Chapter XII (4)

135 Unless, indeed, the consequent was generated, not by the antecedent,
but by the means employed to produce the antecedent. As, however,
these means are under our power, there is so far a probability that
they are also sufficiently within our knowledge to enable us to
judge whether that could be the case or not.

_ 136 Discourse on the Study of Natural Philosophy_, p. 179.

137 For this speculation, as for many other of my scientific
illustrations, I am indebted to Professor Bain, whose subsequent
treatise on Logic abounds with apt illustrations of all the
inductive methods.

138 This view of the necessary co-existence of opposite excitements
involves a great extension of the original doctrine of two
electricities. The early theorists assumed that, when amber was
rubbed, the amber was made positive and the rubber negative to the
same degree; but it never occurred to them to suppose that the
existence of the amber charge was dependent on an opposite charge in
the bodies with which the amber was contiguous, while the existence
of the negative charge on the rubber was equally dependent on a
contrary state of the surfaces that might accidentally be confronted
with it; that, in fact, in a case of electrical excitement by
friction, four charges were the minimum that could exist. But this
double electrical action is essentially implied in the explanation
now universally adopted in regard to the phenomena of the common
electric machine.

139 Pp. 110, 111.

140 Infra, book iv., chap. ii., On Abstraction.

141 I must, however, remark, that this example, which seems to militate
against the assertion we made of the comparative inapplicability of
the Method of Difference to cases of pure observation, is really one
of those exceptions which, according to a proverbial expression,
prove the general rule. For in this case, in which Nature, in her
experiment, seems to have imitated the type of the experiments made
by man, she has only succeeded in producing the likeness of man’s
most imperfect experiments; namely, those in which, though he
succeeds in producing the phenomenon, he does so by employing
complex means, which he is unable perfectly to analyze, and can
form, therefore, no sufficient judgment what portion of the effects
may be due, not to the supposed cause, but to some unknown agency of
the means by which that cause was produced. In the natural
experiment which we are speaking of, the means used was the clearing
off a canopy of clouds; and we certainly do not know sufficiently in
what this process consists, or on what it depends, to be certain _a
priori_ that it might not operate upon the deposition of dew
independently of any thermometric effect at the earth’s surface.
Even, therefore, in a case so favorable as this to Nature’s
experimental talents, her experiment is of little value except in
corroboration of a conclusion already attained through other means.

142 In his subsequent work, _Outlines of Astronomy_ (§ 570), Sir John
Herschel suggests another possible explanation of the acceleration
of the revolution of a comet.

143 Discourse, pp. 156–8, and 171.

144 Outlines of Astronomy, § 856.

_ 145 Philosophy of Discovery_, pp. 263, 264.

146 See, on this point, the second chapter of the present book.

147 Ante, chap. vii., § 1.

148 It seems hardly necessary to say that the word _impinge_, as a
general term to express collision of forces, is here used by a
figure of speech, and not as expressive of any theory respecting the
nature of force.

_ 149 Essays on some Unsettled Questions of Political Economy_, Essay V.

150 It is justly remarked by Professor Bain, that though the Methods of
Agreement and Difference are not applicable to these cases, they are
not wholly inaccessible to the Method of Concomitant Variations. “If
a cause happens to vary alone, the effect will also vary alone: a
cause and effect may be thus singled out under the greatest
complications. Thus, when the appetite for food increases with the
cold, we have a strong evidence of connection between these two
facts, although other circumstances may operate in the same
direction. The assigning of the respective parts of the sun and moon
in the action of the tides may be effected, to a certain degree of
exactness, by the variations of the amount according to the
positions of the two attractive bodies. By a series of experiments
of Concomitant Variations, directed to ascertain the elimination of
nitrogen from the human body under varieties of muscular exercise,
Dr. Parkes obtained the remarkable conclusion, that a muscle grows
during exercise, and loses bulk during the subsequent rest.”
(_Logic_, ii., 83.)

It is, no doubt, often possible to single out the influencing causes
from among a great number of mere concomitants, by noting what are
the antecedents, a variation in which is followed by a variation in
the effect. But when there are many influencing causes, no one of
them greatly predominating over the rest, and especially when some
of these are continually changing, it is scarcely ever possible to
trace such a relation between the variations of the effect and those
of any one cause as would enable us to assign to that cause its real
share in the production of the effect.

151 Bain’s _Logic_, ii., 360.

152 What is said in the text on the applicability of the experimental
methods to resolve particular questions of medical treatment, does
not detract from their efficacy in ascertaining the general laws of
the animal or human system. The functions, for example, of the
different classes of nerves have been discovered, and probably could
only have been discovered, by experiments on living animals.
Observation and experiment are the ultimate basis of all knowledge:
from them we obtain the elementary laws of life, as we obtain all
other elementary truths. It is in dealing with the complex
combinations that the experimental methods are for the most part
illusory, and the deductive mode of investigation must be invoked to
disentangle the complexity.

