§ 1. Some of the most remarkable instances which have occurred since the
great Newtonian generalization, of the explanation of laws of causation
subsisting among complex phenomena, by resolving them into simpler and
more general laws, are to be found among the speculations of Liebig in
organic chemistry. These speculations, though they have not yet been
sufficiently long before the world to entitle us positively to assume that
no well-grounded objection can be made to any part of them, afford,
however, so admirable an example of the spirit of the Deductive Method,
that I may be permitted to present some specimens of them here.
It had been observed in certain cases, that chemical action is, as it
were, contagious; that is to say, a substance which would not of itself
yield to a particular chemical attraction, (the force of the attraction
not being sufficient to overcome cohesion, or to destroy some chemical
combination in which the substance was already held), will nevertheless do
so if placed in contact with some other body which is in the act of
yielding to the same force. Nitric acid, for example, does not dissolve
pure platinum, which may “be boiled with this acid without being oxidized
by it, even when in a state of such fine division that it no longer
reflects light.” But the same acid easily dissolves silver. Now if an
alloy of silver and platinum be treated with nitric acid, the acid does
not, as might naturally be expected, separate the two metals, dissolving
the silver, and leaving the platinum; it dissolves both: the platinum as
well as the silver becomes oxidized, and in that state combines with the
undecomposed portion of the acid. In like manner, “copper does not
decompose water, even when boiled in dilute sulphuric acid; but an alloy
of copper, zinc, and nickel, dissolves easily in this acid with evolution
of hydrogen gas.” These phenomena cannot be explained by the laws of what
is termed chemical affinity. They point to a peculiar law, by which the
oxidation which one body suffers, causes another, in contact with it, to
submit to the same change. And not only chemical composition, but chemical
decomposition, is capable of being similarly propagated. The peroxide of
hydrogen, a compound formed by hydrogen with a greater amount of oxygen
than the quantity necessary to form water, is held together by a chemical
attraction of so weak a nature, that the slightest circumstance is
sufficient to decompose it; and it even, though very slowly, gives off
oxygen and is reduced to water spontaneously (being, I presume, decomposed
by the tendency of its oxygen to absorb heat and assume the gaseous
state). Now it has been observed, that if this decomposition of the
peroxide of hydrogen takes place in contact with some metallic oxides, as
those of silver, and the peroxides of lead and manganese, it superinduces
a corresponding chemical action upon those substances; they also give
forth the whole or a portion of their oxygen, and are reduced to the metal
or to the protoxide; although they do not undergo this change
spontaneously, and there is no chemical affinity at work to make them do
so. Other similar phenomena are mentioned by Liebig. “Now no other
explanation,” he observes, “of these phenomena can be given, than that a
body in the act of combination or decomposition enables another body, with
which it is in contact, to enter into the same state.”
Here, therefore, is a law of nature of great simplicity, but which, owing
to the extremely special and limited character of the phenomena in which
alone it can be detected experimentally, (because in them alone its
results are not intermixed and blended with those of other laws,) had been
very little recognised by chemists, and no one could have ventured, on
experimental evidence, to affirm it as a law common to all chemical
action; owing to the impossibility of a rigorous employment of the Method
of Difference where the properties of different kinds of substance are
involved, an impossibility which we noticed and characterized in a
previous chapter.(90) Now this extremely special and apparently precarious
generalization has, in the hands of Liebig, been converted, by a masterly
employment of the Deductive Method, into a law pervading all nature, in
the same way as gravitation assumed that character in the hands of Newton;
and has been found to explain, in the most unexpected manner, numerous
detached generalizations of a more limited kind, reducing the phenomena
concerned in those generalizations into mere cases of itself.
The contagious influence of chemical action is not a powerful force, and
is only capable of overcoming weak affinities: we, may, therefore, expect
to find it principally exemplified in the decomposition of substances
which are held together by weak chemical forces. Now the force which holds
a compound substance together is generally weaker, the more compound the
substance is; and organic products are the most compound substances known,
those which have the most complex atomic constitution. It is, therefore,
upon such substances that the self-propagating power of chemical action is
likely to exert itself in the most marked manner. Accordingly, first, it
explains the remarkable laws of fermentation, and some of those of
putrefaction. “A little leaven,” that is, dough in a certain state of
chemical action, impresses a similar chemical action upon “the whole
lump.” The contact of any decaying substance, occasions the decay of
matter previously sound. Again, yeast is a substance actually in a process
of decomposition from the action of air and water, evolving carbonic acid
gas. Sugar is a substance which, from the complexity of its composition,
has no great energy of coherence in its existing form, and is capable of
being easily converted (by combination with the elements of water) into
carbonic acid and alcohol. Now the mere presence of yeast, the mere
proximity of a substance of which the elements are separating from each
other, and combining with the elements of water, causes sugar to undergo
the same change, giving out carbonic acid gas, and becoming alcohol. It is
not the elements contained in the yeast which do this. “An aqueous
infusion of yeast may be mixed with a solution of sugar, and preserved in
vessels from which the air is excluded, without either experiencing the
slightest change.” Neither does the insoluble residue of the yeast, after
being treated with water, possess the power of exciting fermentation.
(Here we have the method of Difference). It is not the yeast itself,
therefore; it is the yeast in a state of decomposition. The sugar, which
would not decompose and oxidize by the mere presence of oxygen and water,
is induced to do so when another oxidation is at work in the midst of it.
By the same principle Liebig is enabled to explain many cases of malaria;
the pernicious influence of putrid substances; a variety of poisons;
contagious diseases; and other phenomena. Of all substances, those
composing the animal body are the most complex in their composition, and
are in the least stable condition of union. The blood, in particular, is
the most unstable compound known. It is, therefore, not surprising that
gaseous or other substances, in the act of undergoing the chemical changes
which constitute, for instance, putrefaction, should, when brought into
contact with the tissues by respiration or otherwise, and still more when
introduced by inoculation into the blood itself, impress upon some of the
particles a chemical action similar to its own; which is propagated in
like manner to other particles, until the whole system is placed in a
state of chemical action more or less inconsistent with the chemical
conditions of vitality.
