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 afterward 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 afterward 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 _a 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 can not 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, can not 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
sub-oxide, 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 neighboring 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 rigor 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 hinderance 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 can not be ascertained to agree in any other property
whatsoever. We have thus, in favor 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(137) 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 neighborhood 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 can not 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 can not 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 neighboring
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 can not 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 neighboring 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 neighboring 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
neighboring 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 neighboring 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 neighboring 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.(138)
§ 3. Our third example shall be extracted from Sir John Herschel’s
_Discourse __ course 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
recognized, 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.(139)
“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.(140)
“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 connection 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 upward, 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 can not 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
recognize, 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 heat
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,
etc., as unfavorable, but those of a loose one, as cloth, velvet, wool,
eider-down, cotton, etc., as eminently favorable 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 course
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 co-existence 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 connection 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 vapor 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 vapor 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 vapor
suspended as the air will contain at its existing temperature, any
lowering of that temperature will cause a portion of the vapor 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 co-existence; 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
vapor, 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 vapor 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.(141)
The accumulated proof of which the Theory of Dew has been found
susceptible, is a striking instance of the fullness 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 variations. 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. Paralyzed muscles have greater irritability than healthy muscles.
Now, paralyzed 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 paralyzed muscles have greater
irritability than healthy muscles—he ascertained in various ways, but most
decisively by “comparing the duration of irritability in a paralyzed
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 paralyzed 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 paralyzed
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 paralyzed 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 paralyzed 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.
2d. 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.
3d. 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 connection 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.
4th. 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
connection is, therefore, inductively proved between the degree of the
nutrition, and the slowness and prolongation of the rigidity.
5th. 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.
6th. 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; 2d, hemorrhage in or
around the brain, or in the lungs, the pericardium, etc.; 3d, 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 can not 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 can not 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 may be 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
overexertion, 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 connection
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 can not 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 fulfills 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 can not, 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 Eucke 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 toward 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 re-appearance, or a diminution of
its periodic time, which can not 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.(142)
“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 _a 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
analyzed. 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
every body else threw away.”(143)
“Almost all the greatest discoveries in Astronomy,” says the same
author,(144) “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
toward 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
asserters 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 unfavorable 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:(145)
“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 what
it is to be reduced to, 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 can not 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 practiced 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 can not 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 burned; this is B C: I touch it, and am burned; 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 hypothesis; 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,(146) 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 favor with Dr. Whewell; for it is the peculiarity of his
system, not to recognize, 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.
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 learned from them (and Dr.
Whewell thinks there is no necessity that they should learn) the
principles of inductive _evidence_.