MISCELLANEOUS EXAMPLES OF THE FOUR METHODS.
§ 1. I shall select, as a first example, an interesting speculation of
one of the most eminent of theoretical chemists, Baron Liebig. The
object in view, is to ascertain the immediate cause of the death
produced by metallic poisons.
Arsenious acid, and the salts of lead, bismuth, copper, and mercury, if
introduced into the animal organism, except in the smallest doses,
destroy life. These facts have long been known, as insulated truths of
the lowest order of generalization; but it was reserved for Liebig, by
an apt employment of the first two of our methods of experimental
inquiry, to connect these truths together by a higher induction,
pointing out what property, common to all these deleterious substances,
is the really operating cause of their fatal effect.
When solutions of these substances are placed in sufficiently close
contact with many animal products, albumen, milk, muscular fibre, and
animal membranes, the acid or salt leaves the water in which it was
dissolved, and enters into combination with the animal substance: which
substance, after being thus acted upon, is found to have lost its
tendency to spontaneous decomposition, or putrefaction.
Observation also shows, in cases where death has been produced by these
poisons, that the parts of the body with which the poisonous substances
have been brought into contact, do not afterwards putrefy.
And, finally, when the poison has been supplied in too small a quantity
to destroy life, eschars are produced, that is, certain superficial
portions of the tissues are destroyed, which are afterwards thrown off
by the reparative process taking place in the healthy parts.
These three sets of instances admit of being treated according to the
Method of Agreement. In all of them the metallic compounds are brought
into contact with the substances which compose the human or animal body;
and the instances do not seem to agree in any other circumstance. The
remaining antecedents are as different, and even opposite, as they could
possibly be made; for in some the animal substances exposed to the
action of the poisons are in a state of life, in others only in a state
of organization, in others not even in that. And what is the result
which follows in all the cases? The conversion of the animal substance
(by combination with the poison) into a chemical compound, held together
by so powerful a force as to resist the subsequent action of the
ordinary causes of decomposition. Now, organic life (the necessary
condition of sensitive life) consisting in a continual state of
decomposition and recomposition of the different organs and tissues;
whatever incapacitates them for this decomposition destroys life. And
thus the proximate cause of the death produced by this description of
poisons, is ascertained, as far as the Method of Agreement can ascertain
it.
Let us now bring our conclusion to the test of the Method of Difference.
Setting out from the cases already mentioned, in which the antecedent is
the presence of substances forming with the tissues a compound incapable
of putrefaction, (and _à fortiori_ incapable of the chemical actions
which constitute life,) and the consequent is death, either of the whole
organism, or of some portion of it; let us compare with these cases
other cases, as much resembling them as possible, but in which that
effect is not produced. And, first, "many insoluble basic salts of
arsenious acid are known not to be poisonous. The substance called
alkargen, discovered by Bunsen, which contains a very large quantity of
arsenic, and approaches very closely in composition to the organic
arsenious compounds found in the body, has not the slightest injurious
action upon the organism." Now when these substances are brought into
contact with the tissues in any way, they do not combine with them; they
do not arrest their progress to decomposition. As far, therefore, as
these instances go, it appears that when the effect is absent, it is by
reason of the absence of that antecedent which we had already good
ground for considering as the proximate cause.
But the rigorous conditions of the Method of Difference are not yet
satisfied; for we cannot be sure that these unpoisonous bodies agree
with the poisonous substances in every property, except the particular
one, of entering into a difficultly decomposable compound with the
animal tissues. To render the method strictly applicable, we need an
instance, not of a different substance, but of one of the very same
substances, in circumstances which would prevent it from forming, with
the tissues, the sort of compound in question; and then, if death does
not follow, our case is made out. Now such instances are afforded by the
antidotes to these poisons. For example, in case of poisoning by
arsenious acid, if hydrated peroxide of iron is administered, the
destructive agency is instantly checked. Now this peroxide is known to
combine with the acid, and form a compound, which, being insoluble,
cannot act at all on animal tissues. So, again, sugar is a well-known
antidote to poisoning by salts of copper; and sugar reduces those salts
either into metallic copper, or into the red suboxide, neither of which
enters into combination with animal matter. The disease called painter's
colic, so common in manufactories of white lead, is unknown where the
workmen are accustomed to take, as a preservative, sulphuric acid
lemonade (a solution of sugar rendered acid by sulphuric acid). Now
diluted sulphuric acid has the property of decomposing all compounds of
lead with organic matter, or of preventing them from being formed.
There is another class of instances, of the nature required by the
Method of Difference, which seem at first sight to conflict with the
theory. Soluble salts of silver, such for instance as the nitrate, have
the same stiffening antiseptic effect on decomposing animal substances
as corrosive sublimate and the most deadly metallic poisons; and when
applied to the external parts of the body, the nitrate is a powerful
caustic; depriving those parts of all active vitality, and causing them
to be thrown off by the neighbouring living structures, in the form of
an eschar. The nitrate and the other salts of silver ought, then, it
would seem, if the theory be correct, to be poisonous; yet they may be
administered internally with perfect impunity. From this apparent
exception arises the strongest confirmation which the theory has yet
received. Nitrate of silver, in spite of its chemical properties, does
not poison when introduced into the stomach; but in the stomach, as in
all animal liquids, there is common salt; and in the stomach there is
also free muriatic acid. These substances operate as natural antidotes,
combining with the nitrate, and if its quantity is not too great,
immediately converting it into chloride of silver; a substance very
slightly soluble, and therefore incapable of combining with the tissues,
although to the extent of its solubility it has a medicinal influence,
though an entirely different class of organic actions.