153 Professor Bain, though concurring generally in the views expressed
in this chapter, seems to estimate more highly than I do the scope
for specific experimental evidence in politics. (_Logic_, ii.,
333–337.) There are, it is true, as he remarks (p. 336), some cases
“when an agent suddenly introduced is almost instantaneously
followed by some other changes, as when the announcement of a
diplomatic rupture between two nations is followed the same day by a
derangement of the money-market.” But this experiment would be quite
inconclusive merely as an experiment. It can only serve, as any
experiment may, to verify the conclusion of a deduction. Unless we
already knew by our knowledge of the motives which act on business
men, that the prospect of war _tends_ to derange the money-market,
we should never have been able to prove a connection between the two
facts, unless after having ascertained historically that the one
followed the other in too great a number of instances to be
consistent with their having been recorded with due precautions.
Whoever has carefully examined any of the attempts continually made
to prove economic doctrines by such a recital of instances, knows
well how futile they are. It always turns out that the circumstances
of scarcely any of the cases have been fully stated; and that cases,
in equal or greater numbers, have been omitted which would have
tended to an opposite conclusion.

154 Vide Memoir by Thomas Graham, F.R.S., Master of the Mint, “On Liquid
Diffusion applied to Analysis,” in the _Philosophical Transactions_
for 1862, reprinted in the _Journal of the Chemical Society_, and
also separately as a pamphlet.

155 It was an old generalization in surgery, that tight bandaging had a
tendency to prevent or dissipate local inflammation. This sequence,
being, in the progress of physiological knowledge, resolved into
more general laws, led to the important surgical invention made by
Dr. Arnott, the treatment of local inflammation and tumors by means
of an equable pressure, produced by a bladder partially filled with
air. The pressure, by keeping back the blood from the part, prevents
the inflammation, or the tumor, from being nourished: in the case of
inflammation, it removes the stimulus, which the organ is unfit to
receive; in the case of tumors, by keeping back the nutritive fluid,
it causes the absorption of matter to exceed the supply, and the
diseased mass is gradually absorbed and disappears.

156 Since acknowledged and reprinted in Mr. Martineau’s _Miscellanies_.

_ 157 Dissertations and Discussions_, vol. i., fourth paper.

158 Written before the rise of the new views respecting the relation of
heat to mechanical force; but confirmed rather than contradicted by
them.

159 As is well remarked by Professor Bain, in the very valuable chapter
of his Logic which treats of this subject (ii., 121), “scientific
explanation and inductive generalization being the same thing, the
limits of Explanation are the limits of Induction,” and “the limits
to inductive generalization are the limits to the agreement or
community of facts. Induction supposes similarity among phenomena;
and when such similarity is discovered, it reduces the phenomena
under a common statement. The similarity of terrestrial gravity to
celestial attraction enables the two to be expressed as one
phenomenon. The similarity between capillary attraction, solution,
the operation of cements, etc., leads to their being regarded not as
a plurality, but as a unity, a single causative link, the operation
of a single agency.... If it be asked whether we can merge gravity
itself in some still higher law, the answer must depend upon the
facts. Are there any other forces, at present held distinct from
gravity, that we may hope to make fraternize with it, so as to join
in constituting a higher unity? Gravity is an attractive force; and
another great attractive force is cohesion, or the force that binds
together the atoms of solid matter. Might we, then, join these two
in a still higher unity, expressed under a more comprehensive law?
Certainly we might, but not to any advantage. The two kinds of force
agree in the one point, attraction, but they agree in no other;
indeed, in the manner of the attraction, they differ widely; so
widely that we should have to state totally distinct laws for each.
Gravity is common to all matter, and equal in amount in equal masses
of matter, whatever be the kind; it follows the law of the diffusion
of space from a point (the inverse square of the distance); it
extends to distances unlimited; it is indestructible and invariable.
Cohesion is special for each separate substance; it decreases
according to distance much more rapidly than the inverse square,
vanishing entirely at very small distances. Two such forces have not
sufficient kindred to be generalized into one force; the
generalization is only illusory; the statement of the difference
would still make two forces; while the consideration of one would
not in any way simplify the phenomena of the other, as happened in
the generalization of gravity itself.”

To the impassable limit of the explanation of laws of nature, set
forth in the text, must therefore be added a further limitation.
Although, when the phenomena to be explained are not, in their own
nature, generically distinct, the attempt to refer them to the same
cause is scientifically legitimate; yet to the success of the
attempt it is indispensable that the cause should be shown to be
capable of producing them according to the same law. Otherwise the
unity of cause is a mere guess, and the generalization only a
nominal one, which, even if admitted, would not diminish the number
of ultimate laws of nature.

_ 160 Cours de Philosophie Positive_, ii., 656.

161 Vide supra, book iii., chap. xi.

_ 162 Philosophy of Discovery_, p. 185 et seq.

163 Comte, _Philosophie Positive_, ii., 434–437.

164 As an example of legitimate hypothesis according to the test here
laid down, has been justly cited that of Broussais, who, proceeding
on the very rational principle that every disease must originate in
some definite part or other of the organism, boldly assumed that
certain fevers, which not being known to be local were called
constitutional, had their origin in the mucous membrane of the
alimentary canal. The supposition was, indeed, as is now generally
admitted, erroneous; but he was justified in making it, since by
deducing the consequences of the supposition, and comparing them
with the facts of those maladies, he might be certain of disproving
his hypothesis if it was ill founded, and might expect that the
comparison would materially aid him in framing another more
conformable to the phenomena.

The doctrine now universally received that the earth is a natural
magnet, was originally an hypothesis of the celebrated Gilbert.