Of the three modes in which we observed in the last chapter that the
resolution of a special law into more general ones may take place, this
speculation exemplifies the second. The laws explained are such as this,
that yeast puts sugar into a state of fermentation. Between the remote
cause, the presence of yeast, and the consequent fermentation of the
sugar, there has been interpolated a proximate cause, the chemical action
between the particles of the yeast and the elements of air and water. The
special law is thus resolved into two others, more general than itself:
the first, that yeast is decomposed by the presence of air and water; the
second, that matter undergoing chemical action has a tendency to produce
similar chemical action in other matter in contact with it. But while the
investigation thus aptly exhibits the second mode of the resolution of a
complex law, it no less happily exemplifies the third; the subsumption of
special laws under a more general law, by gathering them up into one more
comprehensive expression which includes them all. For the curious fact of
the contagious nature of chemical action is only raised into a law of
_all_ chemical action by these very investigations; just as the Newtonian
attraction was only recognised as a law of all matter when it was found to
explain the phenomena of terrestrial gravity. Previously to Liebig’s
investigations, the property in question had only been observed in a few
special cases of chemical action; but when his deductive reasonings have
established that innumerable effects produced upon weak compounds, by
substances none of whose known peculiarities would account for their
having such a power, might be explained by considering the supposed
special property to exist in all those cases, these numerous
generalizations on separate substances are brought together into one law
of chemical action in general: the peculiarities of the various substances
being, in fact, eliminated, just as the Newtonian deduction eliminated
from the instances of terrestrial gravity the circumstance of proximity to
the earth.
§ 2. Another speculation of the same chemist, which, if it should
ultimately be found to agree with all the facts of the extremely
complicated phenomenon to which it relates, will constitute one of the
finest examples of the Deductive Method on record, is his theory of
respiration.
The facts of respiration, or in other words the special laws which it is
attempted to explain from, and resolve into, more general ones, are, that
the blood in passing through the lungs absorbs oxygen and gives out
carbonic acid gas, changing thereby its colour from a blackish purple to a
brilliant red. The absorption and exhalation are evidently chemical
phenomena; and the carbon of the carbonic acid must have been derived from
the body, that is, must have been absorbed by the blood from the
substances with which it came into contact in its passage through the
organism. Required to find the intermediate links—the precise nature of
the two chemical actions which take place; first, the absorption of the
carbon or of the carbonic acid by the blood, in its circulation through
the body; next, the excretion of the carbon, or the exchange of the
carbonic acid for oxygen, in its passage through the lungs.
Dr. Liebig believes himself to have found the solution of this _vexata
quæstio_ in a class of chemical actions in which scarcely any less acute
and penetrating inquirer would have thought of looking for it.
Blood is composed of two parts, the serum and the globules. The serum
absorbs and holds in solution carbonic acid in great quantity, but has no
tendency either to part with it or to absorb oxygen. The globules,
therefore, are concluded to be the portion of the blood which is operative
in respiration. These globules contain a certain quantity of iron, which
from chemical tests is inferred to be in the state of oxide.
Dr. Liebig recognised, in the known chemical properties of the oxides of
iron, laws which, if followed out deductively, would lead to the
prediction of the precise series of phenomena which respiration exhibits.
There are two oxides of iron, a protoxide and a peroxide. In the arterial
blood the iron is in the form of peroxide: in the venous blood we have no
direct evidence which of the oxides is present, but the considerations to
be presently stated lead to the conclusion that it is the protoxide. As
arterial and venous blood are in a perpetual state of alternate conversion
into one another, the question arises, in what circumstances the protoxide
of iron is capable of being converted into the peroxide, and _vice versâ_.
Now the protoxide readily combines with oxygen in the presence of water,
forming the hydrated peroxide: these conditions it finds in passing
through the lungs; it derives oxygen from the air, and finds water in the
blood itself. This would already explain one portion of the phenomena of
respiration. But the arterial blood, in quitting the lungs, is charged
with hydrated peroxide: in what manner is the peroxide brought back to its
former state?
The chemical conditions for the reduction of the hydrated peroxide into
the state of protoxide, are precisely those which the blood meets with in
circulating through the body; namely, contact with organic compounds.
Hydrated peroxide of iron, when treated with organic compounds (where no
sulphur is present) gives forth oxygen and water, which oxygen, attracting
the carbon from the organic substance, becomes carbonic acid; while the
peroxide, being reduced to the state of protoxide, combines with the
carbonic acid, and becomes a carbonate. Now this carbonate needs only come
again into contact with oxygen and water to be decomposed; the carbonic
acid being given off, and the protoxide, by the absorption of oxygen and
water, becoming again the hydrated peroxide.
The mysterious chemical phenomena connected with respiration can now, by a
beautiful deductive process, be completely explained. The arterial blood,
containing iron in the form of hydrated peroxide, passes into the
capillaries, where it meets with the decaying tissues, receiving also in
its course certain non-azotised but highly carbonised animal products, in
particular the bile. In these it finds the precise conditions required for
decomposing the peroxide into oxygen and the protoxide. The oxygen
combines with the carbon of the decaying tissues, and forms carbonic acid,
which, though insufficient in amount to neutralize the whole of the
protoxide, combines with a portion (one-fourth) of it, and returns in the
form of a carbonate, along with the other three-fourths of the protoxide,
through the venous system into the lungs. There it again meets with oxygen
and water: the free protoxide becomes hydrated peroxide: the carbonate of
protoxide parts with its carbonic acid, and by absorbing oxygen and water,
enters also into the state of hydrated peroxide. The heat evolved in the
transition from protoxide to peroxide, as well as in the previous
oxidation of the carbon contained in the tissues, is considered by Liebig
as the cause which sustains the temperature of the body. But into this
portion of the speculation we need not enter.(91)
This example displays the second mode of resolving complex laws, by the
interpolation of intermediate links in the chain of causation; and some of
the steps of the deduction exhibit cases of the first mode, that which
infers the joint effect of two or more causes from their separate effects;
but to trace out in detail these exemplifications may be left to the
intelligence of the reader. The third mode is not employed in this
example, since the simpler laws into which those of respiration are
resolved (the laws of the chemical action of the oxides of iron) were laws
already known, and do not acquire any additional generality from their
employment in the present case.
§ 3. The property which salt possesses of preserving animal substances
from putrefaction is resolved by Liebig into two more general laws, the
strong attraction of salt for water, and the necessity of the presence of
water as a condition of putrefaction. The intermediate phenomenon which is
interpolated between the remote cause and the effect, can here be not
merely inferred but seen; for it is a familiar fact, that flesh upon which
salt has been thrown is speedily found swimming in brine.