The preceding instances have afforded an induction of a high order of
conclusiveness, illustrative of the two simplest of our four methods;
though not rising to the maximum of certainty which the Method of
Difference, in its most perfect exemplification, is capable of
affording. For (let us not forget) the positive instance and the
negative one which the rigour of that method requires, ought to differ
only in the presence or absence of one single circumstance. Now, in the
preceding argument, they differ in the presence or absence not of a
single _circumstance_, but of a single _substance_: and as every
substance has innumerable properties, there is no knowing what number of
real differences are involved in what is nominally and apparently only
one difference. It is conceivable that the antidote, the peroxide of
iron for example, may counteract the poison through some other of its
properties than that of forming an insoluble compound with it; and if
so, the theory would fall to the ground, so far as it is supported by
that instance. This source of uncertainty, which is a serious hindrance
to all extensive generalizations in chemistry, is however reduced in the
present case to almost the lowest degree possible, when we find that
not only one substance, but many substances, possess the capacity of
acting as antidotes to metallic poisons, and that all these agree in the
property of forming insoluble compounds with the poisons, while they
cannot be ascertained to agree in any other property whatsoever. We have
thus, in favour of the theory, all the evidence which can be obtained by
what we termed the Indirect Method of Difference, or the Joint Method of
Agreement and Difference; the evidence of which, though it never can
amount to that of the Method of Difference properly so called, may
approach indefinitely near to it.
§ 2. Let the object be[34] to ascertain the law of what is termed
_induced_ electricity; to find under what conditions any electrified
body, whether positively or negatively electrified, gives rise to a
contrary electric state in some other body adjacent to it.
The most familiar exemplification of the phenomenon to be investigated
is the following. Around the prime conductors of an electrical machine,
the atmosphere to some distance, or any conducting surface suspended in
that atmosphere, is found to be in an electric condition opposite to
that of the prime conductor itself. Near and around the positive prime
conductor there is negative electricity, and near and around the
negative prime conductor there is positive electricity. When pith balls
are brought near to either of the conductors, they become electrified
with the opposite electricity to it; either receiving a share from the
already electrified atmosphere by conduction, or acted upon by the
direct inductive influence of the conductor itself: they are then
attracted by the conductor to which they are in opposition; or, if
withdrawn in their electrified state, they will be attracted by any
other oppositely charged body. In like manner the hand, if brought near
enough to the conductor, receives or gives an electric discharge; now we
have no evidence that a charged conductor can be suddenly discharged
unless by the approach of a body oppositely electrified. In the case,
therefore, of the electric machine, it appears that the accumulation of
electricity in an insulated conductor is always accompanied by the
excitement of the contrary electricity in the surrounding atmosphere,
and in every conductor placed near the former conductor. It does not
seem possible, in this case, to produce one electricity by itself.
Let us now examine all the other instances which we can obtain,
resembling this instance in the given consequent, namely, the evolution
of an opposite electricity in the neighbourhood of an electrified body.
As one remarkable instance we have the Leyden jar; and after the
splendid experiments of Faraday in complete and final establishment of
the substantial identity of magnetism and electricity, we may cite the
magnet, both the natural and the electro-magnet, in neither of which it
is possible to produce one kind of electricity by itself, or to charge
one pole without charging an opposite pole with the contrary electricity
at the same time. We cannot have a magnet with one pole: if we break a
natural loadstone into a thousand pieces, each piece will have its two
oppositely electrified poles complete within itself. In the voltaic
circuit, again, we cannot have one current without its opposite. In the
ordinary electric machine, the glass cylinder or plate, and the rubber,
acquire opposite electricities.
From all these instances, treated by the Method of Agreement, a general
law appears to result. The instances embrace all the known modes in
which a body can become charged with electricity; and in all of them
there is found, as a concomitant or consequent, the excitement of the
opposite electric state in some other body or bodies. It seems to follow
that the two facts are invariably connected, and that the excitement of
electricity in any body has for one of its necessary conditions the
possibility of a simultaneous excitement of the opposite electricity in
some neighbouring body.
As the two contrary electricities can only be produced together, so
they can only cease together. This may be shown by an application of the
Method of Difference to the example of the Leyden jar. It needs scarcely
be here remarked that in the Leyden jar, electricity can be accumulated
and retained in considerable quantity, by the contrivance of having two
conducting surfaces of equal extent, and parallel to each other through
the whole of that extent, with a non-conducting substance such as glass
between them. When one side of the jar is charged positively, the other
is charged negatively, and it was by virtue of this fact that the Leyden
jar served just now as an instance in our employment of the Method of
Agreement. Now it is impossible to discharge one of the coatings unless
the other can be discharged at the same time. A conductor held to the
positive side cannot convey away any electricity unless an equal
quantity be allowed to pass from the negative side: if one coating be
perfectly insulated, the charge is safe. The dissipation of one must
proceed _pari passu_ with that of the other.
The law thus strongly indicated admits of corroboration by the Method of
Concomitant Variations. The Leyden jar is capable of receiving a much
higher charge than can ordinarily be given to the conductor of an
electrical machine. Now in the case of the Leyden jar, the metallic
surface which receives the induced electricity is a conductor exactly
similar to that which receives the primary charge, and is therefore as
susceptible of receiving and retaining the one electricity, as the
opposite surface of receiving and retaining the other; but in the
machine, the neighbouring body which is to be oppositely electrified is
the surrounding atmosphere, or any body casually brought near to the
conductor; and as these are generally much inferior in their capacity of
becoming electrified, to the conductor itself, their limited power
imposes a corresponding limit to the capacity of the conductor for being
charged. As the capacity of the neighbouring body for supporting the
opposition increases, a higher charge becomes possible: and to this
appears to be owing the great superiority of the Leyden jar.
A further and most decisive confirmation by the Method of Difference,
is to be found in one of Faraday's experiments in the course of his
researches on the subject of induced electricity.
