John Stuart Mill.

A system of logic, ratiocinative and inductive : being a connected view of the principles of evidence and the methods of scientific investigation online

. (page 20 of 87)
Online LibraryJohn Stuart MillA system of logic, ratiocinative and inductive : being a connected view of the principles of evidence and the methods of scientific investigation → online text (page 20 of 87)
Font size
QR-code for this ebook

to state. Tliis is a natural consequence of having a mind stored
with ' appropriate particulars, and having been long accustomed to
reason at once from these to fresh particulars, without practising the
habit of stating to oneself or to others the coiTesponding general prop-
ositions. An old waiTior, on a rapid glance at the .outlines of the
ground, is able at once to give the necessary orders for a skillful ar-
rangement of his troops ; though if he has received little theoretical
instruction, and has seldom been called upon to answer toother people
for his conduct, he may never have had in his mind a single general
theorem i-especting the relation between ground and array. But his
experience of encampments, under circumstances more or less similar,
has left a numbesr of vivid, unexpressed, ungeneralized analogies in
his mind, the most appropriate of which, instantly suggesting itself,
determines him to a judicious arrangement.

The skill of an uneducated person in the use of weapons, or of tools,
is of a precisely similar nature. The savage who executes unerringly
the exact throw which brings down his game, or his enemy, in the man-
ner most suited to his purpose, under the operation of all tlie conditions
necessarily involved, the weight and form of the weapon, the direction
and distance of the object, the action of the wind, &c., owes this power
to a long series of previous experiments, the results of which he cer-
tainly never framed into any verbal theorems or rules. It is the same
in all extraordinary manual dexterity. Not long ago a Scotch manufac-
turer procured from England, at a high rate of wages, a working dyer,
famous for producing very fine colors, with the view of teaching to his
other workmen the same skill. The workman came ; but his mode of
proportioning the ingredients, in which lay the secret of the effects he
produced, was by talcing them up in handflils, while the common method
was to weigh them. The manufacturer sought to make him turn liis


handling system into an equivalent weighing system, that the general
principle of his peculiar mode of proceeding might be ascertained.
This, liowever, the man found himself quite unable to do, and therefore
could impart his skill to nobody. He had, from the individual cases of
his o^vn experience, established a connexion in his mind between fine
effects of color, and tactual perceptions in handling his dyeing materi-
als ; and from these perceptions he could, in any particular cases, infer
the means to be employed, and the effects which would be produced,
but could not put others in possession of the gi'onnds on which he pro-
ceeded, from having never generalized them in his own. mind, or ex-
pressed them in language.

Almost every one knows Lord Mansfield's advice to a man of prac-
tical good sense, who, being appointed governor of a colony, had to
preside in its court of justice, without previous judicial practice or legal
education. The ad\-ice was, to give his decision boldly, for it would
probably be right ; but never to venture on assigning reasons, for they
would almost infallibly be wi-ong. In cases like this, which are of no
uncommon occurrence, it would be, absurd to suppose that the bad
reason was the source of the good decision. Lord Mansfield knew that
if any reason were assigned it would be necessarily an afterthought,
the judge being in fact guided by impressions from past experience,
without the circuitous process of framing general principles fi-om them,
and that if he attempted to frame any such he would assuredly fail.
Lord Mansfield, however, would not have doubted that a man of equal
experience, who had also a mind stored with general propositions de-
rived by legitimate induction from tliat experience, would have been
greatly preferable as a judge, to one, howpver sagacious, who could
not be trusted with the explanation and justification of his own judg-
ments. The cases of able men performing wonderful things they know
not how, are examples of the less civilized and most spontaneous form
of the operations of superior minds. It is a defect in them, and often
a somxe of eiTors, not to have generalized as they went on ; but gen-
eralization is a help, the most impoitant indeed of all helps, yet not an