Another hypothesis, to the legitimacy of which no objection can lie,
and which is well calculated to light the path of scientific
inquiry, is that suggested by several recent writers, that the brain
is a voltaic pile, and that each of its pulsations is a discharge of
electricity through the system. It has been remarked that the
sensation felt by the hand from the beating of a brain, bears a
strong resemblance to a voltaic shock. And the hypothesis, if
followed to its consequences, might afford a plausible explanation
of many physiological facts, while there is nothing to discourage
the hope that we may in time sufficiently understand the conditions
of voltaic phenomena to render the truth of the hypothesis amenable
to observation and experiment.

The attempt to localize, in different regions of the brain, the
physical organs of our different mental faculties and propensities,
was, on the part of its original author, a legitimate example of a
scientific hypothesis; and we ought not, therefore, to blame him for
the extremely slight grounds on which he often proceeded, in an
operation which could only be tentative, though we may regret that
materials barely sufficient for a first rude hypothesis should have
been hastily worked up into the vain semblance of a science. If
there be really a connection between the scale of mental endowments
and the various degrees of complication in the cerebral system, the
nature of that connection was in no other way so likely to be
brought to light as by framing, in the first instance, an hypothesis
similar to that of Gall. But the verification of any such hypothesis
is attended, from the peculiar nature of the phenomena, with
difficulties which phrenologists have not shown themselves even
competent to appreciate, much less to overcome.

Mr. Darwin’s remarkable speculation on the Origin of Species is
another unimpeachable example of a legitimate hypothesis. What he
terms “natural selection” is not only a _vera causa_, but one proved
to be capable of producing effects of the same kind with those which
the hypothesis ascribes to it; the question of possibility is
entirely one of degree. It is unreasonable to accuse Mr. Darwin (as
has been done) of violating the rules of Induction. The rules of
Induction are concerned with the conditions of Proof. Mr. Darwin has
never pretended that his doctrine was proved. He was not bound by
the rules of Induction, but by those of Hypothesis. And these last
have seldom been more completely fulfilled. He has opened a path of
inquiry full of promise, the results of which none can foresee. And
is it not a wonderful feat of scientific knowledge and ingenuity to
have rendered so bold a suggestion, which the first impulse of every
one was to reject at once, admissible and discussible, even as a
conjecture?

165 Whewell’s _Phil. of Discovery_, pp. 275, 276.

166 What has most contributed to accredit the hypothesis of a physical
medium for the conveyance of light, is the certain fact that light
_travels_ (which can not be proved of gravitation); that its
communication is not instantaneous, but requires time; and that it
is intercepted (which gravitation is not) by intervening objects.
These are analogies between its phenomena and those of the
mechanical motion of a solid or fluid substance. But we are not
entitled to assume that mechanical motion is the only power in
nature capable of exhibiting those attributes.

_ 167 Phil. of Discovery_, p. 274.

168 P. 271.

169 P. 251 and the whole of Appendix G.

170 In Dr. Whewell’s latest version of his theory (_Philosophy of
Discovery_, p. 331) he makes a concession respecting the medium of
the transmission of light, which, taken in conjunction with the rest
of his doctrine on the subject, is not, I confess, very intelligible
to me, but which goes far toward removing, if it does not actually
remove, the whole of the difference between us. He is contending,
against Sir William Hamilton, that all matter has weight. Sir
William, in proof of the contrary, cited the luminiferous ether, and
the calorific and electric fluids, “which,” he said, “we can neither
denude of their character of substance, nor clothe with the
attribute of weight.” “To which,” continues Dr. Whewell, “my reply
is, that precisely because I can not clothe these agents with the
attribute of Weight, I _do_ denude them of the character of
Substance. They are not substances, but agencies. These Imponderable
Agents are not properly called Imponderable Fluids. This I conceive
that I have proved.” Nothing can be more philosophical. But if the
luminiferous ether is not matter, and fluid matter, too, what is the
meaning of its undulations? Can an agency undulate? Can there be
alternate motion forward and backward of the particles of an agency?
And does not the whole mathematical theory of the undulations imply
them to be material? Is it not a series of deductions from the known
properties of elastic fluids? _This_ opinion of Dr. Whewell reduces
the undulations to a figure of speech, and the undulatory theory to
the proposition which all must admit, that the transmission of light
takes place according to laws which present a very striking and
remarkable agreement with those of undulations. If Dr. Whewell is
prepared to stand by this doctrine, I have no difference with him on
the subject.

171 Thus water, of which eight-ninths in weight are oxygen, dissolves
most bodies which contain a high proportion of oxygen, such as all
the nitrates (which have more oxygen than any others of the common
salts), most of the sulphates, many of the carbonates, etc. Again,
bodies largely composed of combustible elements, like hydrogen and
carbon, are soluble in bodies of similar composition; resin, for
instance, will dissolve in alcohol, tar in oil of turpentine. This
empirical generalization is far from being universally true; no
doubt because it is a remote, and therefore easily defeated, result
of general laws too deep for us at present to penetrate; but it will
probably in time suggest processes of inquiry, leading to the
discovery of those laws.

