Chapter XIII: Miscellaneous Examples of the Explanation of Laws of Nature (2)

27 “Few people” (I have said in another place) “have reflected how
great a knowledge of Things is required to enable a man to affirm
that any given argument turns wholly upon words. There is, perhaps,
not one of the leading terms of philosophy which is not used in
almost innumerable shades of meaning, to express ideas more or less
widely different from one another. Between two of these ideas a
sagacious and penetrating mind will discern, as it were intuitively,
an unobvious link of connexion, upon which, though perhaps unable to
give a logical account of it, he will found a perfectly valid
argument, which his critic, not having so keen an insight into the
Things, will mistake for a fallacy turning on the double meaning of
a term. And the greater the genius of him who thus safely leaps over
the chasm, the greater will probably be the crowing and vain-glory
of the mere logician, who, hobbling after him, evinces his own
superior wisdom by pausing on its brink, and giving up as desperate
his proper business of bridging it over.”

28 Contraries:
All A is B
No A is B

Subtraries:
Some A is B
Some A is not B

Contradictories:
All A is B
Some A is not B

Also contradictories:
No A is B
Some A is B

Respectively subalternate:
All A is B; No A is B
Some A is B; and Some A is not B

29 His conclusions are, “The first figure is suited to the discovery or
proof of the properties of a thing; the second to the discovery or
proof of the distinctions between things; the third to the discovery
or proof of instances and exceptions; the fourth to the discovery,
or exclusion, of the different species of a genus.” The reference of
syllogisms in the last three figures to the _dictum de omni et
nullo_ is, in Lambert’s opinion, strained and unnatural: to each of
the three belongs, according to him, a separate axiom, co-ordinate
and of equal authority with that _dictum_, and to which he gives the
names of _dictum de diverso_ for the second figure, _dictum de
exemplo_ for the third, and _dictum de reciproco_ for the fourth.
See part i. or _Dianoiologie_, chap. iv. § 229 _et seqq._

Mr. De Morgan’s “Formal Logic, or the Calculus of Inference,
Necessary and Probable,” (a work published since the statement in
the text was made,) far exceeds in elaborate minuteness Lambert’s
treatise on the syllogism. Mr. De Morgan’s principal object is to
bring within strict technical rules the cases in which a conclusion
can be drawn from premisses of a form usually classed as particular.
He observes, very justly, that from the premisses Most Bs are Cs,
most Bs are As, it may be concluded with certainty that some As are
Cs, since two portions of the class B, each of them comprising more
than half, must necessarily in part consist of the same individuals.
Following out this line of thought, it is equally evident that if we
knew exactly what proportion the “most” in each of the premisses
bear to the entire class B, we could increase in a corresponding
degree the definiteness of the conclusion. Thus if 60 per cent of B
are included in C, and 70 per cent in A, 30 per cent at least must
be common to both; in other words, the number of As which are Cs,
and of Cs which are As, must be at least equal to 30 per cent of the
class B. Proceeding on this conception of “numerically definite
propositions,” and extending it to such forms as these:—“45 Xs (or
more) are each of them one of 70 Ys,” or “45 Xs (or more), are no
one of them to be found among 70 Ys,” and examining what inferences
admit of being drawn from the various combinations which may be made
of premisses of this description, Mr. De Morgan establishes
universal formulæ for such inferences; creating for that purpose not
only a new technical language, but a formidable array of symbols
analogous to those of algebra.

Since it is undeniable that inferences, in the cases examined by Mr.
De Morgan, can legitimately be drawn, and that the ordinary theory
takes no account of them, I will not say that it was not worth while
to show in detail how these also could be reduced to formulae as
rigorous as those of Aristotle. What Mr. De Morgan has done was
worth doing once (perhaps more than once, as a school exercise); but
I question if its results are worth studying and mastering for any
practical purpose. The practical use of technical forms of reasoning
is to bar out fallacies: but the fallacies which require to be
guarded against in ratiocination properly so called, arise from the
incautious use of the common forms of language; and the logician
must track the fallacy into that territory, instead of waiting for
it on a territory of his own. While he remains among propositions
which have acquired the numerical precision of the Calculus of
Probabilities, the enemy is left in possession of the only ground on
which he can be formidable. The “quantification of the predicate,”
an invention to which Sir William Hamilton attaches so much
importance as to have raised an angry dispute with Mr. De Morgan
respecting its authorship, appears to me, I confess, as an accession
to the art of Logic, of singularly small value. It is of course
true, that “All men are mortal” is equivalent to “Every man is
_some_ mortal.” But as mankind certainly will not be persuaded to
“quantify” their predicates in common discourse, they want a logic
which will teach them to reason correctly with propositions in the
usual form, by furnishing them with a type of ratiocination to which
propositions can be referred, retaining that form. Not to mention
that the quantification of the predicate, instead of being a means
of bringing out more clearly the meaning of the proposition,
actually leads the mind out of the proposition, into another order
of ideas. For when we say, All men are mortal, we simply mean to
affirm the attribute mortality of all men; without thinking at all
of the _class_ mortal in the concrete, or troubling ourselves about
whether it contains any other beings or not. It is only for some
artificial purpose that we ever look at the proposition in the
aspect in which the predicate also is thought of as a class-name,
either including the subject only, or the subject and something
more.