Even philosophers, who possess, in the form of general propositions,
a systematic record of the results of the experience of mankind, need
not always revert to those general propositions in order to apply that
experience to a new case. It is justly remarked by Dugald Stewart,
that though our reasonings in mathematics depend entirely upon the
axioms, it is by no means necessary to our seeing the conclusiveness of
the proof, that the axioms should be expressly adverted to. Wlien it
is inferred that A B is equal to C D because each of them is equal to
E F, the most uncultivated understanding, as soon as the propositions
were imderstood, would assent to the inference, without having ever
heard of the general truth that " things which are equal to the same
thing ai-e equal to one another." This remark of Stewart, consistently
followed out, goes to the root, as I conceive, of the philosophy of
ratiocination ; and it is to be regretted that he himself stopped short at
a much more limited application of it. He saw that the general propo-
sitions on which a reasoning is said to depend, may, in certain cases,
be altogedier omitted, without impaii'ing its probative force. But he
imagined this to bo a peculiarity belonging to axioms ; and argued from
it, that axioms are not the foundations or first principles of geometry,


from which all the othei* truths of the science are synthetically deduced
(as the laws of motion and of the composition of forces in mechanics,
the equal mobility of fluids in hydrostatics, the laws of refle.ction and
refraction in optics, are the first princijiles of those sciences) ; but are
merely necessary assumptions, self-evident indeed, and the denial of
which would annihilate all demonstration, but firom which, as premisses,
nothing can be demonstrated. In the present, as in many other in-
stances, this thoughtful and elegant writer has perceived an important
truth, but only by halves. Finding, in the case of geometrical axioms,
that general names have not any talismanic virtue for conjuring new
truths out of the pit of darkness, and not seeing that this is equally ti'ue
in every other case of generalization, he contended that axioms are in
their nature barren of consequences, and that the really fruitful truths,
the real first principles of geometry, are the definitions ; that the defi-
nition, for example, of the circle is to the properties of the circle, what
the laws of equilibrium and of the pressure of the atmosphere are to the
rise of the mercury in the Torricellian tube. Yet all that he had
asserted respecting the function to which the axioms ai"e confined in
the- demonstrations of geometry, holds equally true of the definitions.
Every demonstration in Euclid might be carried on without them.
This is apparent from the ordinary process of proving a proposition of
geometry by means of a diagi'am. What assumption, in fact, do we
set out fi'om, to demonsti'ate by a diagi'am any of the properties of the
circle ] Not that in all circles the radii are equal, but only that they
are so in the circle ABC. As our warrant for assuming this, we
appeal, it is true, to the definition of a circle in general; but it is only
necessary that you should grant the assumption in the case of the par-
ticular circle supposed. From this, which is not a general but a sin-
gular proposition, combined with other propositions of a similar kind,
some of which when generalized are called definitions, and others
axiqms, we prove that a certain conclusion is true, not of all circles,
but of the particular circle ABC; or at least would be so, if the facts
precisely accorded with our assumptions. The enunciation, as it is
called, that is, the general theorem which stands at the head of the
demonstration, is not the proposition actually demonstrated. One
instance only is demonstrated : but the process by which this is done,
is a process which, when we consider its nature, we perceive might be
exactly copied in an indefinite number of other instances ; in every
instance which conforms to certain conditions. The contrivance of
general language furnishing us with terms which connote these con-
ditions, we are able to assert this indefinite multitude of truths in a
single expression, and this expression is the general theorem. By
dropping the use of diagrams, and substituting, in the demonstrations,
general phrases for the letters of the alphabet, we might prove the
general theorem directly, that is, we might demonstrate all the cases
at once ; and to do this we must, of course, employ as our premisses,
the axioms and definitions in their general form. ]3ut this only means,
that if we can prove an individual conclusion by assuming an individual
fact, then in Avhatever case we are waiTanted in making an exactly
similar assumption, we may draw an exactly similar conclusion. The
definition is a sort of notice to ourselves and others, what assumptions
we think ourselves entitled to make. And so in all cases, the general
propositions, whether called definitions, axioms, or laws of nature,