172 Or, according to Laplace’s theory, the sun and the sun’s rotation.

173 Supra, book iii., chap. v., § 7.

174 Supra, book iii., chap. x., § 2

175 In the preceding discussion, the _mean_ is spoken of as if it were
exactly the same thing with the _average_. But the mean, for
purposes of inductive inquiry, is not the average, or arithmetical
mean, though in a familiar illustration of the theory the difference
may be disregarded. If the deviations on one side of the average are
much more numerous than those on the other (these last being fewer
but greater), the effect due to the invariable cause, as distinct
from the variable ones, will not coincide with the average, but will
be either below or above the average, the deviation being toward the
side on which the greatest number of the instances are found. This
follows from a truth, ascertained both inductively and deductively,
that small deviations from the true central point are greatly more
frequent than large ones. The mathematical law is, “that the most
probable determination of one or more invariable elements from
observation is that in which the _sum of the squares_ of the
individual aberrations,” or deviations, “_shall be the least
possible_.” See this principle stated, and its grounds popularly
explained, by Sir John Herschel, in his review of Quetelet on
Probabilities, _Essays_, p. 395 _et seq._

_ 176 Essai Philosophique sur les Probabilités_, fifth Paris edition, p.
7.

177 It even appears to me that the calculation of chances, where there
are no data grounded either on special experience or on special
inference, must, in an immense majority of cases, break down, from
sheer impossibility of assigning any principle by which to be guided
in setting out the list of possibilities. In the case of the colored
balls we have no difficulty in making the enumeration, because we
ourselves determine what the possibilities shall be. But suppose a
case more analogous to those which occur in nature: instead of three
colors, let there be in the box all possible colors, we being
supposed ignorant of the comparative frequency with which different
colors occur in nature, or in the productions of art. How is the
list of cases to be made out? Is every distinct shade to count as a
color? If so, is the test to be a common eye, or an educated eye—a
painter’s, for instance? On the answer to these questions would
depend whether the chances against some particular color would be
estimated at ten, twenty, or perhaps five hundred to one. While if
we knew from experience that the particular color occurs on an
average a certain number of times in every hundred or thousand, we
should not require to know any thing either of the frequency or of
the number of the other possibilities.

_ 178 Prospective Review_ for February, 1850.

179 “If this be not so, why do we feel so much more probability added by
the first instance than by any single subsequent instance? Why,
except that the first instance gives us its possibility (a cause
_adequate_ to it), while every other only gives us the frequency of
its conditions? If no reference to a cause be supposed, possibility
would have no meaning; yet it is clear that, antecedent to its
happening, we might have supposed the event impossible, _i.e._, have
believed that there was no physical energy really existing in the
world equal to producing it.... After the first time of happening,
which is, then, more important to the whole probability than any
other single instance (because proving the possibility), the
_number_ of times becomes important as an index to the intensity or
extent of the cause, and its independence of any particular time. If
we took the case of a tremendous leap, for instance, and wished to
form an estimate of the probability of its succeeding a certain
number of times; the first instance, by showing its possibility
(before doubtful) is of the most importance; but every succeeding
leap shows the power to be more perfectly under control, greater and
more invariable, and so increases the probability; and no one would
think of reasoning in this case straight from one instance to the
next, without referring to the physical energy which each leap
indicated. Is it not, then, clear that we do not ever” (let us
rather say, that we do not in an advanced state of our knowledge)
“conclude directly from the happening of an event to the probability
of its happening again; but that we refer to the cause, regarding
the past cases as an index to the cause, and the cause as our guide
to the future?”—_Ibid._

180 The writer last quoted says that the valuation of chances by
comparing the number of cases in which the event occurs with the
number in which it does not occur, “would generally be wholly
erroneous,” and “is not the true theory of probability.” It is at
least that which forms the foundation of insurance, and of all those
calculations of chances in the business of life which experience so
abundantly verifies. The reason which the reviewer gives for
rejecting the theory is, that it “would regard an event as certain
which had hitherto never failed; which is exceedingly far from the
truth, even for a very large number of constant successes.” This is
not a defect in a particular theory, but in any theory of chances.
No principle of evaluation can provide for such a case as that which
the reviewer supposes. If an event has never once failed, in a
number of trials sufficient to eliminate chance, it really has all
the certainty which can be given by an empirical law; it _is_
certain during the continuance of the same collocation of causes
which existed during the observations. If it ever fails, it is in
consequence of some change in that collocation. Now, no theory of
chances will enable us to infer the future probability of an event
from the past, if the causes in operation, capable of influencing
the event, have intermediately undergone a change.

181 Pp. 18, 19. The theorem is not stated by Laplace in the exact terms
in which I have stated it; but the identity of import of the two
modes of expression is easily demonstrable.

182 For a fuller treatment of the many interesting questions raised by
the theory of probabilities, I may now refer to a recent work by Mr.
Venn, Fellow of Caius College, Cambridge, “The Logic of Chance;” one
of the most thoughtful and philosophical treatises on any subject
connected with Logic and Evidence which have been produced, to my
knowledge, for many years. Some criticisms contained in it have been
very useful to me in revising the corresponding chapters of the
present work. In several of Mr. Venn’s opinions, however, I do not
agree. What these are will be obvious to any reader of Mr. Venn’s
work who is also a reader of this.

