurie says in an able critical article on the methods in JUind

(New Series, vol. ii.) : ** The position from which we are thus


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" invited to set out is very far from the beginning of experi- Book V.
" mental enquiry ; the clear-cut instances supposed are possible ^_1. *
"only in an advanced stage of scientific research" (p. 324).
Whewell is, indeed, quite justified when he says: "Upon
" these methods, the obvious thing to remark is, that they
" take for granted the very thing which is most difficult to
" discover, the reduction of the phenomena to formulae such
"as are here presented to us" {Phil, of Discovery^ p. 263).
Put in other words, the methods can only start with universal
judgments ; for it is just that analysis and elimination which
the methods presuppose which constitute the universal. As
Mr. Bradley says in his searching criticism of the methods :
" The moment you have reduced your particular fact to a
"perfectly definite set of elements, existing in relations
" which are accurately known, there you have left the fact
"behind you. You have already a judgment universal in
" the same sense in which the result of your * induction' is
" universal " {op, cit, p. 335). The demand for a universal
to start from is, indeed, made explicitly by the "Fifth Canon
which speaks of one phenomenon varying toA^n^^r another
varies, thus postulating that a universal connexion between
the two should be established before the method can be
brought to bear upon it. Hence, the methods which are held
out to us " as the only possible modes of experimental en-
" quiry— of direct induction d posteriori" (Mill, III., viii., § 7)
— are seen to presuppose the very work which they them-
selves are set forth as alone capable of accomplishing. Mill MiU's ex-
does, indeed, give two instances in which he applies the ^tart^g^
methods to the actual raw niaterial of experience. " If it pa^c^j^^s
" had been my object," he says, " to justify the processes do not fulfil
" themselves as means of investigation, there would have meJteoTSa
" been no need to look far off, or make use of recondite or cw^o"*-
" complicated instances. As a specimen of a truth ascertained
"by the Method of Agreement, I might have chosen the
" proposition * Dogs bark.' This dog, and that dog, and the
"other dog, answer to ABC, ADE^ AFQ, The circumstance
" of being a dog answers to A, Barking answers to a. As a
"truth made known by the Method of Difference, *Fire


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Book V. *' burns' might have sufficed. Before I touch the fire I am
Ch^ « jjQ^ burned ; this is BC ; I touch it and am burnt ; this is
''ABCy aBC' (III., ix., § 6). On this we cannot do better
than quote Mr. Bradley's brief but sufficient criticism :
" The Canons we think are not hard to content if this will
*' satisfy them. But surely their author had forgotten them
" for the moment. By seeing three barking dogs I perceive

Online LibraryJames WeltonA manual of logic, Volume 2 → online text (page 14 of 29)