30 Suprà, p. 129.

31 Logic, p. 239 (9th ed.)

32 It is hardly necessary to say, that I am not contending for any such
absurdity as that we _actually_ “ought to have known” and considered
the case of every individual man, past, present, and future, before
affirming that all men are mortal: although this interpretation has
been, strangely enough, put upon the preceding observations. There
is no difference between me and Archbishop Whately, or any other
defender of the syllogism, on the practical part of the matter; I am
only pointing out an inconsistency in the logical theory of it, as
conceived by almost all writers. I do not say that a person who
affirmed, before the Duke of Wellington was born, that all men are
mortal, _knew_ that the Duke of Wellington was mortal; but I do say,
that he _asserted_ it; and I ask for an explanation of the apparent
logical fallacy, of adducing in proof of the Duke of Wellington’s
mortality, a general statement which presupposes it. Finding no
sufficient resolution of this difficulty in any of the writers on
Logic, I have attempted to supply one.

_ 33 Of Induction_, p. 85.

34 For August 1846.

35 There is a striking passage in the Metaphysics of Aristotle
(commencement of chap. iii.) on the necessity of beginning the study
of a subject by a clear perception of its difficulties. Εστί τοῖς
εὐπορῆσαι βουλομένοις προῦργου τὸ διαπορῆσαι καλῶς. ἡ γὰρ ὕστερον
εὐπορία λύσις των πρότερον ἀπορουμένων ἐστί. λύειν δ᾽ οὐκ ἔστιν
ἀγνοοῦντα τὸν δεσμόν: ἀλλ᾽ ἡ της διανοίας ἀπορία δηλοῖ τοῦτο περὶ
τοῦ πράγματος ... διὸ δεῖ τὰς δυσχερείας τελεωρηκέναι πάσας
πρότερον, τούτων τε χάριν καὶ διὰ τὸ τοὺς ζητοῦντας ἄνευ τοῦ
διαπορῆσαι πρῶτον, ὁμοίους εἰναὶ τοῖς ποῖ δει βαδίζειν ἀγνοοῦσι: καὶ
πρὸς τούτοις, οὐδ᾽ ἐί ποτε τὸ ζητούμενον εὕρηκεν ἣ μὴ, γενώσκειν. τὸ
γὰρ τέλος τούτῳ μὲν οὐ δῆλον, τῳ δὲ καλῶς προηπορκότι δῆλον.

36 The reviewer misunderstands me when he supposes me to say that “the
conclusion must be admitted _before_ we can admit the major
premiss.” What I say is, that there must be ground for admitting it
_simultaneously_, or else the major premise is not proved.

_ 37 Mechanical Euclid_, pp. 149 _et seqq._

38 We might, it is true, insert this property into the definition of
parallel lines, framing the definition so as to require, _both_ that
when produced indefinitely they shall never meet, and _also_ that
any straight line which intersects one of them shall, if prolonged,
meet the other. But by doing this we by no means get rid of the
assumption; we are still obliged to take for granted the geometrical
truth, that all straight lines in the same plane, which have the
former of these properties, have also the latter. For if it were
possible that they should not, that is, if any straight lines other
than those which are parallel according to the definition, had the
property of never meeting although indefinitely produced, the
demonstrations of the subsequent portions of the theory of parallels
could not be maintained.

39 Whewell’s _Philosophy of the Inductive Sciences_, i. 130.

40 Dr. Whewell (_Of Induction_ p. 84) thinks it unreasonable to contend
that we know by experience, that our idea of a line exactly
resembles a real line. “It does not appear,” he says, “how we can
compare our ideas with the realities, since we know the realities
only by our ideas.” We know the realities (I conceive) by our eyes.
Dr. Whewell surely does not hold the “doctrine of perception by
means of ideas,” which Reid gave himself so much trouble to refute.

Dr. Whewell also says, that it does not appear why this resemblance
of ideas to the sensations of which they are copies, should be
spoken of as if it were a peculiarity of one class of ideas, those
of space. My reply is, that I do not so speak of it. The peculiarity
I contend for is only one of degree. All our ideas of sensation of
course resemble the corresponding sensations, but they do so with
very different degrees of exactness and of reliability. No one, I
presume, can recall in imagination a colour or an odour with the
same distinctness and accuracy with which almost every one can
mentally reproduce an image of a straight line or a triangle. To the
extent, however, of their capabilities of accuracy, our
recollections of colours or of odours may serve as subjects of
experimentation, as well as those of lines and spaces, and may yield
conclusions which will be true of their external prototypes. A
person in whom, either from natural gift or from cultivation, the
impressions of colour were peculiarly vivid and distinct, if asked
which of two blue flowers was of the darkest tinge, though he might
never have compared the two, or even looked at them together, might
be able to give a confident answer on the faith of his distinct
recollection of the colours; that is, he might examine his mental
pictures, and find there a property of the outward objects. But in
hardly any case except that of simple geometrical forms, could this
be done by mankind generally, with a degree of assurance equal to
that which is given by a contemplation of the objects themselves.
Persons differ most widely in the precision of their recollection,
even of forms: one person, when he has looked any one in the face
for half a minute, can draw an accurate likeness of him from memory;
another may have seen him every day for six months, and hardly know
whether his nose is long or short. But everybody has a perfectly
distinct mental image of a straight line, a circle, or a rectangle.
And every one concludes confidently from these mental images to the
corresponding outward things.