The second of the two factors (as they may be termed) into which the
preceding law has been resolved, the necessity of water to putrefaction,
itself affords an additional example of the Resolution of Laws. The law
itself is proved by the Method of Difference, since flesh completely dried
and kept in a dry atmosphere does not putrefy, as we see in the case of
dried provisions, and human bodies in very dry climates. A deductive
explanation of this same law results from Liebig’s speculations. The
putrefaction of animal and other azotised bodies is a chemical process, by
which they are gradually dissipated in a gaseous form, chiefly in that of
carbonic acid and ammonia; now to convert the carbon of the animal
substance into carbonic acid requires oxygen, and to convert the azote
into ammonia requires hydrogen, which are the elements of water. The
extreme rapidity of the putrefaction of azotised substances, compared with
the gradual decay of non-azotised bodies (such as wood and the like) by
the action of oxygen alone, he explains from the general law that
substances are much more easily decomposed by the action of two different
affinities upon two of their elements, than by the action of only one.
The purgative effect of salts with alkaline bases, when administered in
concentrated solutions, is explained from the two following principles:
Animal tissues (such as the stomach) do _not_ absorb concentrated
solutions of alkaline salts; and such solutions _do_ dissolve the solids
contained in the intestines. The simpler laws into which the complex law
is here resolved, are the second of the two foregoing principles combined
with a third, namely that the peristaltic contraction acts easily upon
substances in a state of solution. The negative general proposition, that
animal substances do not absorb these salts, contributes to the
explanation by accounting for the absence of a counteracting cause,
namely, absorption by the stomach, which in the case of other substances
possessed of the requisite chemical properties, interferes to prevent them
from reaching the substances which they are destined to dissolve.
§ 4. From the foregoing and similar instances, we may see the importance,
when a law of nature previously unknown has been brought to light, or when
new light has been thrown upon a known law by experiment, of examining all
cases which present the conditions necessary for bringing that law into
action; a process fertile in demonstrations of special laws previously
unsuspected, and explanations of others already empirically known.
For instance, Faraday discovered by experiment, that voltaic electricity
could be evolved from a natural magnet, provided a conducting body were
set in motion at right angles to the direction of the magnet: and, this he
found to hold not only of small magnets, but of that great magnet, the
earth. The law being thus established experimentally, that electricity is
evolved, by a magnet, and a conductor moving at right angles to the
direction of its poles, we may now look out for fresh instances in which
these conditions meet. Wherever a conductor moves or revolves at right
angles to the direction of the earth’s magnetic poles, there we may expect
an evolution of electricity. In the northern regions, where the polar
direction is nearly perpendicular to the horizon, all horizontal motions
of conductors will produce electricity; horizontal wheels, for example,
made of metal; likewise all running streams will evolve a current of
electricity which will circulate round them; and the air thus charged with
electricity may be one of the causes of the Aurora Borealis. In the
equatorial regions, on the contrary, upright wheels placed parallel to the
equator will originate a voltaic circuit, and waterfalls will naturally
become electric.
For a second example; it has recently been found, chiefly by the
researches of Professor Graham, that gases have a strong tendency to
permeate animal membranes, and diffuse themselves through the spaces which
such membranes inclose, notwithstanding the presence of other gases in
those spaces. Proceeding from this general law, and reviewing a variety of
cases in which gases lie contiguous to membranes, we are enabled to
demonstrate or to explain the following more special laws: 1st. The human
or animal body, when surrounded with any gas not already contained within
the body, absorbs it rapidly; such, for instance, as the gases of
putrefying matters: which helps to explain malaria. 2nd. The carbonic acid
gas of effervescing drinks, evolved in the stomach, permeates its
membranes, and rapidly spreads through the system, where, as suggested in
a former note, it probably combines with the iron contained in the blood.
3rd. Alcohol taken into the stomach passes into vapour and spreads through
the system with great rapidity; (which, combined with the high
combustibility of alcohol, or in other words its ready combination with
oxygen, may perhaps help to explain the bodily warmth immediately
consequent on drinking spirituous liquors.) 4th. In any state of the body
in which peculiar gases are formed within it, these will rapidly exhale
through all parts of the body; and hence the rapidity with which, in
certain states of disease, the surrounding atmosphere becomes tainted.
5th. The putrefaction of the interior parts of a carcase will proceed as
rapidly as that of the exterior, from the ready passage outwards of the
gaseous products. 6th. The exchange of oxygen and carbonic acid in the
lungs is not prevented, but rather promoted, by the intervention of the
membrane of the lungs and the coats of the blood vessels between the blood
and the air. It is necessary, however, that there should be a substance in
the blood with which the oxygen of the air may immediately combine;
otherwise instead of passing into the blood, it would permeate the whole
organism: and it is necessary that the carbonic acid, as it is formed in
the capillaries, should also find a substance in the blood with which it
can combine; otherwise it would leave the body at all points, instead of
being discharged through the lungs.
§ 5. The following is a deduction which confirms, by explaining, the old
but not undisputed empirical generalization, that soda powders weaken the
human system. These powders, consisting of a mixture of tartaric acid with
bicarbonate of soda, from which the carbonic acid is set free, must pass
into the stomach as tartrate of soda. Now, neutral tartrates, citrates,
and acetates of the alkalis are found, in their passage through the
system, to be changed into carbonates; and to convert a tartrate into a
carbonate requires an additional quantity of oxygen, the abstraction of
which must lessen the oxygen destined for assimilation with the blood, on
the quantity of which the vigorous action of the human system partly
depends.
The instances of new theories agreeing with and explaining old
empiricisms, are innumerable. All the just remarks made by experienced
persons on human character and conduct, are so many special laws, which
the general laws of the human mind explain and resolve. The empirical
generalizations on which the operations of the arts have usually been
founded, are continually justified and confirmed on the one hand, or
corrected and improved on the other, by the discovery of the simpler
scientific laws on which the efficacy of those operations depends. The
effects of the rotation of crops, of the various manures, and other
processes of improved agriculture, have been for the first time resolved
in our own day into known laws of chemical and organic action, by Davy and
Liebig. The processes of the medical art are even now mostly empirical:
their efficacy is concluded, in each instance, from a special and most
precarious experimental generalization: but as science advances in
discovering the simple laws of chemistry and physiology, progress is made
in ascertaining the intermediate links in the series of phenomena, and the
more general laws on which they depend; and thus, while the old processes
are either exploded, or their efficacy, in so far as real, explained,
better processes, founded on the knowledge of proximate causes, are
continually suggested and brought into use.(92) Many even of the truths of
geometry were generalizations from experience before they were deduced
from first principles. The quadrature of the cycloid is said to have been
first effected by measurement, or rather by weighing a cycloidal card, and
comparing its weight with that of a piece of similar card of known
dimensions.