Since common or machine electricity, and voltaic electricity, may be
considered for the present purpose to be identical, Faraday wished to
know whether, as the prime conductor develops opposite electricity upon
a conductor in its vicinity, so a voltaic current running along a wire
would induce an opposite current upon another wire laid parallel to it
at a short distance. Now this case is similar to the cases previously
examined, in every circumstance except the one to which we have ascribed
the effect. We found in the former instances that whenever electricity
of one kind was excited in one body, electricity of the opposite kind
must be excited in a neighbouring body. But in Faraday's experiment this
indispensable opposition exists within the wire itself. From the nature
of a voltaic charge, the two opposite currents necessary to the
existence of each other are both accommodated in one wire; and there is
no need of another wire placed beside it to contain one of them, in the
same way as the Leyden jar must have a positive and a negative surface.
The exciting cause can and does produce all the effect which its laws
require, independently of any electric excitement of a neighbouring
body. Now the result of the experiment with the second wire was, that no
opposite current was produced. There was an instantaneous effect at the
closing and breaking of the voltaic circuit; electric inductions
appeared when the two wires were moved to and from one another; but
these are phenomena of a different class. There was no induced
electricity in the sense in which this is predicated of the Leyden jar;
there was no sustained current running up the one wire while an opposite
current ran down the neighbouring wire; and this alone would have been a
true parallel case to the other.
It thus appears by the combined evidence of the Method of Agreement, the
Method of Concomitant Variations, and the most rigorous form of the
Method of Difference, that neither of the two kinds of electricity can
be excited without an equal excitement of the other and opposite kind:
that both are effects of the same cause; that the possibility of the one
is a condition of the possibility of the other, and the quantity of the
one an impassable limit to the quantity of the other. A scientific
result of considerable interest in itself, and illustrating those three
methods in a manner both characteristic and easily intelligible.[35]
§ 3. Our third example shall be extracted from Sir John Herschel's
_Discourse on the Study of Natural Philosophy_, a work replete with
happily-selected exemplifications of inductive processes from almost
every department of physical science, and in which alone, of all books
which I have met with, the four methods of induction are distinctly
recognised, though not so clearly characterized and defined, nor their
correlation so fully shown, as has appeared to me desirable. The present
example is described by Sir John Herschel as "one of the most beautiful
specimens" which can be cited "of inductive experimental inquiry lying
within a moderate compass;" the theory of dew, first promulgated by the
late Dr. Wells, and now universally adopted by scientific authorities.
The passages in inverted commas are extracted verbatim from the
Discourse.[36]
"Suppose _dew_ were the phenomenon proposed, whose cause we would know.
In the first place" we must determine precisely what we mean by dew:
what the fact really is, whose cause we desire to investigate. "We must
separate dew from rain, and the moisture of fogs, and limit the
application of the term to what is really meant, which is the
spontaneous appearance of moisture on substances exposed in the open air
when no rain or _visible_ wet is falling." This answers to a preliminary
operation which will be characterized in the ensuing book, treating of
operations subsidiary to induction.[37]
"Now, here we have analogous phenomena in the moisture which bedews a
cold metal or stone when we breathe upon it; that which appears on a
glass of water fresh from the well in hot weather; that which appears on
the inside of windows when sudden rain or hail chills the external air;
that which runs down our walls when, after a long frost, a warm moist
thaw comes on." Comparing these cases, we find that they all contain the
phenomenon which was proposed as the subject of investigation. Now "all
these instances agree in one point, the coldness of the object dewed, in
comparison with the air in contact with it." But there still remains the
most important case of all, that of nocturnal dew: does the same
circumstance exist in this case? "Is it a fact that the object dewed is
colder than the air? Certainly not, one would at first be inclined to
say; for what is to _make_ it so? But ... the experiment is easy: we
have only to lay a thermometer in contact with the dewed substance, and
hang one at a little distance above it, out of reach of its influence.
The experiment has been therefore made, the question has been asked, and
the answer has been invariably in the affirmative. Whenever an object
contracts dew, it _is_ colder than the air."
Here then is a complete application of the Method of Agreement,
establishing the fact of an invariable connexion between the deposition
of dew on a surface, and the coldness of that surface compared with the
external air. But which of these is cause, and which effect? or are they
both effects of something else? On this subject the Method of Agreement
can afford us no light: we must call in a more potent method. "We must
collect more facts, or, which comes to the same thing, vary the
circumstances; since every instance in which the circumstances differ is
a fresh fact: and especially, we must note the contrary or negative
cases, _i.e._ where no dew is produced:" a comparison between instances
of dew and instances of no dew, being the condition necessary to bring
the Method of Difference into play.
"Now, first, no dew is produced on the surface of polished metals, but
it _is_ very copiously on glass, both exposed with their faces upwards,
and in some cases the under side of a horizontal plate of glass is also
dewed." Here is an instance in which the effect is produced, and another
instance in which it is not produced; but we cannot yet pronounce, as
the canon of the Method of Difference requires, that the latter instance
agrees with the former in all its circumstances except one; for the
differences between glass and polished metals are manifold, and the only
thing we can as yet be sure of is, that the cause of dew will be found
among the circumstances by which the former substance is distinguished
from the latter. But if we could be sure that glass, and the various
other substances on which dew is deposited, have only one quality in
common, and that polished metals and the other substances on which dew
is not deposited have also nothing in common but the one circumstance,
of not having the one quality which the others have; the requisitions of
the Method of Difference would be completely satisfied, and we should
recognise, in that quality of the substances, the cause of dew. This,
accordingly, is the path of inquiry which is next to be pursued.