_ 41 Phil. Ind. Sc._ i. 59-61.

42 Ibid. 57.

43 Ibid. 54, 55.

44 “If all mankind had spoken one language, we cannot doubt that there
would have been a powerful, perhaps a universal, school of
philosophers, who would have believed in the inherent connexion
between names and things, who would have taken the sound _man_ to be
the mode of agitating the air which is essentially communicative of
the ideas of reason, cookery, bipedality, &c.” De Morgan, _Formal
Logic_, p. 246.

45 It would be difficult to name a man more remarkable at once for the
greatness and the wide range of his mental accomplishments, than
Leibnitz. Yet this eminent man gave as a reason for rejecting
Newton’s scheme of the solar system, that God _could not_ make a
body revolve round a distant centre, unless either by some impelling
mechanism, or by miracle:—“Tout ce qui n’est pas explicable,” says
he in a letter to the Abbé Conti, “par la nature des créatures, est
miraculeux. Il ne suffit pas de dire: Dieu a fait une telle loi de
nature; donc la chose est naturelle. Il faut que la loi soit
exécutable par les natures des créatures. Si Dieu donnait cette loi,
par exemple, à un corps libre, de tourner à l’entour d’un certain
centre, _il faudrait ou qu’il y joignît d’autres corps qui par leur
impulsion l’obligeassent de rester toujours dans son orbite
circulaire, ou quil mît un ange à ses trousses, ou enfin il faudrait
qu’il y concourût extraordinairement_; car naturellement il
s’écartera par la tangente.”—_Works of Leibnitz_, ed. Dutens, iii.
446.

_ 46 Phil. Ind. Sc._ ii. 174.

_ 47 Phil. Ind. Sc._ i., 238.

_ 48 Phil. Ind. Sc._ i. 237.

_ 49 Ibid._ 213.

_ 50 Ibid._ 384, 385.

51 In his recent pamphlet (p. 81), Dr. Whewell greatly attenuates the
opinion here quoted, reducing it to a surmise “that if we could
conceive the composition of bodies distinctly, we might be able to
see that it is necessary that the modes of their composition should
be definite.” The passage in the text asserts that we already see,
or may and ought to see, this necessity; giving as the reason, that
no other mode of combination is conceivable. That Dr. Whewell should
ever have made this statement, is enough for the purposes of my
illustration. To what he now says I have nothing to object.
Undoubtedly, if we understood the ultimate molecular composition of
bodies, we might find that their combining with one another in
definite proportions is, in the present order of nature, a
_necessary consequence_ of that molecular composition; and has thus
the only kind of necessity of which, in my view of the subject, any
law of nature is susceptible. But in that case, the doctrine would
be taken out of the class of axioms altogether. It would be no
longer an ultimate principle, but a mere derivative law; regarded as
necessary, not because self-evident, but because demonstrable.

52 The _Quarterly Review_ for June 1841, contains an article of great
ability on Dr. Whewell’s two great works, the writer of which
maintains, on the subject of axioms, the doctrine advanced in the
text, that they are generalizations from experience, and supports
that opinion by a line of argument strikingly coinciding with mine.
When I state that the whole of the present chapter was written
before I had seen the article, (the greater part, indeed, before it
was published,) it is not my object to occupy the reader’s attention
with a matter so unimportant as the degree of originality which may
or may not belong to any portion of my own speculations, but to
obtain for an opinion which is opposed to reigning doctrines, the
recommendation derived from a striking concurrence of sentiment
between two inquirers entirely independent of one another. I embrace
the opportunity of citing from a writer of the extensive
acquirements in physical and metaphysical knowledge and the capacity
of systematic thought which the article evinces, passages so
remarkably in unison with my own views as the following:—

“The truths of geometry are summed up and embodied in its
definitions and axioms.... Let us turn to the axioms, and what do we
find? A string of propositions concerning magnitude in the abstract,
which are equally true of space, time, force, number, and every
other magnitude susceptible of aggregation and subdivision. Such
propositions, where they are not mere definitions, as some of them
are, carry their inductive origin on the face of their
enunciation.... Those which declare that two straight lines cannot
inclose a space, and that two straight lines which cut one another
cannot both be parallel to a third, are in reality the only ones
which express characteristic properties of space, and these it will
be worth while to consider more nearly. Now the only clear notion we
can form of straightness is uniformity of direction, for space in
its ultimate analysis is nothing but an assemblage of distances and
directions. And (not to dwell on the notion of continued
contemplation, _i.e._, mental experience, as included in the very
idea of uniformity; nor on that of transfer of the contemplating
being from point to point, and of experience, during such transfer,
of the homogeneity of the interval passed over) we cannot even
propose the proposition in an intelligible form, to any one whose
experience ever since he was born has not assured him of the fact.
The unity of direction, or that we cannot march from a given point
by more than one path direct to the same object, is matter of
practical experience long before it can by possibility become matter
of abstract thought. _We cannot attempt mentally to exemplify the
conditions of the assertion in an imaginary case opposed to it,
without violating our habitual recollection of this experience, and
defacing our mental picture of space as grounded on it._ What but
experience, we may ask, can possibly assure us of the homogeneity of
the parts of distance, time, force, and measurable aggregates in
general, on which the truth of the other axioms depends? As regards
the latter axiom, after what has been said it must be clear that the
very same course of remarks equally applies to its case, and that
its truth is quite as much forced on the mind as that of the former
by daily and hourly experience ... _including always, be it
observed, in our notion of experience, that which is gained by
contemplation of the inward picture which the mind forms to itself
in any proposed case, or which it arbitrarily selects as an
example—such picture, in virtue of the extreme simplicity of these
primary relations, being called up by the imagination with as much
vividness and clearness as could be done by any external impression,
which is the only meaning we can attach to the word intuition, as
applied to such relations._”