§ 6. To the foregoing examples from physical science, let us add another
from mental. The following is one of the simple laws of mind: Ideas of a
pleasurable or painful character form associations more easily and
strongly than other ideas, that is, they become associated after fewer
repetitions, and the association is more durable. This is an experimental
law, grounded on the Method of Difference. By deduction from this law,
many of the more special laws which experience shows to exist among
particular mental phenomena may be demonstrated and explained:—the ease
and rapidity, for instance, with which thoughts connected with our
passions or our more cherished interests are excited, and the firm hold
which the facts relating to them have on our memory; the vivid
recollection we retain of minute circumstances which accompanied any
object or event that deeply interested us, and of the times and places in
which we have been very happy or very miserable; the horror with which we
view the accidental instrument of any occurrence which shocked us, or the
locality where it took place, and the pleasure we derive from any memorial
of past enjoyment; all these effects being proportional to the sensibility
of the individual mind, and to the consequent intensity of the pain or
pleasure from which the association originated. It has been suggested by
the able writer of a biographical sketch of Dr. Priestley in a monthly
periodical, that the same elementary law of our mental constitution,
suitably followed out, would explain a variety of mental phenomena
hitherto inexplicable, and in particular some of the fundamental
diversities of human character and genius. Associations being of two
sorts, either between synchronous, or between successive impressions; and
the influence of the law which renders associations stronger in proportion
to the pleasurable or painful character of the impressions, being felt
with peculiar force in the synchronous class of associations; it is
remarked by the writer referred to, that in minds of strong organic
sensibility synchronous associations will be likely to predominate,
producing a tendency to conceive things in pictures and in the concrete,
richly clothed in attributes and circumstances, a mental habit which is
commonly called Imagination, and is one of the peculiarities of the
painter and the poet; while persons of more moderate susceptibility to
pleasure and pain will have a tendency to associate facts chiefly in the
order of their succession, and such persons, if they possess mental
superiority, will addict themselves to history or science rather than to
creative art. This interesting speculation the author of the present work
has endeavoured, on another occasion, to pursue farther, and to examine
how far it will avail towards explaining the peculiarities of the poetical
temperament. It is at least an example which may serve, instead of many
others, to show the extensive scope which exists for deductive
investigation in the important and hitherto so imperfect Science of Mind.
§ 7. The copiousness with which I have exemplified the discovery and
explanation of special laws of phenomena by deduction from simpler and
more general ones, was prompted by a desire to characterize clearly, and
place in its due position of importance, the Deductive Method; which in
the present state of knowledge is destined henceforth irrevocably to
predominate in the course of scientific investigation. A revolution is
peaceably and progressively effecting itself in philosophy, the reverse of
that to which Bacon has attached his name. That great man changed the
method of the sciences from deductive to experimental, and it is now
rapidly reverting from experimental to deductive. But the deductions which
Bacon abolished were from premisses hastily snatched up, or arbitrarily
assumed. The principles were neither established by legitimate canons of
experimental inquiry, nor the results tested by that indispensable element
of a rational Deductive Method, verification by specific experience.
Between the primitive method of Deduction and that which I have attempted
to characterize, there is all the difference which exists between the
Aristotelian physics and the Newtonian theory of the heavens.
It would, however, be a mistake to expect that those great
generalizations, from which the subordinate truths of the more backward
sciences will probably at some future period be deduced by reasoning (as
the truths of astronomy are deduced from the generalities of the Newtonian
theory,) will be found, in all, or even in most cases, among truths now
known and admitted. We may rest assured, that many of the most general
laws of nature are as yet entirely unthought of; and that many others,
destined hereafter to assume the same character, are known, if at all,
only as laws or properties of some limited class of phenomena; just as
electricity, now recognised as one of the most universal of natural
agencies, was once known only as a curious property which certain
substances acquired by friction, of first attracting and then repelling
light bodies. If the theories of heat, cohesion, crystallization, and
chemical action, are destined, as there can be little doubt that they are,
to become deductive, the truths which will then be regarded as the
_principia_ of those sciences would probably, if now announced, appear
quite as novel as the law of gravitation appeared to the cotemporaries of
Newton; possibly even more so, since Newton’s law, after all, was but an
extension of the law of weight—that is, of a generalization familiar from
of old, and which already comprehended a not inconsiderable body of
natural phenomena. The general laws, of a similarly commanding character,
which we still look forward to the discovery of, may not always find so
much of their foundations already laid.
These general truths will doubtless make their first appearance in the
character of hypotheses; not proved, nor even admitting of proof, in the
first instance, but assumed as premisses for the purpose of deducing from
them the known laws of concrete phenomena. But this, though their initial,
cannot be their final state. To entitle an hypothesis to be received as
one of the truths of nature, and not as a mere technical help to the human
faculties, it must be capable of being tested by the canons of legitimate
induction, and must actually have been submitted to that test. When this
shall have been done, and done successfully, premisses will have been
obtained from which all the other propositions of the science will
thenceforth be presented as conclusions, and the science will, by means of
a new and unexpected Induction, be rendered Deductive.
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FOOTNOTES
1 In the later editions of Archbishop Whately’s _Logic_ and _Rhetoric_
there are some expressions, which, though indefinite, resemble a
disclaimer of the opinion here ascribed to him. If I have imputed
that opinion to him erroneously, I am glad to find myself mistaken;
but he has not altered the passages in which the opinion appeared to
me to be conveyed, and which I still think inconsistent with the
belief that Induction can be reduced to strict rules.
2 Archbishop Whately.
3 This important theory has recently been called in question by a
writer of deserved reputation, Mr. Samuel Bailey; but I do not
conceive that the grounds on which it has been admitted as an
established doctrine for a century past, have been at all shaken by
that gentleman’s objections. I have elsewhere said what appeared to
me necessary in reply to his arguments (_Westminster Review, for
October 1842_.) It may be necessary to add, that some other
processes of comparison than those described in the text (but
equally the result of experience), appear occasionally to enter into
our judgment of distances by the eye.