"In the cases of polished metal and polished glass, the contrast shows
evidently that the _substance_ has much to do with the phenomenon;
therefore let the substance _alone_ be diversified as much as possible,
by exposing polished surfaces of various kinds. This done, a _scale of
intensity_ becomes obvious. Those polished substances are found to be
most strongly dewed which conduct heat worst; while those which conduct
well, resist dew most effectually." The complication increases; here is
the Method of Concomitant Variations called to our assistance; and no
other method was practicable on this occasion; for the quality of
conducting heat could not be excluded, since all substances conduct heat
in some degree. The conclusion obtained is, that _cæteris paribus_ the
deposition of dew is in some proportion to the power which the body
possesses of resisting the passage of heat; and that this, therefore,
(or something connected with this,) must be at least one of the causes
which assist in producing the deposition of dew on the surface.
"But if we expose rough surfaces instead of polished, we sometimes find
this law interfered with. Thus, roughened iron, especially if painted
over or blackened, becomes dewed sooner than varnished paper; the kind
of _surface_, therefore, has a great influence. Expose, then, the _same_
material in very diversified states as to surface," (that is, employ the
Method of Difference to ascertain concomitance of variations,) "and
another scale of intensity becomes at once apparent; those _surfaces_
which _part with their heat_ most readily by radiation, are found to
contract dew most copiously." Here, therefore, are the requisites for a
second employment of the Method of Concomitant Variations; which in this
case also is the only method available, since all substances radiate
heat in some degree or other. The conclusion obtained by this new
application of the method is, that _cæteris paribus_ the deposition of
dew is also in some proportion to the power of radiating heat; and that
the quality of doing this abundantly (or some cause on which that
quality depends) is another of the causes which promote the deposition
of dew on the substance.
"Again, the influence ascertained to exist of _substance_ and _surface_
leads us to consider that of _texture_: and here, again, we are
presented on trial with remarkable differences, and with a third scale
of intensity, pointing out substances of a close firm texture, such as
stones, metals, &c., as unfavourable, but those of a loose one, as
cloth, velvet, wool, eider-down, cotton, &c., as eminently favourable to
the contraction of dew." The Method of Concomitant Variations is here,
for the third time, had recourse to; and, as before, from necessity,
since the texture of no substance is absolutely firm or absolutely
loose. Looseness of texture, therefore, or something which is the cause
of that quality, is another circumstance which promotes the deposition
of dew; but this third cause resolves itself into the first, viz. the
quality of resisting the passage of heat: for substances of loose
texture "are precisely those which are best adapted for clothing, or for
impeding the free passage of heat from the skin into the air, so as to
allow their outer surfaces to be very cold, while they remain warm
within;" and this last is, therefore, an induction (from fresh
instances) simply _corroborative_ of a former induction.
It thus appears that the instances in which much dew is deposited, which
are very various, agree in this, and, so far as we are able to observe,
in this only, that they either radiate heat rapidly or conduct it
slowly: qualities between which there is no other circumstance of
agreement, than that by virtue of either, the body tends to lose heat
from the surface more rapidly than it can be restored from within. The
instances, on the contrary, in which no dew, or but a small quantity of
it, is formed, and which are also extremely various, agree (as far as we
can observe) in nothing except in _not_ having this same property. We
seem, therefore, to have detected the characteristic difference between
the substances on which dew is produced, and those on which it is not
produced. And thus have been realized the requisitions of what we have
termed the Indirect Method of Difference, or the Joint Method of
Agreement and Difference. The example afforded of this indirect method,
and of the manner in which the data are prepared for it by the Methods
of Agreement and of Concomitant Variations, is the most important of all
the illustrations of induction afforded by this interesting speculation.
We might now consider the question, on what the deposition of dew
depends, to be completely solved, if we could be quite sure that the
substances on which dew is produced differ from those on which it is
not, in _nothing_ but in the property of losing heat from the surface
faster than the loss can be repaired from within. And though we never
can have that complete certainty, this is not of so much importance as
might at first be supposed; for we have, at all events, ascertained
that even if there be any other quality hitherto unobserved which is
present in all the substances which contract dew, and absent in those
which do not, this other property must be one which, in all that great
number of substances, is present or absent exactly where the property of
being a better radiator than conductor is present or absent; an extent
of coincidence which affords a strong presumption of a community of
cause, and a consequent invariable coexistence between the two
properties; so that the property of being a better radiator than
conductor, if not itself the cause, almost certainly always accompanies
the cause, and, for purposes of prediction, no error is likely to be
committed by treating it as if it were really such.
Reverting now to an earlier stage of the inquiry, let us remember that
we had ascertained that, in every instance where dew is formed, there is
actual coldness of the surface below the temperature of the surrounding
air; but we were not sure whether this coldness was the cause of dew, or
its effect. This doubt we are now able to resolve. We have found that,
in every such instance, the substance is one which, by its own
properties or laws, would, if exposed in the night, become colder than
the surrounding air. The coldness therefore being accounted for
independently of the dew, while it is proved that there is a connexion
between the two, it must be the dew which depends on the coldness; or in
other words, the coldness is the cause of the dew.