which we lay down at the beginning of our reasonings, are merely
abi-idged statements in a kind of short hand, of the particular facts,
which, as occasion aiises, we either think we may proceed upon as
proved, or intend to assume. In any one demonstration it is enough
if we assume for a particular case, suitably selected, what by the state-
ment of the definition or principle we announce that we intend to
assume in all cases which may arise. The definition of the circle,
therefore, is to one of Euclid's demonstrations, exactly what, according
to Stewart, the axioms are ; that is, the demonstration does not depend
upon it, but yet if we deny it the demonstration fails. The proof does
not rest upon the general assumption, but upon a similar assumption
confined to the particular case : that case, however, being chosen as a
specimen or paradigm of the whole class of cases included in the theo-
rem, there can be no gi'ound for making the assumption in that case
which does not exist in every other ; and if you deny the assumption as
a general truth, you deny the right to make it in the particular instance.
There are, undoubtedly, the most ample reasons for stating both the
principles and the theorems in their general fonn, and these will be
explained presently, so far as explanation is requisite. But, that an
unpractised learner, even in making use of , one theorem to demon-
strate another, reasons rather from particular to particular tlian from
the general proposition, is manifest from the difiiculty he finds in ap-
plying a theorem to a case in which the configuration of the diagram
is exti'emely unlike that of the diagi'am by which the original theorem
was demonstrated. A difficulty which, except in cases of unusual
mental power, long practice can alone remove, and removes chiefly by
rendering us familiar with all the configurations consistent with the
general conditions of the theorem.

§ 4. From the considerations now adduced, the following conclu-
sions seem to be established: All inference is from particulars to par-
ticulars : General propositions are mei-ely registers of such inferences
already made, and short formulae for making more : The major premiss
of a syllogism, consequently, is a formula of this description : and
the conclusion is not an inference drawn from the formula, but an in-
ference drawn according to the formula : the real logical antecedent,
or premisses, being the particular facts firom which the general propo-
sition was collected by induction.. Those facts, and the individual in-
stances which supplied them, may have been forgotten ; but a record
remains, not indeed descriptive of the facts themselves, but showing
how those cases may be distinguished respecting which the facts, when
known, were considered to warrant a given inference. According to
the indications of this record, we draw our conclusion ; which is, to all
intents and pui-poses, a conclusion from the forgotten facts. For this
it is essential that we should read the rccoi-d correctly : and the rules
of the syllogism are a set of precautions to insure our doing so.

This \dew of the functions of the syllogism is confinned by the con-
sideration of precisely those cases which might be expected to be least
favorable to it, namely, those in which ratiocination is independent of
any previous induction. We have already obsei-\'ed that the syllogism,
in the ordinary course of our reasoning, is only the latter half of the
process of ti-avelling fi'om premisses to a conclusion. There are, how-
evex", some peculiai' cases in which it is the whole process. Particu-


lars alone are capable of being subjected to observation ; and all knowl-
edge which is derived from observation, begins, therefore, of necessity,
in particiilai-s ; but our knowledge may, in cases of a certain descrip-
tion, be conceived as coming to us from other sources than observa-
tion. It may pi'esent itself as coming from revelation ; and the knowl-
edore, thus supernaturally communicated, may be conceived to com- '
prise not only particular facts "but general propositions, such as; occur
so abundantly in the A\Titings of Solomon and in the apostolic epistles.
Or the generalization may not be, in the ordinary sense, an assertion at
all, but a command ; a law, not- in the philosophical, but in the moral
and political sense of the term' : an .expression of the desire of a supe-
rior, that we, or any number of other persons, shall conform our con-
duct to certain general instriictions. So far as this asserts a fact,
namely, a volition of the legislator, that fact is an individual fact, and
the proposition, therefore, is not a general proposition. But the de-
scription therein contained of the conduct which it is the Avill of the
legislator that his subjects should observe, is general. The proposi-
tion asserts, not that all men ore anything, but that all men sJiall do
something. These two cases, of a truth revealed in general terms, and
a command intimated in the like manner, might be exchanged for the
more extensive cases, of any general statement received upon testimony,
and any general practical precept. But the more limited illustrations
suit us better, being drawn from subjects where long and complicated
trains of ratiocination have actually been grounded upon premisses
which came to mankind from the first in a general form, the subjects
of Scriptural Theology and of positive Law.