And again, of the axioms of mechanics:—“As we admit no such
propositions, other than as truths inductively collected from
observation, even in geometry itself, it can hardly be expected
that, in a science of obviously contingent relations, we should
acquiesce in a contrary view. Let us take one of these axioms and
examine its evidence: for instance, that equal forces
perpendicularly applied at the opposite ends of equal arms of a
straight lever will balance each other. What but experience, we may
ask, in the first place, can possibly inform us that a force so
applied will have any tendency to turn the lever on its centre at
all? or that force can be so transmitted along a rigid line
perpendicular to its direction, as to act elsewhere in space than
along its own line of action? Surely this is so far from being
self-evident that it has even a paradoxical appearance, which is
only to be removed by giving our lever thickness, material
composition, and molecular powers. Again we conclude, that the two
forces, being equal and applied under precisely similar
circumstances, must, if they exert any effort at all to turn the
lever, exert equal and opposite efforts: but what _à priori_
reasoning can possibly assure us that they _do_ act under precisely
similar circumstances? that points which differ in place _are_
similarly circumstanced as regards the exertion of force? that
universal space may not have relations to universal force—or, at all
events, that the organization of the material universe may not be
such as to place that portion of space occupied by it in such
relations to the forces exerted in it, as may invalidate the
absolute similarity of circumstances assumed? Or we may argue, what
have we to do with the notion of angular movement in the lever at
all? The case is one of rest, and of quiescent destruction of force
by force. Now how is this destruction effected? Assuredly by the
counter-pressure which supports the fulcrum. But would not this
destruction equally arise, and by the same amount of counteracting
force, if each force simply pressed its own half of the lever
against the fulcrum? And what can assure us that it is not so,
except removal of one or other force, and consequent tilting of the
lever? The other fundamental axiom of statics, that the pressure on
the point of support is the sum of the weights ... is merely a
scientific transformation and more refined mode of stating a coarse
and obvious result of universal experience, viz. that the weight of
a rigid body is the same, handle it or suspend it in what position
or by what point we will, and that whatever sustains it sustains its
total weight. Assuredly, as Mr. Whewell justly remarks, ‘No one
probably ever made a trial for the purpose of showing that the
pressure on the support is equal to the sum of the weights’ ... But
it is precisely because in every action of his life from earliest
infancy he has been continually making the trial, and seeing it made
by every other living being about him, that he never dreams of
staking its result on one additional attempt made with scientific
accuracy. This would be as if a man should resolve to decide by
experiment whether his eyes were useful for the purpose of seeing,
by hermetically sealing himself up for half an hour in a metal
case.”

On the “paradox of universal propositions obtained by experience,”
the same writer says: “If there be necessary and universal truths
expressible in propositions of axiomatic simplicity and obviousness,
and having for their subject-matter the elements of all our
experience and all our knowledge, surely these are the truths which,
if experience suggest to us any truths at all, it ought to suggest
most readily, clearly, and unceasingly. If it were a truth,
universal and necessary, that a net is spread over the whole surface
of every planetary globe, we should not travel far on our own
without getting entangled in its meshes, and making the necessity of
some means of extrication an axiom of locomotion.... There is,
therefore, nothing paradoxical, but the reverse, in our being led by
observation to a recognition of such truths, as _general_
propositions, coextensive at least with all human experience. That
they pervade all the objects of experience, must ensure their
continual suggestion _by_ experience; that they are true, must
ensure that consistency of suggestion, that iteration of
uncontradicted assertion, which commands implicit assent, and
removes all occasion of exception; that they are simple, and admit
of no misunderstanding, must secure their admission by every mind.”

“A truth, necessary and universal, relative to any object of our
knowledge, must verify itself in every instance where that object is
before our contemplation, and if at the same time it be simple and
intelligible, its verification must be obvious. _The sentiment of
such a truth cannot, therefore, but be present to our minds whenever
that object is contemplated, and must therefore make a part of the
mental picture or idea of that object which we may on any occasion
summon before our imagination.... All propositions, therefore,
become not only untrue but inconceivable_, if ... axioms be violated
in their enunciation.”

Another high authority (if indeed it be another authority) may be
cited in favour of the doctrine that axioms rest on the evidence of
induction. “The axioms of geometry themselves may be regarded as in
some sort an appeal to experience, not corporeal, but mental. When
we say, the whole is greater than its part, we announce a general
fact, which rests, it is true, on our ideas of whole and part; but,
in abstracting these notions, we begin by considering them as
subsisting in space, and time, and body, and again, in linear, and
superficial, and solid space. Again, when we say, the equals of
equals are equal, we mentally make comparisons, in equal spaces,
equal times, &c., so that these axioms, however self-evident, are
still general propositions so far of the inductive kind, that,
independently of experience, they would not present themselves to
the mind. The only difference between these and axioms obtained from
extensive induction is this, that, in raising the axioms of
geometry, the instances offer themselves spontaneously, and without
the trouble of search, and are few and simple; in raising those of
nature, they are infinitely numerous, complicated, and remote, so
that the most diligent research and the utmost acuteness are
required to unravel their web and place their meaning in
evidence.”—SIR J. HERSCHEL’s _Discourse on the Study of Natural
Philosophy_, pp. 95, 96.