This law of causation, already so amply established, admits, however, of
efficient additional corroboration in no less than three ways. First, by
deduction from the known laws of aqueous vapour when diffused through
air or any other gas; and though we have not yet come to the Deductive
Method, we will not omit what is necessary to render this speculation
complete. It is known by direct experiment that only a limited quantity
of water can remain suspended in the state of vapour at each degree of
temperature, and that this maximum grows less and less as the
temperature diminishes. From this it follows, deductively, that if there
is already as much vapour suspended as the air will contain at its
existing temperature, any lowering of that temperature will cause a
portion of the vapour to be condensed, and become water. But, again, we
know deductively, from the laws of heat, that the contact of the air
with a body colder than itself, will necessarily lower the temperature
of the stratum of air immediately applied to its surface; and will
therefore cause it to part with a portion of its water, which
accordingly will, by the ordinary laws of gravitation or cohesion,
attach itself to the surface of the body, thereby constituting dew. This
deductive proof, it will have been seen, has the advantage of at once
proving causation as well as coexistence; and it has the additional
advantage that it also accounts for the exceptions to the occurrence of
the phenomenon, the cases in which, although the body is colder than the
air, yet no dew is deposited; by showing that this will necessarily be
the case when the air is so under-supplied with aqueous vapour,
comparatively to its temperature, that even when somewhat cooled by the
contact of the colder body, it can still continue to hold in suspension
all the vapour which was previously suspended in it: thus in a very dry
summer there are no dews, in a very dry winter no hoar frost. Here,
therefore, is an additional condition of the production of dew, which
the methods we previously made use of failed to detect, and which might
have remained still undetected, if recourse had not been had to the plan
of deducing the effect from the ascertained properties of the agents
known to be present.
The second corroboration of the theory is by direct experiment,
according to the canon of the Method of Difference. We can, by cooling
the surface of any body, find in all cases some temperature, (more or
less inferior to that of the surrounding air, according to its
hygrometric condition,) at which dew will begin to be deposited. Here,
too, therefore, the causation is directly proved. We can, it is true,
accomplish this only on a small scale; but we have ample reason to
conclude that the same operation, if conducted in Nature's great
laboratory, would equally produce the effect.
And, finally, even on that great scale we are able to verify the result.
The case is one of those rare cases, as we have shown them to be, in
which nature works the experiment for us in the same manner in which we
ourselves perform it; introducing into the previous state of things a
single and perfectly definite new circumstance, and manifesting the
effect so rapidly that there is not time for any other material change
in the pre-existing circumstances. "It is observed that dew is never
copiously deposited in situations much screened from the open sky, and
not at all in a cloudy night; but _if the clouds withdraw even for a few
minutes, and leave a clear opening, a deposition of dew presently
begins_, and goes on increasing.... Dew formed in clear intervals will
often even evaporate again when the sky becomes thickly overcast." The
proof, therefore, is complete, that the presence or absence of an
uninterrupted communication with the sky causes the deposition or
non-deposition of dew. Now, since a clear sky is nothing but the absence
of clouds, and it is a known property of clouds, as of all other bodies
between which and any given object nothing intervenes but an elastic
fluid, that they tend to raise or keep up the superficial temperature of
the object by radiating heat to it, we see at once that the
disappearance of clouds will cause the surface to cool; so that Nature,
in this case, produces a change in the antecedent by definite and known
means, and the consequent follows accordingly: a natural experiment
which satisfies the requisitions of the Method of Difference.[38]
The accumulated proof of which the Theory of Dew has been found
susceptible, is a striking instance of the fulness of assurance which
the inductive evidence of laws of causation may attain, in cases in
which the invariable sequence is by no means obvious to a superficial
view.
§ 4. The admirable physiological investigations of Dr. Brown-Séquard
afford brilliant examples of the application of the Inductive Methods to
a class of inquiries in which, for reasons which will presently be
given, direct induction takes place under peculiar difficulties and
disadvantages. As one of the most apt instances I select his speculation
(in the Proceedings of the Royal Society for May 16, 1861) on the
relations between muscular irritability, cadaveric rigidity, and
putrefaction.
The law which Dr. Brown-Séquard's investigation tends to establish, is
the following:--"The greater the degree of muscular irritability at the
time of death, the later the cadaveric rigidity sets in, and the longer
it lasts, and the later also putrefaction appears, and the slower it
progresses." One would say at first sight that the method here required
must be that of Concomitant Variations. But this is a delusive
appearance, arising from the circumstance that the conclusion to be
tested is itself a fact of concomitant variation. For the establishment
of that fact any of the Methods may be put in requisition, and it will
be found that the fourth Method, though really employed, has only a
subordinate place in this particular investigation.
The evidences by which Dr. Brown-Séquard establishes the law may be
enumerated as follows:--
1st. Paralysed muscles have greater irritability than healthy muscles.
Now, paralysed muscles are later in assuming the cadaveric rigidity than
healthy muscles, the rigidity lasts longer, and putrefaction sets in
later and proceeds more slowly.
Both these propositions had to be proved by experiment; and for the
experiments which prove them, science is also indebted to Dr.
Brown-Séquard. The former of the two--that paralysed muscles have
greater irritability than healthy muscles--he ascertained in various
ways, but most decisively by "comparing the duration of irritability in
a paralysed muscle and in the corresponding healthy one of the opposite
side, while they are both submitted to the same excitation." He "often
found in experimenting in that way, that the paralysed muscle remained
irritable twice, three times, or even four times as long as the healthy
one." This is a case of induction by the Method of Difference. The two
limbs, being those of the same animal, were presumed to differ in no
circumstance material to the case except the paralysis, to the presence
and absence of which, therefore, the difference in the muscular
irritability was to be attributed. This assumption of complete
resemblance in all material circumstances save one, evidently could not
be safely made in any one pair of experiments, because the two legs of
any given animal might be accidentally in very different pathological
conditions; but if, besides taking pains to avoid any such difference,
the experiment was repeated sufficiently often in different animals to
exclude the supposition that any abnormal circumstance could be present
in them all, the conditions of the Method of Difference were adequately
secured.