_ 4 Computation or Logic_, chap. ii.
5 In the original, “had, _or had not_.” These last words, as involving
a subtlety foreign to our present purpose, I have forborne to quote.
6 It would, perhaps, be more correct to say that inflected cases are
names and something more; and that this addition prevents them from
being used as the subjects of propositions. But the purposes of our
inquiry do not demand that we should enter with scrupulous accuracy
into similar minutiæ.
_ 7 Notare_ to mark; _con_notare, to mark _along with_; to mark one
thing _with_ or _in addition to_ another.
8 Archbishop Whately, who in the more recent editions of his _Elements
of Logic_ has aided in reviving the important distinction treated of
in the text, proposes the term “Attributive” as a substitute for
“Connotative,” (p. 122, 9th ed.) The expression is, in itself,
appropriate; but, as it has not the advantage of being connected
with any verb, of so markedly distinctive a character as “to
connote,” it is not, I think, fitted to supply the place of the word
Connotative in scientific use.
9 It would be well if this degeneracy of language took place only in
the hands of the untaught vulgar; but some of the most remarkable
instances are to be found in terms of art, and among technically
educated persons, such as English lawyers. _Felony_, for example, is
a law term, with the sound of which all are familiar; but there is
no lawyer who would undertake to tell what a felony is, otherwise
than by enumerating the various offences which are so called.
Originally the word felony had a meaning; it denoted all offences,
the penalty of which included forfeiture of lands or goods; but
subsequent acts of parliament have declared various offences to be
felonies without enjoining that penalty, and have taken away the
penalty from others which continue nevertheless to be called
felonies, insomuch that the acts so called have now no property
whatever in common, save that of being unlawful and punishable.
10 Before quitting the subject of connotative names, it is proper to
observe, that the first writer who, in our own times, has adopted
from the schoolmen the word _to connote_, Mr. Mill, in his _Analysis
of the Phenomena of the Human Mind_, employs it in a signification
different from that in which it is here used. He uses the word in a
sense coextensive with its etymology, applying it to every case in
which a name, while pointing directly to one thing, (which is
consequently termed its signification,) includes also a tacit
reference to some other thing. In the case considered in the text,
that of concrete general names, his language and mine are the
converse of one another. Considering (very justly) the signification
of the name to lie in the attribute, he speaks of the word as
_noting_ the attribute, and _connoting_ the things possessing the
attribute. And he describes abstract names as being properly
concrete names with their connotation dropped: whereas, in my view,
it is the _de_notation which would be said to be dropped, what was
previously connoted becoming the whole signification.
In adopting a phraseology at variance with that which so high an
authority, and one which I am less likely than any other person to
undervalue, has deliberately sanctioned, I have been influenced by
the urgent necessity for a term exclusively appropriated to express
the manner in which a concrete general name serves to mark the
attributes which are involved in its signification. This necessity
can scarcely be felt in its full force by any one who has not found
by experience, how vain is the attempt to communicate clear ideas on
the philosophy of language without such a word. It is hardly an
exaggeration to say, that some of the most prevalent of the errors
with which logic has been infected, and a large part of the
cloudiness and confusion of ideas which have enveloped it, would, in
all probability, have been avoided, if a term had been in common use
to express exactly what I have signified by the term _to connote_.
And the schoolmen, to whom we are indebted for the greater part of
our logical language, gave us this also, and in this very sense. For
although some of their general expressions countenance the use of
the word in the more extensive and vague acceptation in which it is
taken by Mr. Mill, yet when they had to define it specifically as a
technical term, and to fix its meaning as such, with that admirable
precision which always characterizes their definitions, they clearly
explained that nothing was said to be connoted except _forms_, which
word may generally, in their writings, be understood as synonymous
with _attributes_.
Now, if the word _to connote_, so well suited to the purpose to
which they applied it, be diverted from that purpose by being taken
to fulfil another, for which it does not seem to me to be at all
required; I am unable to find any expression to replace it, but such
as are commonly employed in a sense so much more general, that it
would be useless attempting to associate them peculiarly with this
precise idea. Such are the words, to involve, to imply, &c. By
employing these, I should fail of attaining the object for which
alone the name is needed, namely, to distinguish this particular
kind of involving and implying from all other kinds, and to assure
to it the degree of habitual attention which its importance demands.
11 Or rather, all objects except itself and the percipient mind; for,
as we shall see hereafter, to ascribe any attribute to an object
necessarily implies a mind to perceive it.
_ 12 Philosophy of the Inductive Sciences_, vol. i. p. 40.
13 This doctrine is laid down in the clearest and strongest terms by M.
Cousin, whose observations on the subject are the more worthy of
attention, as, in consequence of the ultra-German and ontological
character of his philosophy considered generally, they may be
regarded as the admissions of an opponent.
“Nous savons qu’il existe quelque chose hors de nous, parceque nous
ne pouvons expliquer nos perceptions sans les rattacher à des causes
distinctes de nous-mêmes; nous savons de plus que ces causes, dont
nous ne connaissons pas d’ailleurs l’essence, produisent les effets
les plus variables, les plus divers, et même les plus contraires,
selon qu’elles rencontrent telle nature ou telle disposition du
sujet. Mais savons-nous quelque chose de plus? et même, vu le
caractère indéterminé des causes que nous concevons dans les corps,
y a-t-il quelque chose de plus à savoir? Y a-t-il lieu de nous
enquérir si nous percevons les choses telles qu’elles sont? Non
évidemment.... Je ne dis pas que le problème est insoluble, _je dis
qu’il est absurde et enferme une contradiction_. Nous _ne savons pas
ce que ces causes sont en elles-mêmes_, et la raison nous défend de
chercher à le connaître: mais il est bien évident _à priori_,
qu’_elles ne sont pas en elles-mêmes ce quelles sont par rapport à
nous_, puisque la présence du sujet modifie nécessairement leur
action. Supprimez tout sujet sentant, il est certain que ces causes
agiraient encore puisqu’elles continueraient d’exister; mais elles
agiraient autrement; elles seraient encore des qualités et des
propriétés, mais qui ne resembleraient à rien de ce que nous
connaissons. Le feu ne manifesterait plus aucune des propriétés que
nous lui connaissons: que serait-il? C’est ce que nous ne saurons
jamais. _C’est d’ailleurs peut-être un problème qui ne répugne pas
seulement à la nature de notre esprit, mais à l’essence même des
choses._ Quand même en effet on supprimerait par la pensée tous les
sujets sentants, il faudrait encore admettre que nul corps ne
manifesterait ses propriétés autrement qu’en relation avec un sujet
quelconque, et dans ce cas _ses propriétés ne seraient encore que
relatives_: en sorte qu’il me paraît fort raisonnable d’admettre que
les propriétés déterminées des corps n’existent pas independamment
d’un sujet quelconque, et que quand on demande si les propriétés de
la matière sont telles que nous les percevons, il faudrait voir
auparavant si elles sont en tant que déterminées, et dans quel sens
il est vrai de dire qu’elles sont.”—_Cours d’Histoire de la
Philosophie Morale au 18me siècle_, 8me leçon.