183 Hartley’s _Observations on Man_, vol. i., p. 16. The passage is not
in Priestley’s curtailed edition.

184 I am happy to be able to quote the following excellent passage from
Mr. Baden Powell’s _Essay on the Inductive Philosophy_, in
confirmation, both in regard to history and to doctrine, of the
statement made in the text. Speaking of the “conviction of the
universal and permanent uniformity of nature,” Mr. Powell says (pp.
98–100):

“We may remark that this idea, in its proper extent, is by no means
one of popular acceptance or natural growth. Just so far as the
daily experience of every one goes, so far indeed he comes to
embrace a certain persuasion of this kind, but merely to this
limited extent, that what is going on around him at present, in his
own narrow sphere of observation, will go on in like manner in
future. The peasant believes that the sun which rose to-day will
rise again to-morrow; that the seed put into the ground will be
followed in due time by the harvest this year as it was last year,
and the like; but has no notion of such inferences in subjects
beyond his immediate observation. And it should be observed that
each class of persons, in admitting this belief within the limited
range of his own experience, though he doubt or deny it in every
thing beyond, is, in fact, bearing unconscious testimony to its
universal truth. Nor, again, is it only among the _most_ ignorant
that this limitation is put upon the truth. There is a very general
propensity to believe that every thing beyond common experience, or
especially ascertained laws of nature, is left to the dominion of
chance or fate or arbitrary intervention; and even to object to any
attempted explanation by physical causes, if conjecturally thrown
out for an apparently unaccountable phenomenon.

“The precise doctrine of the _generalization_ of this idea of the
uniformity of nature, so far from being obvious, natural, or
intuitive, is utterly beyond the attainment of the many. In all the
extent of its universality it is characteristic of the philosopher.
It is clearly the result of philosophic cultivation and training,
and by no means the spontaneous offspring of any primary principle
naturally inherent in the mind, as some seem to believe. It is no
mere vague persuasion taken up without examination, as a common
prepossession to which we are always accustomed; on the contrary,
all common prejudices and associations are against it. It is
pre-eminently _an acquired idea_. It is not attained without deep
study and reflection. The best informed philosopher is the man who
most firmly believes it, even in opposition to received notions; its
acceptance depends on the extent and profoundness of his inductive
studies.”

185 Supra, book iii., chap. iii., § 1

186 It deserves remark, that these early generalizations did not, like
scientific inductions, presuppose causation. What they did
presuppose, was _uniformity_ in physical facts. But the observers
were as ready to presume uniformity in the co-existence of facts as
in the sequences. On the other hand, they never thought of assuming
that this uniformity was a principle pervading all nature: their
generalizations did not imply that there was uniformity in every
thing, but only that as much uniformity as existed within their
observation, existed also beyond it. The induction, fire burns, does
not require for its validity that all nature should observe uniform
laws, but only that there should be uniformity in one particular
class of natural phenomena; the effects of fire on the senses and on
combustible substances. And uniformity to this extent was not
assumed, anterior to the experience, but proved by the experience.
The same observed instances which proved the narrower truth, proved
as much of the wider one as corresponded to it. It is from losing
sight of this fact, and considering the law of causation in its full
extent as necessarily presupposed in the very earliest
generalizations, that persons have been led into the belief that the
law of causation is known _a priori_, and is not itself a conclusion
from experience.

187 Book ii., chap. iii.

188 One of the most rising thinkers of the new generation in France, M.
Taine (who has given, in the _Revue des Deux Mondes_, the most
masterly analysis, at least in one point of view, ever made of the
present work), though he rejects, on this and similar points of
psychology, the intuition theory in its ordinary form, nevertheless
assigns to the law of causation, and to some other of the most
universal laws, that certainty beyond the bounds of human
experience, which I have not been able to accord to them. He does
this on the faith of our faculty of abstraction, in which he seems
to recognize an independent source of evidence, not indeed
disclosing truths not contained in our experience, but affording an
assurance which experience can not give, of the universality of
those which it does contain. By abstraction M. Taine seems to think
that we are able, not merely to analyze that part of nature which we
see, and exhibit apart the elements which pervade it, but to
distinguish such of them as are elements of the system of nature
considered as a whole, not incidents belonging to our limited
terrestrial experience. I am not sure that I fully enter into M.
Taine’s meaning; but I confess I do not see how any mere abstract
conception, elicited by our minds from our experience, can be
evidence of an objective fact in universal Nature, beyond what the
experience itself bears witness of; or how, in the process of
interpreting in general language the testimony of experience, the
limitations of the testimony itself can be cast off.

Dr. Ward, in an able article in the _Dublin Review_ for October,
1871, contends that the uniformity of nature can not be proved from
experience, but from “transcendental considerations” only, and that,
consequently, all physical science would be deprived of its basis,
if such transcendental proof were impossible.

When physical science is said to depend on the assumption that the
course of nature is invariable, all that is meant is that the
conclusions of physical science are not known as _absolute_ truths:
the truth of them is _conditional_ on the uniformity of the course
of nature; and all that the most conclusive observations and
experiments can prove, is that the result arrived at will be true
if, and as long as, the present laws of nature are valid. But this
is all the assurance we require for the guidance of our conduct. Dr.
Ward himself does not think that his transcendental proofs make it
practically greater; for he believes, as a Catholic, that the course
of nature not only has been, but frequently and even daily is,
suspended by supernatural intervention.