In the same manner in which Dr. Brown-Séquard proved that paralysed
muscles have greater irritability, he also proved the correlative
proposition respecting cadaveric rigidity and putrefaction. Having, by
section of the roots of the sciatic nerve, and again of a lateral half
of the spinal cord, produced paralysis in one hind leg of an animal
while the other remained healthy, he found that not only did muscular
irritability last much longer in the paralysed limb, but rigidity set in
later and ended later, and putrefaction began later and was less rapid
than on the healthy side. This is a common case of the Method of
Difference, requiring no comment. A further and very important
corroboration was obtained by the same method. When the animal was
killed, not shortly after the section of the nerve, but a month later,
the effect was reversed; rigidity set in sooner, and lasted a shorter
time, than in the healthy muscles. But after this lapse of time, the
paralysed muscles, having been kept by the paralysis in a state of rest,
had lost a great part of their irritability, and instead of more, had
become less irritable than those on the healthy side. This gives the A B
C, a b c, and B C, b c, of the Method of Difference. One antecedent,
increased irritability, being changed, and the other circumstances being
the same, the consequence did not follow; and moreover, when a new
antecedent, contrary to the first, was supplied, it was followed by a
contrary consequent. This instance is attended with the special
advantage, of proving that the retardation and prolongation of the
rigidity do not depend directly on the paralysis, since that was the
same in both the instances; but specifically on one effect of the
paralysis, namely, the increased irritability; since they ceased when it
ceased, and were reversed when it was reversed.
2ndly. Diminution of the temperature of muscles before death increases
their irritability. But diminution of their temperature also retards
cadaveric rigidity and putrefaction.
Both these truths were first made known by Dr. Brown-Séquard himself,
through experiments which conclude according to the Method of
Difference. There is nothing in the nature of the process requiring
specific analysis.
3rdly. Muscular exercise, prolonged to exhaustion, diminishes the
muscular irritability. This is a well-known truth, dependent on the most
general laws of muscular action, and proved by experiments under the
Method of Difference, constantly repeated. Now it has been shown by
observation that overdriven cattle, if killed before recovery from their
fatigue, become rigid and putrefy in a surprisingly short time. A
similar fact has been observed in the case of animals hunted to death;
cocks killed during or shortly after a fight; and soldiers slain in the
field of battle. These various cases agree in no circumstance, directly
connected with the muscles, except that these have just been subjected
to exhausting exercise. Under the canon, therefore, of the Method of
Agreement, it may be inferred that there is a connexion between the two
facts. The Method of Agreement, indeed, as has been shown, is not
competent to prove causation. The present case, however, is already
known to be a case of causation, it being certain that the state of the
body after death must somehow depend upon its state at the time of
death. We are therefore warranted in concluding that the single
circumstance in which all the instances agree, is the part of the
antecedent which is the cause of that particular consequent.
4thly. In proportion as the nutrition of muscles is in a good state,
their irritability is high. This fact also rests on the general evidence
of the laws of physiology, grounded on many familiar applications of the
Method of Difference. Now, in the case of those who die from accident or
violence, with their muscles in a good state of nutrition, the muscular
irritability continues long after death, rigidity sets in late, and
persists long without the putrefactive change. On the contrary, in cases
of disease in which nutrition has been diminished for a long time before
death, all these effects are reversed. These are the conditions of the
Joint Method of Agreement and Difference. The cases of retarded and long
continued rigidity here in question, agree only in being preceded by a
high state of nutrition of the muscles; the cases of rapid and brief
rigidity agree only in being preceded by a low state of muscular
nutrition; a connexion is therefore inductively proved between the
degree of the nutrition, and the slowness and prolongation of the
rigidity.
5thly. Convulsions, like exhausting exercise, but in a still greater
degree, diminish the muscular irritability. Now, when death follows
violent and prolonged convulsions, as in tetanus, hydrophobia, some
cases of cholera, and certain poisons, rigidity sets in very rapidly,
and after a very brief duration, gives place to putrefaction. This is
another example of the Method of Agreement, of the same character with
No. 3.
6thly. The series of instances which we shall take last, is of a more
complex character, and requires a more minute analysis.
It has long been observed that in some cases of death by lightning,
cadaveric rigidity either does not take place at all, or is of such
extremely brief duration as to escape notice, and that in these cases
putrefaction is very rapid. In other cases, however, the usual cadaveric
rigidity appears. There must be some difference in the cause, to account
for this difference in the effect. Now "death by lightning may be the
result of, 1st, a syncope by fright, or in consequence of a direct or
reflex influence of lightning on the par vagum; 2ndly, hemorrhage in or
around the brain, or in the lungs, the pericardium, &c.; 3rdly,
concussion, or some other alteration in the brain;" none of which
phenomena have any known property capable of accounting for the
suppression, or almost suppression, of the cadaveric rigidity. But the
cause of death may also be that the lightning produces "a violent
convulsion of every muscle in the body," of which, if of sufficient
intensity, the known effect would be that "muscular irritability ceases
almost at once." If Dr. Brown-Séquard's generalization is a true law,
these will be the very cases in which rigidity is so much abridged as to
escape notice; and the cases in which, on the contrary, rigidity takes
place as usual, will be those in which the stroke of lightning operates
in some of the other modes which have been enumerated. How, then, is
this brought to the test? By experiments not on lightning, which cannot
be commanded at pleasure, but on the same natural agency in a manageable
form, that of artificial galvanism. Dr. Brown-Séquard galvanized the
entire bodies of animals immediately after death. Galvanism cannot
operate in any of the modes in which the stroke of lightning may have
operated, except the single one of producing muscular convulsions. If,
therefore, after the bodies have been galvanized, the duration of
rigidity is much shortened and putrefaction much accelerated, it is
reasonable to ascribe the same effects when produced by lightning, to
the property which galvanism shares with lightning, and not to those
which it does not. Now this Dr. Brown-Séquard found to be the fact. The
galvanic experiment was tried with charges of very various degrees of
strength; and the more powerful the charge, the shorter was found to be
the duration of rigidity, and the more speedy and rapid the
putrefaction. In the experiment in which the charge was strongest, and
the muscular irritability most promptly destroyed, the rigidity only
lasted fifteen minutes. On the principle, therefore, of the Method of
Concomitant Variations, it maybe inferred that the duration of the
rigidity depends on the degree of the irritability; and that if the
charge had been as much stronger than Dr. Brown-Séquard's strongest, as
a stroke of lightning must be stronger than any electric shock which we
can produce artificially, the rigidity would have been shortened in a
corresponding ratio, and might have disappeared altogether. This
conclusion having been arrived at, the case of an electric shock,
whether natural or artificial, becomes an instance in addition to all
those already ascertained, of correspondence between the irritability of
the muscle and the duration of rigidity.