14 An attempt, indeed, has been made by Reid and others, to establish
that although some of the properties we ascribe to objects exist
only in our sensations, others exist in the things themselves, being
such as cannot possibly be copies of any impression upon the senses;
and they ask, from what sensations our notions of extension and
figure have been derived? The gauntlet thrown down by Reid was taken
up by Brown, who, applying greater powers of analysis than had
previously been applied to the notions of extension and figure,
showed clearly what are the sensations from which those notions are
derived, viz. sensations of touch, combined with sensations of a
class previously too little adverted to by metaphysicians, those
which have their seat in our muscular frame. Whoever wishes to be
more particularly acquainted with this excellent specimen of
metaphysical analysis, may consult the first volume of Brown’s
_Lectures_, or Mill’s _Analysis of the Mind_.
On this subject also, M. Cousin may be quoted in favour of
conclusions rejected by some of the most eminent thinkers of the
school to which he belongs. M. Cousin recognises, in opposition to
Reid, the essential _subjectivity_ of our conceptions of the primary
qualities of matter, as extension, solidity, &c., equally with those
of colour, heat, and the remainder of what are called secondary
qualities.—_Cours_, ut supra, 9me leçon.
_ 15 Analysis of the Human Mind_, i. 126 et seqq.
16 Dr. Whewell (_Of Induction_, p. 10) questions this statement, and
asks, “Are we to say that a mole cannot dig the ground, except he
has an idea of the ground, and of the snout and paws with which he
digs it?” I thought it had been evident that I was here speaking of
rational digging, and not of digging by instinct.
17 “From hence also this may be deduced, that the first truths were
arbitrarily made by those that first of all imposed names upon
things, or received them from the imposition of others. For it is
true (for example) that _man is a living creature_, but it is for
this reason, that it pleased men to impose both these names on the
same thing.”—_Computation or Logic_, ch. iii. sect. 8.
18 “Men are subject to err not only in affirming and denying, but also
in perception, and in silent cogitation.... Tacit errors, or the
errors of sense and cogitation, are made by passing from one
imagination to the imagination of another different thing; or by
feigning that to be past, or future, which never was, nor ever shall
be; as when, by seeing the image of the sun in water, we imagine the
sun itself to be there; or by seeing swords, that there has been or
shall be, fighting, because it uses to be so for the most part; or
when from promises we feign the mind of the promiser to be such and
such; or, lastly, when from any sign we vainly imagine something to
be signified which is not. And errors of this sort are common to all
things that have sense.”—_Computation or Logic_, ch. v., sect. 1.
19 Ch. iii. sect. 3.
20 Book iv. ch. vii.
21 Καθόλου μὲν οὖν πᾱσα διαφορὰ προγινομένη τινὶ ἑτεροῖον ποιεῖ; ἀλλ᾽
αἱ μὲν κοινῶς τε καὶ ἰδίως (differences in the accidental
properties) ἀλλοῖον ποιοῦσιν; αἱ δὲ ἰδιαίτατα (differences in the
essential properties) ἄλλο—_Isag._ cap. iii.
22 Few among the great names in mental science have met with a harder
measure of justice from the present generation than Locke; the
unquestioned founder of the analytic philosophy of mind, but whose
doctrines were first caricatured, then, when the reaction arrived,
cast off by the prevailing school even with contumely, and who is
now regarded by one of the conflicting parties in philosophy as an
apostle of heresy and sophistry, while among those who still adhere
to the standard which he raised, there has been a disposition in
later times to sacrifice his reputation in favour of Hobbes; a great
writer, and a great thinker for his time, but inferior to Locke not
only in sober judgment but even in profundity and original genius.
Locke, the most candid of philosophers, and one whose speculations
bear on every subject the strongest marks of having been wrought out
from the materials of his own mind, has been mistaken for an
unworthy plagiarist, while Hobbes has been extolled as having
anticipated many of his leading doctrines. He did anticipate many of
them, and the present is an instance in what manner it was generally
done. They both rejected the scholastic doctrine of essences; but
Locke understood and explained what these supposed essences really
were; Hobbes, instead of explaining the distinction between
essential and accidental properties, and between essential and
accidental propositions, jumped over it, and gave a definition which
suits at most only essential propositions, and scarcely those, as
the definition of Proposition in general.
23 The always acute and often profound author of _An Outline of
Sematology_ (Mr. B. H. Smart) justly says, “Locke will be much more
intelligible if, in the majority of places, we substitute ‘the
knowledge of’ for what he calls ‘the idea of’ ” (p. 10). Among the
many criticisms on Locke’s use of the word Idea, this is the only
one which, as it appears to me, precisely hits the mark; and I quote
it for the additional reason that it precisely expresses the point
of difference respecting the import of Propositions, between my view
and what I have spoken of as the Conceptualist view of them. Where a
Conceptualist says that a name or a proposition expresses our Idea
of a thing, I should generally say (instead of our Idea) our
Knowledge, or Belief, concerning the thing itself.
24 If we allow a differentia to what is not really a species. For the
distinction of Kinds, in the sense explained by us, not being in any
way applicable to attributes, it of course follows that although
attributes may be put into classes, those classes can be admitted to
be genera or species only by courtesy.