But though this conditional conclusiveness of the evidence of
experience, which is sufficient for the purposes of life, is all
that I was necessarily concerned to prove, I have given reasons for
thinking that the uniformity, as itself a part of experience, is
sufficiently proved to justify undoubting reliance on it. This Dr.
Ward contests, for the following reasons:

First (p. 315), supposing it true that there has hitherto been no
well authenticated case of a breach in the uniformity of nature;
“the number of natural agents constantly at work is incalculably
large; and the observed cases of uniformity in their action must be
immeasurably fewer than one thousandth of the whole. Scientific men,
we assume for the moment, have discovered that in a certain
proportion of instances—immeasurably fewer than one thousandth of
the whole—a certain fact has prevailed; the fact of uniformity; and
they have not found a single instance in which that fact does _not_
prevail. Are they justified, we ask, in inferring from these
premises that the fact is universal? Surely the question answers
itself. Let us make a very grotesque supposition, in which, however,
the conclusion would really be tried according to the arguments
adduced. In some desert of Africa there is an enormous connected
edifice, surrounding some vast space, in which dwell certain
reasonable beings, who are unable to leave the inclosure. In this
edifice are more than a thousand chambers, which some years ago were
entirely locked up, and the keys no one knew where. By constant
diligence twenty-five keys have been found, out of the whole number;
and the corresponding chambers, situated promiscuously throughout
the edifice, have been opened. Each chamber, when examined, is found
to be in the precise shape of a dodecahedron. Are the inhabitants
justified on that account in holding with certitude that the
remaining 975 chambers are built on the same plan?”

Not with perfect certitude, but (if the chambers to which the keys
have been found are really “situated promiscuously”) with so high a
degree of probability that they would be justified in acting upon
the presumption until an exception appeared.

Dr. Ward’s argument, however, does not touch mine as it stands in
the text. My argument is grounded on the fact that the uniformity of
the course of nature as a whole, is constituted by the uniform
sequences of special effects from special natural agencies; that the
number of these natural agencies in the part of the universe known
to us is not incalculable, nor even extremely great; that we have
now reason to think that at least the far greater number of them, if
not separately, at least in some of the combinations into which they
enter, have been made sufficiently amenable to observation, to have
enabled us actually to ascertain some of their fixed laws; and that
this amount of experience justifies the same degree of assurance
that the course of nature is uniform throughout, which we previously
had of the uniformity of sequence among the phenomena best known to
us. This view of the subject, if correct, destroys the force of Dr.
Ward’s first argument.

His second argument is, that many or most persons, both scientific
and unscientific, believe that there _are_ well authenticated cases
of breach in the uniformity of nature, namely, miracles. Neither
does this consideration touch what I have said in the text. I admit
no other uniformity in the events of nature than the law of
Causation; and (as I have explained in the chapter of this volume
which treats of the Grounds of Disbelief) a miracle is no exception
to that law. In every case of alleged miracle, a _new antecedent_ is
affirmed to exist; a _counteracting cause_, namely, the volition of
a supernatural being. To all, therefore, to whom beings with
superhuman power over nature are a _vera causa_, a miracle is a
_case_ of the Law of Universal Causation, not a deviation from it.

Dr. Ward’s last, and as he says, strongest argument, is the familiar
one of Reid, Stewart, and their followers—that whatever knowledge
experience gives us of the past and present, it gives us none of the
future. I confess that I see no force whatever in this argument.
Wherein does a future fact differ from a present or a past fact,
except in their merely momentary relation to the human beings at
present in existence? The answer made by Priestley, in his
_Examination of Reid_, seems to me sufficient, viz., that though we
have had no experience of what _is_ future, we have had abundant
experience of what _was_ future. The “leap in the dark” (as
Professor Bain calls it) from the past to the future, is exactly as
much in the dark and no more, as the leap from a past which we have
personally observed, to a past which we have not. I agree with Mr.
Bain in the opinion that the resemblance of what we have not
experienced to what we have, is, by a law of our nature, presumed
through the mere energy of the idea, before experience has proved
it. This _psychological_ truth, however, is not, as Dr. Ward when
criticising Mr. Bain appears to think, inconsistent with the
_logical_ truth that experience does prove it. The proof comes after
the presumption, and consists in its invariable _verification_ by
experience when the experience arrives. The fact which while it was
future could not be observed, having as yet no existence, is always,
when it becomes present and _can_ be observed, found conformable to
the past.

Dr. M’Cosh maintains (_Examination of Mr. J. S. Mill’s Philosophy_,
p. 257) that the uniformity of the course of nature is a different
thing from the law of causation; and while he allows that the former
is only proved by a long continuance of experience, and that it is
not inconceivable nor necessarily incredible that there may be
worlds in which it does not prevail, he considers the law of
causation to be known intuitively. There is, however, no other
uniformity in the events of nature than that which arises from the
law of causation: so long therefore as there remained any doubt that
the course of nature was uniform throughout, at least when not
modified by the intervention of a new (supernatural) cause, a doubt
was necessarily implied, not indeed of the reality of causation, but
of its universality. If the uniformity of the course of nature has
any exceptions—if any events succeed one another without fixed
laws—to that extent the law of causation fails; there are events
which do not depend on causes.