53 Dr. Whewell thinks it improper to apply the term Induction to any
operation not terminating in the establishment of a general truth.
Induction, he says (in p. 15 of his pamphlet) “is not the same thing
as experience and observation. Induction is experience or
observation _consciously_ looked at in a _general_ form. This
consciousness and generality are necessary parts of that knowledge
which is science.” And he objects (p. 8) to the mode in which the
word Induction is employed in this work, as an undue extension of
that term “not only to the cases in which the general induction is
consciously applied to a particular instance, but to the cases in
which the particular instance is dealt with by means of experience
in that rude sense in which experience can be asserted of brutes,
and in which of course we can in no way imagine that the law is
possessed or understood as a general proposition.” This use of the
term he deems a “confusion of knowledge with practical tendencies.”

I disclaim, as strongly as Dr. Whewell can do, the application of
such terms as induction, inference, or reasoning, to operations
performed by mere instinct, that is, from an animal impulse, without
the exertion of any intelligence. But I perceive no ground for
confining the use of those terms to cases in which the inference is
drawn in the forms and with the precautions required by scientific
propriety. To the idea of Science, an express recognition and
distinct apprehension of general laws as such, is essential: but
nine-tenths of the conclusions drawn from experience in the course
of practical life, are drawn without any such recognition: they are
direct inferences from known cases, to a case supposed to be
similar. I have endeavoured to shew that this is not only as
legitimate an operation, but substantially the same operation, as
that of ascending from known cases to a general proposition; (except
that the latter process has one great security for correctness which
the former does not possess). In Science, the inference must
necessarily pass through the intermediate stage of a general
proposition, because Science wants its conclusions for record, and
not for instantaneous use. But the inferences drawn for the guidance
of practical affairs, by persons who would often be quite incapable
of expressing in unexceptionable terms the corresponding
generalizations, may and frequently do exhibit intellectual powers
quite equal to any which have ever been displayed in Science: and if
these inferences are not inductive, what are they? The limitation
imposed on the term by Dr. Whewell seems perfectly arbitrary;
neither justified by any fundamental distinction between what he
includes and what he desires to exclude, nor sanctioned by usage, at
least from the time of Reid and Stewart, the principal legislators
(as far as the English language is concerned) of modern metaphysical
terminology.

54 Suprà, p. 214.

_ 55 Phil. Ind. Sc._ ii. 213, 214.

_ 56 Ibid._

_ 57 Phil. Ind. Sc._ ii. p. 173.

_ 58 Cours de Philosophie Positive_, vol. ii, p. 202.

59 Dr. Whewell, in his reply, contests the distinction here drawn, and
maintains, that not only different descriptions, but different
explanations of a phenomenon, may all be true. Of the three theories
respecting the motions of the heavenly bodies, he says (p. 25):
“Undoubtedly all these explanations may be true and consistent with
each other, and would be so if each had been followed out so as to
shew in what manner it could be made consistent with the facts. And
this was, in reality, in a great measure done. The doctrine that the
heavenly bodies were moved by vortices was successively modified, so
that it came to coincide in its results with the doctrine of an
inverse-quadratic centripetal force.... When this point was reached,
the vortex was merely a machinery, well or ill devised, for
producing such a centripetal force, and therefore did not contradict
the doctrine of a centripetal force. Newton himself does not appear
to have been averse to explaining gravity by impulse. So little is
it true that if one theory be true the other must be false. The
attempt to explain gravity by the impulse of streams of particles
flowing through the universe in all directions, which I have
mentioned in the _Philosophy_, is so far from being inconsistent
with the Newtonian theory, that it is founded entirely upon it. And
even with regard to the doctrine, that the heavenly bodies move by
an inherent virtue; if this doctrine had been maintained in any such
way that it was brought to agree with the facts, the inherent virtue
must have had its laws determined; and then it would have been found
that the virtue had a reference to the central body; and so, the
‘inherent virtue’ must have coincided in its effect with the
Newtonian force; and then, the two explanations would agree, except
so far as the word ‘inherent’ was concerned. And if such a part of
an earlier theory as this word _inherent_ indicates, is found to be
untenable, it is of course rejected in the transition to later and
more exact theories, in Inductions of this kind, as well as in what
Mr. Mill calls Descriptions. There is, therefore, still no validity
discoverable in the distinction which Mr. Mill attempts to draw
between descriptions like Kepler’s law of elliptical orbits, and
other examples of induction.”