In both these cases the generalities are given to us, and the pattic-
ulars are elicited from them by a process which correctly resolves itself
into a series of syllogisms. The real nature, however, of the supposed
deductive process, is evident enough. It is a search for ti-uth, no doubt,
but through the medium of an inquiry into the meaning- of a fonn of
words. The only point to be determined is, whether the authority
which declared the general proposition, intended, to include this case
in it ; and whether the legislator intended his command to apply to the
presetit case among others, or not. This is a question, as the Gennans
express it, of hermeneutics ; it relates to the meaning of a certain fonn
of discourse. The operation is not a process of inference, but a pro-
cess of interpretation.

In this last phrase we have obtained an expression which appears to
me to characterize, more aptly than any other, the functions of the
syllogism in all cases. When the premisses are given by authority,
the function of Reasoning is to ascertain the testimony of a witness,
or the will of a legislator, by intei-preting the signs in which the one
has intimated hife assertion and the other his command. In like man-
ner, when the premisses are derived from observation, the function of
Reasoning is to ascertain w'hat we (or our predecessors) formerly
thought might be infen-ed from the observed facts, and to do this by
intei-preting a memorandum of ours, or of theirs. The memorandum
reminds us, that from evidence, more or less carefully weighed, it
formerly appeared that a certain attribute might be infeiTed wherever
we perceive a certain mark. The proposition. All men are mortal,
(for instance,) shows that we have had experience from which we
thought it followed that the attributes connoted by the tcnn man, aie


a mark of mortality. But wlicn we conclude tliat the Duke of Wel-
lington is mortal, we Jo not infer this from the memorandum, but from
the former experience. All that we infer from the memorandum, is
our own previous belief, (or that of those who transmitted to us the
pixiposition,) concerning the inferences which that former experience
would waiTant.

This view of the nature of the syllogism renders consistent and
intelligible what otherwise remains obscure and confused in the theory
of Archbishop Whately and other enlightened defendei's of the
syllogistic doctrine, respecting the limits to which its functions are
confined. They all affirm, in as explicit terms as can be used, that
the sole office of general reasoning is to prevent inconsistency in our
opinions; to prevent us from assenting to anything, the truth of which
would contradict something to which we had previously on good
grounds given our assent. And they tell us, that the sole gi'ound
which a syllogism aftbrds for assenting to the conclusion, is that the
supposition of its being false, combined with the supposition that the
premisses are true, would lead to a contradiction in terms. Now this
would be but a lame account of the real grounds which we have for
beheving the facts which we leani from reasoning, in contradistinction
to observation. The true reason why we believe that the Duke of
Wellington ^\'ill die, is that his fathers, and our fathers, and all other
persons wlio were contemporary with them, have died. Those facts
are the real premisses of the reasoning. But we are not led to infer
the conclusion from those premisses, by the necessity of avoiding any-
verbal inconsistency. There is no contradiction in supposing that all
those persons have died, and that the Duke of Wellington may, not-
withstanding, live for ever. But there would be a contradiction if we
first, on the gi'ound of those same premisses, made a general assertion
including and covering the case of the Duke of Wellington, and then
refused to stand to it in the individual case. There is an inconsistency
to be avoided between the memorandum we make of the inferences
Avhich may be justly drawn in future 'cases, and the inferences we
actually draw in those cases when they arise. With this vaew we
interpret our own formula, precisely as a judge intei-prets a law: in
order that we may avoid drawing any inferences not confoi'mable to
our former intention, as a judge avoids giving any decision' not con-
formable to the legislator's intention. The rules for this interpretation
are the rules of the syllogism : and its sole purpose is to maintain
consistency between the conclusions we draw in every particular case,
and the previous general directions for drawing them ; whether those
general directions were framed by ourselves as the result of induction,
or were received by us from an authority competent to give them.