25 In the fuller discussion which Archbishop Whately has given to this
subject in his later editions, he almost ceases to regard the
definitions of names and those of things as, in any important sense,
distinct. He seems (9th ed. p. 145) to limit the notion of a Real
Definition to one which “explains anything _more_ of the nature of
the thing than is implied in the name;” (including under the word
“implied,” not only what the name connotes, but everything which can
be deduced by reasoning from the attributes connoted). Even this, as
he adds, is usually called, not a Definition, but a Description; and
(as it seems to me) rightly so called. A Description, I conceive,
can only be ranked among Definitions, when taken (as in the case of
the zoological definition of man) to fulfil the true office of a
Definition, by declaring the connotation given to a word in some
special use, as a term of science or art; which special connotation
of course would _not_ be expressed by the proper definition of the
word in its ordinary employment.
Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,
understands by a Real Definition one which contains _less_ than the
Nominal Definition, provided only that what it contains is
sufficient for distinction. “By _real_ definition I mean such an
explanation of the word, be it the whole of the meaning or only
part, as will be sufficient to separate the things contained under
that word from all others. Thus the following, I believe, is a
complete definition of an elephant: An animal which naturally drinks
by drawing the water into its nose, and then spirting it into its
mouth.”—_Formal Logic_, p. 36. Mr. De Morgan’s general proposition
and his example are at variance; for the peculiar mode of drinking
of the elephant certainly forms no part of the meaning of the word
elephant. It could not be said, because a person happened to be
ignorant of this property, that he did not know what an elephant
means.
26 In the only attempt which, so far as I know, has been made to refute
the preceding argumentation, it is maintained that in the first form
of the syllogism,
A dragon is a thing which breathes flame,
A dragon is a serpent,
Therefore some serpent or serpents breathe flame,
“there is just as much truth in the conclusion as there is in the
premisses, or rather, no more in the latter than in the former. If
the general name serpent includes both real and imaginary serpents,
there is no falsity in the conclusion; if not, there is falsity in
the minor premiss.”
Let us, then, try to set out the syllogism on the hypothesis that
the name serpent includes imaginary serpents. We shall find that it
is now necessary to alter the predicates; for it cannot be asserted
that an imaginary creature breathes flame: in predicating of it such
a fact, we assert by the most positive implication that it is real
and not imaginary. The conclusion must run thus, “Some serpent or
serpents either do or are _imagined_ to breathe flame.” And to prove
this conclusion by the instance of dragons, the premisses must be, A
dragon is _imagined_ as breathing flame, A dragon is a (real or
imaginary) serpent: from which it undoubtedly follows, that there
are serpents which are imagined to breathe flame; but the major
premiss is not a definition, nor part of a definition; which is all
that I am concerned to prove.
Let us now examine the other assertion—that if the word serpent
stands for none but real serpents, the minor premiss (A dragon is a
serpent) is false. This is exactly what I have myself said of the
premiss, considered as a statement of fact: but it is not false as
part of the definition of a dragon; and since the premisses, or one
of them, _must_ be false, (the conclusion being so,) the real
premiss cannot be the definition, which is true, but the statement
of fact, which is false.
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.
79 This view of the necessary coexistence 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.
80 Pp. 159-162.
81 Infra, book iv., chap. ii. On Abstraction.
82 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 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 analyse, 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 _à
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 favourable as this to Nature’s
experimental talents, her experiment is of little value except in
corroboration of a conclusion already attained through other means.
83 Discourse, pp. 156-8, and 171.
_ 84 Outlines of Astronomy_, p. 584.
85 Dr. Whewell, in his reply, expresses a very unfavourable opinion of
the utility of the Four Methods, as well as of the aptness of the
examples by which I have attempted to illustrate them. His words are
these (pp. 44-6):
“Upon these methods, the obvious thing to remark is, that they take
for granted the very thing which is most difficult to discover, the
reduction of the phenomena to formulæ such as are here presented to
us. When we have any set of complex facts offered to us; for
instance, those which were offered in the cases of discovery which I
have mentioned,—the facts of the planetary paths, of falling bodies,
of refracted rays, of cosmical motions, of chemical analysis; and
when, in any of these cases, we would discover the law of nature
which governs them, or, if any one chooses so to term it, the
feature in which all the cases agree, where are we to look for our
A, B, C, and _a, b, c_? Nature does not present to us the cases in
this form; and how are we to reduce them to this form? You say,
_when_ we find the combination of A B C with _a b c_ and A B D with
_a b d_, then we may draw our inference. Granted; but when and where
are we to find such combinations? Even now that the discoveries are
made, who will point out to us what are the A, B, C, and _a, b, c_
elements of the cases which have just been enumerated? Who will tell
us which of the methods of inquiry those historically real and
successful inquiries exemplify? Who will carry these formulæ through
the history of the sciences, as they have really grown up; and shew
us that these four methods have been operative in their formation;
or that any light is thrown upon the steps of their progress by
reference to these formulæ?”
He adds that, in this work, the methods have not been applied “to a
large body of conspicuous and undoubted examples of discovery,
extending along the whole history of science,” which ought to have
been done in order that the methods might be shown to possess the
“advantage” (which he claims as belonging to his own) of being those
“by which all great discoveries in science have really been
made.”—(p. 66.)
There is a striking similarity between the objections here made
against Canons of Induction, and what was alleged, in the last
century, by as able men as Dr. Whewell, against the acknowledged
Canon of Ratiocination. Those who protested against the Aristotelian
Logic said of the Syllogism, what Dr. Whewell says of the Inductive
Methods, that it “takes for granted the very thing which is most
difficult to discover, the reduction of the argument to formulæ such
as are here presented to us.” The grand difficulty, they said, is to
obtain your syllogism, not to judge of its correctness when
obtained. On the matter of fact, both they and Dr. Whewell are
right. The greatest difficulty in both cases is first that of
obtaining the evidence, and next, of reducing it to the form which
tests its conclusiveness. But if we try so to reduce it without
knowing _to what_, we are not likely to make much progress. It is a
more difficult thing to solve a geometrical problem, than to judge
whether a proposed solution is correct: but if people were not able
to judge of the solution when found, they would have little chance
of finding it. And it cannot be pretended that to judge of an
induction when found, is perfectly easy, is a thing for which aids
and instruments are superfluous; for erroneous inductions, false
inferences from experience, are quite as common, on some subjects
much commoner, than true ones. The business of Inductive Logic is to
provide rules and models (such as the Syllogism and its rules are
for ratiocination) to which if inductive arguments conform, those
arguments are conclusive, and not otherwise. This is what the Four
Methods profess to be, and what I believe they are universally
considered to be by experimental philosophers, who had practised all
of them long before any one sought to reduce the practice to theory.