If the doctrine of vortices had meant, not that vortices existed,
but only that the planets moved _in the same manner_ as if they had
been whirled by vortices; if the hypothesis had been merely a mode
of representing the facts, not an attempt to account for them; if,
in short, it had been only a Description; it would, no doubt, have
been reconcileable with the Newtonian theory. The vortices, however,
were not a mere aid to conceiving the motions of the planets, but a
supposed physical agent, actively impelling them; a material fact,
which might be true or not true, but could not be both true and not
true. According to Descartes’ theory it was true, according to
Newton’s it was not true. Dr. Whewell probably means that since the
phrases, centripetal and projectile force, do not declare the nature
but only the direction of the forces, the Newtonian theory does not
absolutely contradict any hypothesis which may be framed respecting
the mode of their production. The Newtonian theory, regarded as a
mere _description_ of the planetary motions, does not; but the
Newtonian theory as an _explanation_ of them does. For in what does
the explanation consist? In ascribing those motions to a general law
which obtains between all particles of matter, and in identifying
this with the law by which bodies fall to the ground; a kind of
motion which the vortices did not, and as it was rectilineal, could
not, explain. The one explanation, therefore, absolutely excludes
the other. Either the planets are not moved by vortices, or they do
not move by the law by which heavy bodies fall. It is impossible
that both opinions can be true. As well might it be said that there
is no contradiction between the assertions, that a man died because
somebody killed him, and that he died a natural death.

So, again, the theory that the planets move by a virtue inherent in
their celestial nature, is incompatible with either of the two
others; either that of their being moved by vortices, or that which
regards them as moving by a property which they have in common with
the earth and all terrestrial bodies. Dr. Whewell says, that the
theory of an inherent virtue agrees with Newton’s when the word
inherent is left out, which of course it would be (he says) if
“found to be untenable.” But leave that out, and where is the
theory? The word inherent _is_ the theory. When that is omitted,
there remains nothing except that the heavenly bodies move by “a
virtue,” _i.e._ by a power of some sort.

If Dr. Whewell is not yet satisfied, any other subject will serve
equally well to test his doctrine. He will hardly say that there is
no contradiction between the emission theory and the undulatory
theory of light; or that there can be both one and two
electricities; or that the hypothesis of the production of the
higher organic forms by development from the lower, and the
supposition of separate and successive acts of creation, are quite
reconcileable; or that the theory that volcanoes are fed from a
central fire, and the doctrines which ascribe them to chemical
action at a comparatively small depth below the earth’s surface, are
consistent with one another, and all true as far as they go.

If different explanations of the same fact cannot both be true,
still less, surely, can different predictions. Dr. Whewell quarrels
(on what ground it is not necessary to consider) with the example I
had chosen on this point, and thinks an objection to an illustration
a sufficient answer to a theory. Examples not liable to his
objection are easily found, if the proposition that conflicting
predictions cannot both be true, can be made clearer by any
examples. Suppose the phenomenon to be a newly-discovered comet, and
that one astronomer predicts its return once in every 300
years—another, once in every 400: can they both be right? When
Columbus predicted that by sailing constantly westward he should in
time return to the point from which he set out, while others
asserted that he could never do so except by turning back, were both
he and his opponents true prophets? Were the predictions which
foretold the wonders of railways and steamships, and those which
averred that the Atlantic could never be crossed by steam
navigation, nor a railway train propelled ten miles an hour, both
(in Dr. Whewell’s words) “true, and consistent with one another”?

Dr. Whewell sees no distinction between holding contradictory
opinions on a question of fact, and merely employing different
analogies to facilitate the conception of the same fact. The case of
different Inductions belongs to the former class, that of different
Descriptions to the latter.

_ 60 Of Induction_, p. 33.

61 But though it is a condition of the validity of every induction that
there be uniformity in the course of nature, it is not a necessary
condition that the uniformity should pervade all nature. It is
enough that it pervades the particular class of phenomena to which
the induction relates. An induction concerning the motions of the
planets, or the properties of the magnet, would not be vitiated
though we were to suppose that wind and weather are the sport of
chance, provided it be assumed that astronomical and magnetic
phenomena are under the dominion of general laws. Otherwise the
early experience of mankind would have rested on a very weak
foundation; for in the infancy of science it could not be said to be
known that _all_ phenomena are regular in their course.

Neither would it be correct to say that every induction by which we
infer any truth, implies the general fact of uniformity _as
foreknown_, even in reference to the kind of phenomena concerned. It
implies, _either_ that this general fact is already known, _or_ that
we may now know it: as the conclusion, The Duke of Wellington is
mortal, drawn from the instances A, B, and C, implies either that we
have already concluded all men to be mortal, or that we are now
entitled to do so from the same evidence. A vast amount of confusion
and paralogism respecting the grounds of Induction would be
dispelled by keeping in view these simple considerations.

62 Infra, chap. xxi.

63 Infra, chap. xxi, xxii.

64 Dr. Whewell (_Of Induction_, p. 16) will not allow these and similar
erroneous opinions to be called inductions; inasmuch as such
superstitious fancies “were not collected from the facts by seeking
a law of their occurrence, but were suggested by an imagination of
the anger of superior powers, shown by such deviations from the
ordinary course of nature.” I conceive the question to be, not in
what manner these notions were at first suggested, but by what
evidence they have, from time to time, been supposed to be
substantiated. If the believers in these erroneous opinions had been
put on their defence, they would have referred to experience; to the
comet which preceded the assassination of Julius Cæsar, or to
oracles and other prophecies known to have been fulfilled. It is by
such appeals to facts that all analogous superstitions, even in our
day, attempt to justify themselves; the supposed evidence of
experience is what really gives them their hold on the mind. I quite
admit that the influence of such coincidences would not be what it
is, if strength were not lent to it by an antecedent presumption;
but this is not peculiar to such cases; preconceived notions of
probability form part of the explanation of many other cases of
belief on insufficient evidence. The _à priori_ prejudice does not
prevent the erroneous opinion from being sincerely regarded as a
legitimate conclusion from experience; but is, on the contrary, the
very thing which predisposes the mind to that interpretation of
experience.