189 Book i., chap. vii.

190 In some cases, a Kind is sufficiently identified by some one
remarkable property: but most commonly several are required; each
property considered singly, being a joint property of that and of
other Kinds. The color and brightness of the diamond are common to
it with the paste from which false diamonds are made; its octohedral
form is common to it with alum, and magnetic iron ore; but the color
and brightness and the form together, identify its Kind: that is,
are a mark to us that it is combustible; that when burned it
produces carbonic acid; that it can not be cut with any known
substance; together with many other ascertained properties, and the
fact that there exist an indefinite number still unascertained.

191 This doctrine of course assumes that the allotropic forms of what is
chemically the same substance are so many different Kinds; and such,
in the sense in which the word Kind is used in this treatise, they
really are.

192 Professor Bain (Logic, ii., 13) mentions two empirical laws, which
he considers to be, with the exception of the law connecting Gravity
with Resistance to motion, “the two most widely operating laws as
yet discovered whereby two distinct properties are conjoined
throughout substances generally.” The first is, “a law connecting
Atomic Weight and Specific Heat by an inverse proportion. For equal
weights of the simple bodies, the atomic weight multiplied by a
number expressing the specific heat, gives a nearly uniform product.
The products, for all the elements, are near the constant number 6.”
The other is a law which obtains “between the specific gravity of
substances in the gaseous state, and the atomic weights. The
relationship of the two numbers is in some instances equality; in
other instances the one is a multiple of the other.”

Neither of these generalizations has the smallest appearance of
being an ultimate law. They point unmistakably to higher laws. Since
the heat necessary to raise to a given temperature the same weight
of different substances (called their specific heat) is inversely as
their atomic weight, that is, directly as the number of atoms in a
given weight of the substance, it follows that a single atom of
every substance requires the same amount of heat to raise it to a
given temperature; a most interesting and important law, but a law
of causation. The other law mentioned by Mr. Bain points to the
conclusion, that in the gaseous state all substances contain, in the
same space, the same number of atoms; which, as the gaseous state
suspends all cohesive force, might naturally be expected, though it
could not have been positively assumed. This law may also be a
result of the mode of action of causes, namely, of molecular
motions. The cases in which one of the numbers is not identical with
the other, but a multiple of it, may be explained on the nowise
unlikely supposition, that in our present estimate of the atomic
weights of some substances, we mistake two, or three, atoms for one,
or one for several.

193 Dr. M’Cosh (p. 324 of his book) considers the laws of the chemical
composition of bodies as not coming under the principle of
Causation; and thinks it an omission in this work not to have
provided special canons for their investigation and proof. But every
case of chemical composition is, as I have explained, a case of
causation. When it is said that water is composed of hydrogen and
oxygen, the affirmation is that hydrogen and oxygen, by the action
on one another which they exert under certain conditions, _generate_
the properties of water. The Canons of Induction, therefore, as laid
down in this treatise, are applicable to the case. Such special
adaptations as the Inductive methods may require in their
application to chemistry, or any other science, are a proper subject
for any one who treats of the logic of the special sciences, as
Professor Bain has done in the latter part of his work; but they do
not appertain to General Logic.

Dr. M’Cosh also complains (p. 325) that I have given no canons for
those sciences in which “the end sought is not the discovery of
Causes or of Composition, but of Classes; that is, Natural Classes.”
Such canons could be no other than the principles and rules of
Natural Classification, which I certainly thought that I had
expounded at considerable length. But this is far from the only
instance in which Dr. M’Cosh does not appear to be aware of the
contents of the books he is criticising.

194 Mr. De Morgan, in his _Formal Logic_, makes the just remark, that
from two such premises as Most A are B, and Most A are C, we may
infer with certainty that some B are C. But this is the utmost limit
of the conclusions which can be drawn from two approximate
generalizations, when the precise degree of their approximation to
universality is unknown or undefined.

_ 195 Rationale of Judicial Evidence_, vol. iii., p. 224.

196 The evaluation of the chances in this statement has been objected to
by a mathematical friend. The correct mode, in his opinion, of
setting out the possibilities is as follows. If the thing (let us
call it T) which is both an A and a C, is a B, something is true
which is only true twice in every thrice, and something else which
is only true thrice in every four times. The first fact being true
eight times in twelve, and the second being true six times in every
eight, and consequently six times in those eight; both facts will be
true only six times in twelve. On the other hand, if T, although it
is both an A and a C, is not a B, something is true which is only
true once in every thrice, and something else which is only true
once in every four times. The former being true four times out of
twelve, and the latter once in every four, and therefore once in
those four; both are only true in one case out of twelve. So that T
is a B six times in twelve, and T is not a B, only once: making the
comparative probabilities, not eleven to one, as I had previously
made them, but six to one.

In the last edition I accepted this reasoning as conclusive. More
attentive consideration, however, has convinced me that it contains
a fallacy.

The objector argues, that the fact of A’s being a B is true eight
times in twelve, and the fact of C’s being a B six times in eight,
and consequently six times in those eight; both facts, therefore,
are true only six times in every twelve. That is, he concludes that
because among As taken indiscriminately only eight out of twelve are
Bs and the remaining four are not, it must equally hold that four
out of twelve are not Bs when the twelve are taken from the select
portion of As which are also Cs. And by this assumption he arrives
at the strange result, that there are fewer Bs among things which
are both As and Cs than there are among either As or Cs taken
indiscriminately; so that a thing which has both chances of being a
B, is less likely to be so than if it had only the one chance or
only the other.