All these instances are summed up in the following statement:--"That
when the degree of muscular irritability at the time of death is
considerable, either in consequence of a good state of nutrition, as in
persons who die in full health from an accidental cause, or in
consequence of rest, as in cases of paralysis, or on account of the
influence of cold, cadaveric rigidity in all these cases sets in late
and lasts long, and putrefaction appears late, and progresses slowly:"
but "that when the degree of muscular irritability at the time of death
is slight, either in consequence of a bad state of nutrition, or of
exhaustion from over-exertion, or from convulsions caused by disease or
poison, cadaveric rigidity sets in and ceases soon, and putrefaction
appears and progresses quickly." These facts present, in all their
completeness, the conditions of the Joint Method of Agreement and
Difference. Early and brief rigidity takes place in cases which agree
only in the circumstance of a low state of muscular irritability.
Rigidity begins late and lasts long in cases which agree only in the
contrary circumstance, of a muscular irritability high and unusually
prolonged. It follows that there is a connexion through causation
between the degree of muscular irritability after death, and the
tardiness and prolongation of the cadaveric rigidity. This
investigation places in a strong light the value and efficacy of the
Joint Method. For, as we have already seen, the defect of that Method
is, that like the Method of Agreement, of which it is only an improved
form, it cannot prove causation. But in the present case (as in one of
the steps in the argument which led up to it) causation is already
proved; since there could never be any doubt that the rigidity
altogether, and the putrefaction which follows it, are caused by the
fact of death: the observations and experiments on which this rests are
too familiar to need analysis, and fall under the Method of Difference.
It being, therefore, beyond doubt that the aggregate antecedent, the
death, is the actual cause of the whole train of consequents, whatever
of the circumstances attending the death can be shown to be followed in
all its variations by variations in the effect under investigation, must
be the particular feature of the fact of death on which that effect
depends. The degree of muscular irritability at the time of death
fulfils this condition. The only point that could be brought into
question, would be whether the effect depended on the irritability
itself, or on something which always accompanied the irritability: and
this doubt is set at rest by establishing, as the instances do, that by
whatever cause the high or low irritability is produced, the effect
equally follows; and cannot, therefore, depend upon the causes of
irritability, nor upon the other effects of those causes, which are as
various as the causes themselves; but upon the irritability, solely.
§ 5. The last two examples will have conveyed to any one by whom they
have been duly followed, so clear a conception of the use and practical
management of three of the four methods of experimental inquiry, as to
supersede the necessity of any further exemplification of them. The
remaining method, that of Residues, not having found a place in any of
the preceding investigations, I shall quote from Sir John Herschel some
examples of that method, with the remarks by which they are introduced.
"It is by this process, in fact, that science, in its present advanced
state, is chiefly promoted. Most of the phenomena which Nature presents
are very complicated; and when the effects of all known causes are
estimated with exactness, and subducted, the residual facts are
constantly appearing in the form of phenomena altogether new, and
leading to the most important conclusions.
"For example: the return of the comet predicted by Professor Encke, a
great many times in succession, and the general good agreement of its
calculated with its observed place during any one of its periods of
visibility, would lead us to say that its gravitation towards the sun
and planets is the sole and sufficient cause of all the phenomena of its
orbitual motion; but when the effect of this cause is strictly
calculated and subducted from the observed motion, there is found to
remain behind a _residual phenomenon_, which would never have been
otherwise ascertained to exist, which is a small anticipation of the
time of its reappearance, or a diminution of its periodic time, which
cannot be accounted for by gravity, and whose cause is therefore to be
inquired into. Such an anticipation would be caused by the resistance of
a medium disseminated through the celestial regions; and as there are
other good reasons for believing this to be a _vera causa_," (an
actually existing antecedent,) "it has therefore been ascribed to such a
resistance.[39]
"M. Arago, having suspended a magnetic needle by a silk thread, and set
it in vibration, observed, that it came much sooner to a state of rest
when suspended over a plate of copper, than when no such plate was
beneath it. Now, in both cases there were two _veræ causæ_" (antecedents
known to exist) "why it _should_ come at length to rest, viz. the
resistance of the air, which opposes, and at length destroys, all
motions performed in it; and the want of perfect mobility in the silk
thread. But the effect of these causes being exactly known by the
observation made in the absence of the copper, and being thus allowed
for and subducted, a residual phenomenon appeared, in the fact that a
retarding influence was exerted by the copper itself; and this fact,
once ascertained, speedily led to the knowledge of an entirely new and
unexpected class of relations." This example belongs, however, not to
the Method of Residues but to the Method of Difference, the law being
ascertained by a direct comparison of the results of two experiments,
which differed in nothing but the presence or absence of the plate of
copper. To have made it exemplify the Method of Residues, the effect of
the resistance of the air and that of the rigidity of the silk should
have been calculated _à priori_, from the laws obtained by separate and
foregone experiments.
"Unexpected and peculiarly striking confirmations of inductive laws
frequently occur in the form of residual phenomena, in the course of
investigations of a widely different nature from those which gave rise
to the inductions themselves. A very elegant example may be cited in the
unexpected confirmation of the law of the development of heat in elastic
fluids by compression, which is afforded by the phenomena of sound. The
inquiry into the cause of sound had led to conclusions respecting its
mode of propagation, from which its velocity in the air could be
precisely calculated. The calculations were performed; but, when
compared with fact, though the agreement was quite sufficient to show
the general correctness of the cause and mode of propagation assigned,
yet the _whole_ velocity could not be shown to arise from this theory.