Thus much in defence of the sort of examples objected to. But it
would be easy to produce instances, equally adapted to the purpose,
and in which no antecedent prejudice is at all concerned. “For many
ages,” says Archbishop Whately, “all farmers and gardeners were
firmly convinced—and convinced of their knowing it by
experience—that the crops would never turn out good unless the seed
were sown during the increase of the moon.” This was induction, but
bad induction: just as a vicious syllogism is reasoning, but bad
reasoning.

65 The assertion, that any and every one of the conditions of a
phenomenon may be and is, on some occasions and for some purposes,
spoken of as the cause, has been disputed by an intelligent reviewer
of this work, (_Prospective Review_ for February 1850,) who
maintains that “we always apply the word cause rather to that
element in the antecedents which exercises _force_, and which would
_tend_ at all times to produce the same or a similar effect to that
which, under certain conditions, it would actually produce.” And he
says, that “every one would feel” the expression, that the cause of
a surprise was the sentinel’s being off his post, to be incorrect;
but that “the allurement or force which _drew_ him off his post,
might be so called, because in doing so it removed a resisting power
which would have prevented the surprise.” I cannot think that it
would be wrong to say, that the event took place because the
sentinel was absent, and yet right to say that it took place because
he was bribed to be absent. Since the only direct effect of the
bribe was his absence, the bribe could be called the remote cause of
the surprise, only on the supposition that the absence was the
proximate cause; nor does it seem to me that any one, who had not a
theory to support, would use the one expression and reject the
other.

The reviewer observes, that when a person dies of poison, his
possession of bodily organs is a necessary condition, but that no
one would ever speak of it as the cause. I admit the fact; but I
believe the reason to be, that the occasion could never arise for so
speaking of it; for when in the inaccuracy of common discourse we
are led to speak of some one condition of a phenomenon as its cause,
the condition so spoken of is always one which it is at least
possible that the hearer may require to be informed of. The
possession of bodily organs is a known condition, and to give that
as the answer, when asked the cause of a person’s death, would not
supply the information sought. Once conceive that a doubt could
exist as to his having bodily organs, or that he were to be compared
with some being who had them not, and cases may be imagined in which
it might be said that his possession of them was the cause of his
death. If Faust and Mephistopheles together took poison, it might be
said that Faust died because he was a human being, and had a body,
while Mephistopheles survived because he was a spirit.

It is for the same reason, that no one (as the reviewer remarks)
“calls the cause of a leap, the muscles or sinews of the body,
though they are necessary conditions; nor the cause of a
self-sacrifice, the knowledge which was necessary for it; nor the
cause of writing a book, that a man has time for it, which is a
necessary condition.” These conditions (besides that they are
antecedent _states_, and not proximate antecedent _events_, and are
therefore never the conditions in closest apparent proximity to the
effect) are all of them so obviously implied, that it is hardly
possible there should exist that necessity for insisting on them,
which alone gives occasion for speaking of a single condition as if
it were the cause. Wherever this necessity exists in regard to some
one condition, and does not exist in regard to any other, I conceive
that it is consistent with usage, when scientific accuracy is not
aimed at, to apply the name cause to that one condition. If the only
condition which can be supposed to be unknown is a negative
condition, the negative condition may be spoken of as the cause. It
might be said that a person died for want of medical advice: though
this would not be likely to be said, unless the person was already
understood to be ill; and in order to indicate that this negative
circumstance was what made the illness fatal, and not the weakness
of his constitution, or the original virulence of the disease. It
might be said that a person was drowned because he could not swim;
the positive condition, namely that he fell into the water, being
already implied in the word drowned. And here let me remark, that
his falling into the water is in this case the only positive
condition: all the conditions not expressly or virtually included in
this (as that he could not swim, that nobody helped him, and so
forth) are negative. Yet, if it were simply said that the cause of a
man’s death was falling into the water, there would be quite as
great a sense of impropriety in the expression, as there would be if
it were said that the cause was his inability to swim; because,
though the one condition is positive and the other negative, it
would be felt that neither of them was sufficient, without the
other, to produce death.

With regard to the assertion that nothing is termed the cause,
except the element which exerts active force; I waive the question
as to the meaning of active force, and accepting the phrase in its
popular sense, I revert to a former example, and I ask, would it be
more agreeable to custom to say that a man fell because his foot
slipped in climbing a ladder, or that he fell because of his
weight—for his weight, and not the motion of his foot, was the
active force which determined his fall. If a person walking out in a
frosty day, stumbled and fell, it might be said that he stumbled
because the ground was slippery, or because he was not sufficiently
careful; but few people, I suppose, would say that he stumbled
because he walked. Yet the only active force concerned was that
which he exerted in walking: the others were mere negative
conditions; but they happened to be the only ones which there could
be any necessity to state; for he walked, most likely, in exactly
his usual manner, and the negative conditions made all the
difference. Again, if a person were asked why the army of Xerxes
defeated that of Leonidas, he would probably say, because they were
a thousand times the number; but I do not think he would say, it was
because they fought; although that was the element of active force.
The reviewer adds, “there are some conditions absolutely passive,
and yet absolutely necessary to physical phenomena, viz., the
relations of space and time; and to these no one ever applies the
word cause without being immediately arrested by those who hear
him.” Even from this statement I am compelled to dissent. Few
persons would feel it incongruous to say (for example) that a secret
became known because it was spoken of when A. B. was within hearing;
which is a condition of space; or that the cause why one of two
particular trees is taller than the other, is that it has been
longer planted; which is a condition of time.