The objector (as has been acutely remarked by another correspondent)
applies to the problem under consideration, a mode of calculation
only suited to the reverse problem. Had the question been—If two of
every three Bs are As and three out of every four Bs are Cs, how
many Bs will be both As and Cs, his reasoning would have been
correct. For the Bs that are both As and Cs must be fewer than
either the Bs that are As or the Bs that are Cs, and to find their
number we must abate either of these numbers in the ratio due to the
other. But when the problem is to find, not how many Bs are both As
and Cs, but how many things that are both As and Cs are Bs, it is
evident that among these the proportion of Bs must be not less, but
greater, than among things which are only A, or among things which
are only B.

The true theory of the chances is best found by going back to the
scientific grounds on which the proportions rest. The degree of
frequency of a coincidence depends on, and is a measure of, the
frequency, combined with the efficacy, of the causes in operation
that are favorable to it. If out of every twelve As taken
indiscriminately eight are Bs and four are not, it is implied that
there are causes operating on A which tend to make it a B, and that
these causes are sufficiently constant and sufficiently powerful to
succeed in eight out of twelve cases, but fail in the remaining
four. So if of twelve Cs, nine are Bs and three are not, there must
be causes of the same tendency operating on C, which succeed in nine
cases and fail in three. Now suppose twelve cases which are both As
and Cs. The whole twelve are now under the operation of both sets of
causes. One set is sufficient to prevail in eight of the twelve
cases, the other in nine. The analysis of the cases shows that six
of the twelve will be Bs through the operation of both sets of
causes; two more in virtue of the causes operating on A; and three
more through those operating on C, and that there will be only one
case in which all the causes will be inoperative. The total number,
therefore, which are Bs will be eleven in twelve, and the evaluation
in the text is correct.

197 Supra, book i., chap. v.

198 Supra, book i., chap. v., § 1, and book ii., chap, v., § 5.

199 The axiom, “Equals subtracted from equals leave equal differences,”
may be demonstrated from the two axioms in the text. If A = _a_ and
B = _b_, A-B = _a-b_. For if not, let A-B = _a-b+c_. Then since B =
_b_, adding equals to equals, A = _a+c_. But A = _a_. Therefore _a =
a+c_, which is impossible.

This proposition having been demonstrated, we may, by means of it,
demonstrate the following: “If equals be added to unequals, the sums
are unequal.” If A = _a_ and B not = _b_, A+B is not = _a+b_. For
suppose it to be so. Then, since A = _a_ and A+B = _a+b_,
subtracting equals from equals, B = _b_; which is contrary to the
hypothesis.

So again, it may be proved that two things, one of which is equal
and the other unequal to a third thing, are unequal to one another.
If A = _a_ and A not = B, neither is _a_ = B. For suppose it to be
equal. Then since A = _a_ and _a_ = B, and since things equal to the
same thing are equal to one another A = B; which is contrary to the
hypothesis.

200 Geometers have usually preferred to define parallel lines by the
property of being in the same plane and never meeting. This,
however, has rendered it necessary for them to assume, as an
additional axiom, some other property of parallel lines; and the
unsatisfactory manner in which properties for that purpose have been
selected by Euclid and others has always been deemed the opprobrium
of elementary geometry. Even as a verbal definition, equidistance is
a fitter property to characterize parallels by, since it is the
attribute really involved in the signification of the name. If to be
in the same plane and never to meet were all that is meant by being
parallel, we should feel no incongruity in speaking of a curve as
parallel to its asymptote. The meaning of parallel lines is, lines
which pursue exactly the same direction, and which, therefore,
neither draw nearer nor go farther from one another; a conception
suggested at once by the contemplation of nature. That the lines
will never meet is of course included in the more comprehensive
proposition that they are everywhere equally distant. And that any
straight lines which are in the same plane and not equidistant will
certainly meet, may be demonstrated in the most rigorous manner from
the fundamental property of straight lines assumed in the text,
viz., that if they set out from the same point, they diverge more
and more without limit.

_ 201 Philosophie Positive_, iii., 414–416.

202 See the two remarkable notes (A) and (F), appended to his _Inquiry
into the Relation of Cause and Effect_.

203 Supra, p. 413.

204 A writer to whom I have several times referred, gives as the
definition of an impossibility, that which there exists in the world
no cause adequate to produce. This definition does not take in such
impossibilities as these—that two and two should make five; that two
straight lines should inclose a space; or that any thing should
begin to exist without a cause. I can think of no definition of
impossibility comprehensive enough to include all its varieties,
except the one which I have given: viz., An impossibility is that,
the truth of which would conflict with a complete induction, that
is, with the most conclusive evidence which we possess of universal
truth.

As to the reputed impossibilities which rest on no other grounds
than our ignorance of any cause capable of producing the supposed
effects; very few of them are certainly impossible, or permanently
incredible. The facts of traveling seventy miles an hour, painless
surgical operations, and conversing by instantaneous signals between
London and New York, held a high place, not many years ago, among
such impossibilities.