There was still a residual velocity to be accounted for, which placed
dynamical philosophers for a long time in great dilemma. At length
Laplace struck on the happy idea, that this might arise from the _heat_
developed in the act of that condensation which necessarily takes place
at every vibration by which sound is conveyed. The matter was subjected
to exact calculation, and the result was at once the complete
explanation of the residual phenomenon, and a striking confirmation of
the general law of the development of heat by compression, under
circumstances beyond artificial imitation."
"Many of the new elements of chemistry have been detected in the
investigation of residual phenomena. Thus Arfwedson discovered lithia by
perceiving an excess of weight in the sulphate produced from a small
portion of what he considered as magnesia present in a mineral he had
analysed. It is on this principle, too, that the small concentrated
residues of great operations in the arts are almost sure to be the
lurking places of new chemical ingredients: witness iodine, brome,
selenium, and the new metals accompanying platina in the experiments of
Wollaston and Tennant. It was a happy thought of Glauber to examine what
everybody else threw away."[40]
"Almost all the greatest discoveries in Astronomy," says the same
author,[41] "have resulted from the consideration of residual phenomena
of a quantitative or numerical kind.... It was thus that the grand
discovery of the precession of the equinoxes resulted as a residual
phenomenon, from the imperfect explanation of the return of the seasons
by the return of the sun to the same apparent place among the fixed
stars. Thus, also, aberration and nutation resulted as residual
phenomena from that portion of the changes of the apparent places of the
fixed stars which was left unaccounted for by precession. And thus again
the apparent proper motions of the stars are the observed residues of
their apparent movements outstanding and unaccounted for by strict
calculation of the effects of precession, nutation, and aberration. The
nearest approach which human theories can make to perfection is to
diminish this residue, this _caput mortuum_ of observation, as it may be
considered, as much as practicable, and, if possible, to reduce it to
nothing, either by showing that something has been neglected in our
estimation of known causes, or by reasoning upon it as a new fact, and
on the principle of the inductive philosophy ascending from the effect
to its cause or causes."
The disturbing effects mutually produced by the earth and planets upon
each other's motions were first brought to light as residual phenomena,
by the difference which appeared between the observed places of those
bodies, and the places calculated on a consideration solely of their
gravitation towards the sun. It was this which determined astronomers
to consider the law of gravitation as obtaining between all bodies
whatever, and therefore between all particles of matter; their first
tendency having been to regard it as a force acting only between each
planet or satellite and the central body to whose system it belonged.
Again, the catastrophists, in geology, be their opinion right or wrong,
support it on the plea, that after the effect of all causes now in
operation has been allowed for, there remains in the existing
constitution of the earth a large residue of facts, proving the
existence at former periods either of other forces, or of the same
forces in a much greater degree of intensity. To add one more example:
those who assert, what no one has shown any real ground for believing,
that there is in one human individual, one sex, or one race of mankind
over another, an inherent and inexplicable superiority in mental
faculties, could only substantiate their proposition by subtracting from
the differences of intellect which we in fact see, all that can be
traced by known laws either to the ascertained differences of physical
organization, or to the differences which have existed in the outward
circumstances in which the subjects of the comparison have hitherto been
placed. What these causes might fail to account for, would constitute a
residual phenomenon, which and which alone would be evidence of an
ulterior original distinction, and the measure of its amount. But the
assertors of such supposed differences have not provided themselves with
these necessary logical conditions of the establishment of their
doctrine.
The spirit of the Method of Residues being, it is hoped, sufficiently
intelligible from these examples, and the other three methods having
already been so fully exemplified, we may here close our exposition of
the four methods, considered as employed in the investigation of the
simpler and more elementary order of the combinations of phenomena.
§ 6. Dr. Whewell has expressed 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:--[42]
"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 show 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. 277.)
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 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 processes reducible to
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 showing, the pyramid of science is supplied with its
base. In vain he attempts to escape from this conclusion 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. 265), nor must any of them be drawn from mental and
social subjects (p. 269), nor from ordinary observation and practical
life (pp. 241-247). 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 is misled by their absence into
representing 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,[43] 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 _disprove_ 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.
So real and practical is the need of a test for induction, similar to
the syllogistic test of ratiocination, that inferences which bid
defiance to the most elementary notions of inductive logic are put forth
without misgiving by persons eminent in physical science, as soon as
they are off the ground on which they are conversant with the facts, and
not reduced to judge only by the arguments; and as for educated persons
in general, it may be doubted if they are better judges of a good or a
bad induction than they were before Bacon wrote. The improvement in the
results of thinking has seldom extended to the processes; or has
reached, if any process, that of investigation only, not that of proof.
A knowledge of many laws of nature has doubtless been arrived at, by
framing hypotheses and finding that the facts corresponded to them; and
many errors have been got rid of by coming to a knowledge of facts which
were inconsistent with them, but not by discovering that the mode of
thought which led to the errors was itself faulty, and might have been
known to be such independently of the facts which disproved the
specific conclusion. Hence it is, that while the thoughts of mankind
have on many subjects worked themselves practically right, the thinking
power remains as weak as ever: and on all subjects on which the facts
which would check the result are not accessible, as in what relates to
the invisible world, and even, as has been seen lately, to the visible
world of the planetary regions, men of the greatest scientific
acquirements argue as pitiably as the merest ignoramus. For though they
have made many sound inductions, they have not learnt from them (and Dr.
Whewell thinks there is no necessity that they should learn) the
principles of inductive _evidence_.