66 There are a few exceptions; for there are some properties of objects
which seem to be purely preventive; as the property of opaque
bodies, by which they intercept the passage of light. This, as far
as we are able to understand it, appears an instance not of one
cause counteracting another by the same law whereby it produces its
own effects, but of an agency which manifests itself in no other way
than in defeating the effects of another agency. If we knew on what
other relations to light, or on what peculiarities of structure,
opacity depends, we might find that this is only an apparent, not a
real, exception to the general proposition in the text. In any case
it needs not affect the practical application. The formula which
includes all the negative conditions of an effect in the single one
of the absence of counteracting causes, is not violated by such
cases as this; though, if all counteracting agencies were of this
description, there would be no purpose served by employing the
formula, since we should still have to enumerate specially the
negative conditions of each phenomenon, instead of regarding them as
implicitly contained in the positive laws of the various other
agencies in nature.

67 I use the words “straight line” for brevity and simplicity. In
reality the line in question is not exactly straight, for, from the
effect of refraction, we actually see the sun for a short interval
during which the opaque mass of the earth is interposed in a direct
line between the sun and our eyes; thus realizing, though but to a
limited extent, the coveted desideratum of seeing round a corner.

68 The reviewer of Dr. Whewell in the _Quarterly Review_.

69 To the universality which mankind are agreed in ascribing to the Law
of Causation, there is one claim of exception, one disputed case,
that of the Human Will; the determinations of which, a large class
of metaphysicians are not willing to regard as following the causes
called motives, according to as strict laws as those which they
suppose to exist in the world of mere matter. This controverted
point will undergo a special examination when we come to treat
particularly of the Logic of the Moral Sciences, (Book vi. ch. 2).
In the meantime I may remark that these metaphysicians, who, it must
be observed, ground the main part of their objection on the supposed
repugnance of the doctrine in question to our consciousness, seem to
me to mistake the fact which consciousness testifies against. What
is really in contradiction to consciousness, they would, I think, on
strict self-examination, find to be, the application to human
actions and volitions of the ideas involved in the common use of the
term Necessity; which I agree with them in objecting to. But if they
would consider that by saying that a person’s actions _necessarily_
follow from his character, all that is really meant (for no more is
meant in any case whatever of causation) is that he invariably
_does_ act in conformity to his character, and that any one who
thoroughly knew his character could certainly predict how he would
act in any supposable case; they probably would not find this
doctrine either contrary to their experience or revolting to their
feelings. And no more than this is contended for by any one but an
Asiatic fatalist.

70 Unless we are to consider as such the following statement, by one of
the writers quoted in the text: “In the case of mental exertion, the
result to be accomplished is _preconsidered_ or meditated, and is
therefore known _à priori_, or before experience.”—(Bowen’s _Lowell
Lectures on the Application of Metaphysical and Ethical Science to
the Evidence of Religion_, Boston, 1849.) This is merely saying that
when we will a thing we have an idea of it. But to have an idea of
what we wish to happen, does not imply a prophetic knowledge that it
will happen. Perhaps it will be said that the _first time_ we
exerted our will, when we had of course no experience of any of the
powers residing in us, we nevertheless must already have known that
we possessed them, since we cannot _will_ that which we do not
believe to be in our power. But the impossibility is perhaps in the
words only, and not in the facts; for we may _desire_ what we do not
know to be in our power; and finding by experience that our bodies
move according to our _desire_, we may then, and only then, pass
into the more complicated mental state which is termed will.

After all, even if we had an instinctive knowledge that our actions
would follow our will, this, as Brown remarks, would prove nothing
as to the nature of Causation. Our knowing, previous to experience,
that an antecedent will be followed by a certain consequent, would
not prove the relation between them to be anything _more_ than
antecedence and consequence.

71 Reid’s _Essays on the Active Powers_, Essay iv. ch. 3.

_ 72 Prospective Review_ for February 1850.

_ 73 Vide supra_, p. 267, note.

74 In combating the theory, that Volition is the universal cause, I
have purposely abstained from one of the strongest positive
arguments against it—that volitions themselves obey causes, and even
external causes, namely, the inducements, or motives, which
determine the will to act; because an objector might say that to
employ this argument would be begging the question against the
freedom of the will. Though it is not begging the question to affirm
a doctrine, referring elsewhere for the proof of it, I am unwilling
without necessity to build any part of my reasoning on a proposition
which I am aware that those opposed to me in the present discussion
do not admit.

75 I omit, for simplicity, to take into account the effect, in this
latter case, of the diminution of pressure, in diminishing the flow
of water through the drain; which evidently in no way affects the
truth or applicability of the principle.

76 Unless, indeed, the consequent was generated not by the antecedent,
but by the means we 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.

_ 77 Discourse on the Study of Natural Philosophy_, p. 179.

78 For this speculation I am indebted to Mr. Alexander Bain.