The assailants of the Syllogism had also anticipated Dr. Whewell in
the other branch of his argument. They said that no discoveries were
ever made by syllogism; and Dr. Whewell says, or seems to say, that
none were ever made by the four Methods of Induction. To the former
objectors, Archbishop Whately very pertinently answered, that their
argument, if good at all, was good against the reasoning process
altogether; for whatever cannot be reduced to syllogism, is not
reasoning. And Dr. Whewell’s argument, if good at all, is good
against all inferences from experience. In saying that no
discoveries were ever made by the four Methods, he affirms that none
were ever made by observation and experiment; for assuredly if any
were, it was by one or other of those methods.
This difference between us accounts for the dissatisfaction which my
examples give him; for I did not select them with a view to satisfy
any one who required to be convinced that observation and experiment
are modes of acquiring knowledge: I confess that in the choice of
them I thought only of illustration, and of facilitating the
_conception_ of the Methods by concrete instances. If it had been my
object to justify the processes themselves as means of
investigation, there would have been no need to look far off, or
make use of recondite or complicated instances. As a specimen of a
truth ascertained by the Method of Agreement, I might have chosen
the proposition, “Dogs bark.” This dog, and that dog, and the other
dog, answer to A B C, A D E, A F G. The circumstance of being a dog,
answers to A. Barking answers to _a_. As a truth made known by the
Method of Difference, “Fire burns” might have sufficed. Before I
touch the fire I am not burnt; this is B C; I touch it, and am
burnt; this is A B C, _a_ B C.
Such familiar experimental processes are not regarded as inductions
by Dr. Whewell; but they are perfectly homogeneous with those by
which, even on his own shewing, the pyramid of science is supplied
with its base. In vain he attempts to escape from this truth by
laying the most arbitrary restrictions on the choice of examples
admissible as instances of Induction: they must neither be such as
are still matter of discussion (p. 47), nor must any of them be
drawn from mental and social subjects (p. 53), nor from ordinary
observation and practical life (pp. 11-15). They must be taken
exclusively from the generalizations by which scientific thinkers
have ascended to great and comprehensive laws of natural phenomena.
Now it is seldom possible, in these complicated inquiries, to go
much beyond the initial steps, without calling in the instrument of
Deduction, and the temporary aid of hypotheses; as I myself, in
common with Dr. Whewell, have maintained against the purely
empirical school. Since therefore such cases could not conveniently
be selected to illustrate the principles of mere observation and
experiment, Dr. Whewell takes advantage of their absence to
represent the Experimental Methods as serving no purpose in
scientific investigation; forgetting that if those methods had not
supplied the first generalizations, there would have been no
materials for his own conception of Induction to work upon.
His challenge, however, to point out which of the four methods are
exemplified in certain important cases of scientific inquiry, is
easily answered. “The planetary paths,” as far as they are a case of
induction at all, (see, on this point, the second chapter of the
present Book) fall under the Method of Agreement. The law of
“falling bodies,” namely that they describe spaces proportional to
the squares of the times, was historically a deduction from the
first law of motion; but the experiments by which it was verified,
and by which it might have been discovered, were examples of the
Method of Agreement; and the apparent variation from the true law,
caused by the resistance of the air, was cleared up by experiments
_in vacuo_, constituting an application of the Method of Difference.
The law of “refracted rays,” (the constancy of the ratio between the
sines of incidence and of refraction for each refracting substance)
was ascertained by direct measurement, and therefore by the Method
of Agreement. The “cosmical motions” were determined by highly
complex processes of thought, in which Deduction was predominant,
but the Methods of Agreement and of Concomitant Variations had a
large part in establishing the empirical laws. Every case without
exception of “chemical analysis” constitutes a well marked example
of the Method of Difference. To any one acquainted with the
subjects—to Dr. Whewell himself, there would not be the smallest
difficulty in setting out “the A B C and _a b c_ elements” of these
cases.
If discoveries are ever made by observation and experiment without
Deduction, the four methods are methods of discovery: but even if
they were not methods of discovery, it would not be the less true
that they are the sole methods of Proof; and in that character, even
the results of Deduction are amenable to them. The great
generalizations which begin as Hypotheses must end by being proved,
and are in reality (as will be shown hereafter) proved by the Four
Methods. Now it is with Proof, as such, that Logic is principally
concerned. This distinction has indeed no chance of finding favour
with Dr. Whewell; for it is the peculiarity of his system not to
recognise, in cases of Induction, any necessity for proof. If, after
assuming an hypothesis and carefully collating it with facts,
nothing is brought to light inconsistent with it, that is, if
experience does not _dis_prove it, he is content: at least until a
simpler hypothesis, equally consistent with experience, presents
itself. If this be Induction, doubtless there is no necessity for
the four methods. But to suppose that it is so, appears to me a
radical misconception of the nature of the evidence of physical
truths.
_ 86 Ante_, p. 378.
87 It seems hardly necessary to say that the word _impinges_, as a
general term to express collision of forces, was here used by a
figure of speech, and not as expressive of any theory respecting the
nature of force.
_ 88 Essays on some Unsettled Questions of Political Economy_, Essay V.
89 There is no danger of confounding this acceptation of the term with
the peculiar employment of the phrase “tangential force” in the
theory of the planetary perturbations.
90 Suprà, p. 420.
91 As corroborating the opinion that the protoxide of iron in the
venous blood is only partially carbonated, the fact has been
suggested, that the system shows great readiness to absorb an extra
quantity of carbonic acid, as furnished in effervescing drinks. In
such cases the acid must combine with something, and that something
is not improbably the free protoxide. It would be worth ascertaining
whether the protoxide itself or its carbonate has the greatest
facility in absorbing oxygen and turning itself into hydrated
peroxide in the lungs. If the carbonate, then the beneficial effect,
on the animal economy, of drinks which give an artificial supply of
carbonic acid to the system, would be, to that extent, deductively
established.
92 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 tumours 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 tumour, from being nourished; in the case
of inflammation, it removes the stimulus, which the organ is unfit
to receive: in the case of tumours, 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.