§ 5. In the above observations it has, I think, been clearly shown,
that, although there is always a process of reasoning or inference
where a syllogism is used, the syllogism is not a coiTect analysis of
that process of reasoning or inference ; which is, on the contrary,
(when not a mere inference fi-ora testimony,) an inference from partic-
ulars to particulars; authoi-ized by a previous inference from particu-
lars to generals, and substantially the same with it ; of the nature,
therefore, of Induction. But while these conclusions appear to me
undeniable, I must yet enter a protest, as strong as that of Archbishop


Whately himself, against the doctrine that the syllogistic art is useless
for tiie purposes of reasoning. The reasoning lies in the act of gen-
eralization, not in intei-preting the record of that act ; but the syllogistic
form is an indispensable collateral security for the con-ectness of the
generalization itself.

It has already been seen, that if we have a collection of particulars
sufficient for grounding an induction, we need not frame a general
proposition ; we may reason at once from those particulars to other
particulars. But it is to be remarked withal, that whenever, from a
set of particular cases, we can legitimately draw any inference, we
may legitimately make our inference a general one. If, from obser-
vation and experiment, we can conclude to one new case, so may we
to an indefinite number. If that which has held true in our past
experience will therefore hold in time to come, it will hold not merely
in some individual case, but in all cases of a given description. Every
induction, therefore, which suffices to prove one fact, proves an indefi-
nite multitude of facts : the expei'ience which justifies a single predic-
tion must be such as will suffice to bear out a general theorem. This
theorem it is extremely important to ascertain and declare, in its
broadest form of generality ; and thus to place before our minds, in
its full extent, the whole of what our evidence must prove if it proves
anything. ^ ^.

This throwing of the whole body of possible inferences from a given
set of particulars, into one general expression, operates as" a security
for their being just inferences in more ways than one. . First, the gen-
eral principle presents a larger object to the imagination than any of
the singular propositions which it contains. A process of thought which
leads to a comprehensive genei'ality, is felt as of ,gi-eater importance
than one which terminates in an insulated fact ; and the mind is, even
unconsciously, led to bestow greater attention upon the process, and
to weigh more carefully the sufficiency of the experience appealed to,
for supporting the inference grounded upon it. There is another, and
a more important, advantage. In reasoning from a coiu'se of individ-
ual observations to some new and unobserved case, which we are but
imperfectly acquainted with (or we should not be inquiring into it),
and in which, since we are inquiring into it, we probably feel a pecu-
liar interest ; there is very little to prevent us from giving way to
negligence, or to any bias which may affect our wishes or our imagina-
tion, and, under that influience, accepting insufficient evidence as suffi-
cient. But if, instead of concluding sfcfaight to the particular case, we
place before ourselves an entire class of facts, the whole contents of a
general proposition, every tittle of which is legitimately inferable from
our premisses, if that one particular conclusion is so ; there is then a
considerable likelihood that if the premisses are insufficient, and the
general inference, therefore, groundless, it Avill comprise within it some
fact or facts the reverse of which we already know to be true ; and
we shall thus discover the eiTor in our generalization, by what the
schoolmen termed a reductio ad impossihile.

Thus if, during the reign of Marcus Aurelius, a subject of the Roman
empire, under the bias naturally given to the imagination and expec-
tations by the lives and characters of the Antonines, had been disposed
to conclude that Commodus would be a just ruler: supposing him to
Stop there, he might only have been undeceived by sad experience.


But if lie reflected that this conclusion could not be justifi;il>lc unless
from the same evidence he was also warranted in concluding some gen-
eral proposition, as, for instance, that all Roman emperors are just
rulers ; he would immediately have thought of Nero, Domitian, and
other instances, which, showing the falsity of the general conclusion, and
therefore the insufficiency of the premisses, would have warned him
that those premisses could not prove in the instance of Commodus,
what they were inadequate to prove in any collection of cases in which
his was included.

The advantage, in judging whetlier any controvei'ted inference is
legitimate, of referring to a parallel case, is universally acknowledged.

Online LibraryJohn Stuart MillA system of logic, ratiocinative and inductive : being a connected view of the principles of evidence and the methods of scientific investigation → online text (page 20 of 87)