Of The Limits To The Explanation Of Laws Of Nature; And Of Hypotheses.
§ 1. The preceding considerations have led us to recognize a distinction
between two kinds of laws, or observed uniformities in nature: ultimate
laws, and what may be termed derivative laws. Derivative laws are such as
are deducible from, and may, in any of the modes which we have pointed
out, be resolved into, other and more general ones. Ultimate laws are
those which can not. We are not sure that any of the uniformities with
which we are yet acquainted are ultimate laws; but we know that there must
be ultimate laws; and that every resolution of a derivative law into more
general laws brings us nearer to them.
Since we are continually discovering that uniformities, not previously
known to be other than ultimate, are derivative, and resolvable into more
general laws; since (in other words) we are continually discovering the
explanation of some sequence which was previously known only as a fact; it
becomes an interesting question whether there are any necessary limits to
this philosophical operation, or whether it may proceed until all the
uniform sequences in nature are resolved into some one universal law. For
this seems, at first sight, to be the ultimatum toward which the progress
of induction by the Deductive Method, resting on a basis of observation
and experiment, is tending. Projects of this kind were universal in the
infancy of philosophy; any speculations which held out a less brilliant
prospect being in these early times deemed not worth pursuing. And the
idea receives so much apparent countenance from the nature of the most
remarkable achievements of modern science, that speculators are even now
frequently appearing, who profess either to have solved the problem, or to
suggest modes in which it may one day be solved. Even where pretensions of
this magnitude are not made, the character of the solutions which are
given or sought of particular classes of phenomena, often involves such
conceptions of what constitutes explanation, as would render the notion of
explaining all phenomena whatever by means of some one cause or law,
perfectly admissible.
§ 2. It is, therefore, useful to remark that the ultimate Laws of Nature
can not possibly be less numerous than the distinguishable sensations or
other feelings of our nature; those, I mean, which are distinguishable
from one another in quality, and not merely in quantity or degree. For
example: since there is a phenomenon _sui generis_, called color, which
our consciousness testifies to be not a particular degree of some other
phenomenon, as heat or odor or motion, but intrinsically unlike all
others, it follows that there are ultimate laws of color; that though the
facts of color may admit of explanation, they never can be explained from
laws of heat or odor alone, or of motion alone, but that, however far the
explanation may be carried, there will always remain in it a law of color.
I do not mean that it might not possibly be shown that some other
phenomenon, some chemical or mechanical action, for example, invariably
precedes, and is the cause of, every phenomenon of color. But though this,
if proved, would be an important extension of our knowledge of nature, it
would not explain how or why a motion, or a chemical action, can produce a
sensation of color; and, however diligent might be our scrutiny of the
phenomena, whatever number of hidden links we might detect in the chain of
causation terminating in the color, the last link would still be a law of
color, not a law of motion, nor of any other phenomenon whatever. Nor does
this observation apply only to color, as compared with any other of the
great classes of sensations; it applies to every particular color, as
compared with others. White color can in no manner be explained
exclusively by the laws of the production of red color. In any attempt to
explain it, we can not but introduce, as one element of the explanation,
the proposition that some antecedent or other produces the sensation of
white.
The ideal limit, therefore, of the explanation of natural phenomena
(toward which as toward other ideal limits we are constantly tending,
without the prospect of ever completely attaining it) would be to show
that each distinguishable variety of our sensations, or other states of
consciousness, has only one sort of cause; that, for example, whenever we
perceive a white color, there is some one condition or set of conditions
which is always present, and the presence of which always produces in us
that sensation. As long as there are several known modes of production of
a phenomenon (several different substances, for instance, which have the
property of whiteness, and between which we can not trace any other
resemblance) so long it is not impossible that one of these modes of
production may be resolved into another, or that all of them may be
resolved into some more general mode of production not hitherto
recognized. But when the modes of production are reduced to one, we can
not, in point of simplification, go any further. This one may not, after
all, be the ultimate mode; there may be other links to be discovered
between the supposed cause and the effect; but we can only further resolve
the known law, by introducing some other law hitherto unknown, which will
not diminish the number of ultimate laws.
In what cases, accordingly, has science been most successful in explaining
phenomena, by resolving their complex laws into laws of greater simplicity
and generality? Hitherto chiefly in cases of the propagation of various
phenomena through space; and, first and principally, the most extensive
and important of all facts of that description, mechanical motion. Now
this is exactly what might be expected from the principles here laid down.
Not only is motion one of the most universal of all phenomena, it is also
(as might be expected from that circumstance) one of those which,
apparently at least, are produced in the greatest number of ways; but the
phenomenon itself is always, to our sensations, the same in every respect
but degree. Differences of duration or of velocity, are evidently
differences in degree only; and differences of direction in space, which
alone has any semblance of being a distinction in kind, entirely disappear
(so far as our sensations are concerned) by a change in our own position;
indeed, the very same motion appears to us, according to our position, to
take place in every variety of direction, and motions in every different
direction to take place in the same. And again, motion in a straight line
and in a curve are no otherwise distinct than that the one is motion
continuing in the same direction, the other is motion which at each
instant changes its direction. There is, therefore, according to the
principles I have stated, no absurdity in supposing that all motion may be
produced in one and the same way, by the same kind of cause. Accordingly,
the greatest achievements in physical science have consisted in resolving
one observed law of the production of motion into the laws of other known
modes of production, or the laws of several such modes into one more
general mode; as when the fall of bodies to the earth, and the motions of
the planets, were brought under the one law of the mutual attraction of
all particles of matter; when the motions said to be produced by magnetism
were shown to be produced by electricity; when the motions of fluids in a
lateral direction, or even contrary to the direction of gravity, were
shown to be produced by gravity; and the like. There is an abundance of
distinct causes of motion still unresolved into one another: gravitation,
heat, electricity, chemical action, nervous action, and so forth; but
whether the efforts of the present generation of savants to resolve all
these different modes of production into one are ultimately successful or
not, the attempt so to resolve them is perfectly legitimate. For, though
these various causes produce, in other respects, sensations intrinsically
different, and are not, therefore, capable of being resolved into one
another, yet, in so far as they all produce motion, it is quite possible
that the immediate antecedent of the motion may in all these different
cases be the same; nor is it impossible that these various agencies
themselves may, as the new doctrines assert, all of them have for their
own immediate antecedent modes of molecular motion.
We need not extend our illustration to other cases, as, for instance, to
the propagation of light, sound, heat, electricity, etc., through space,
or any of the other phenomena which have been found susceptible of
explanation by the resolution of their observed laws into more general
laws. Enough has been said to display the difference between the kind of
explanation and resolution of laws which is chimerical, and that of which
the accomplishment is the great aim of science; and to show into what sort
of elements the resolution must be effected, if at all.(159)
§ 3. As, however, there is scarcely any one of the principles of a true
method of philosophizing which does not require to be guarded against
errors on both sides, I must enter a caveat against another
misapprehension, of a kind directly contrary to the preceding. M. Comte,
among other occasions on which he has condemned, with some asperity, any
attempt to explain phenomena which are “evidently primordial” (meaning,
apparently, no more than that every peculiar phenomenon must have at least
one peculiar and therefore inexplicable law), has spoken of the attempt to
furnish any explanation of the color belonging to each substance, “la
couleur élémentaire propre à chaque substance,” as essentially illusory.
“No one,” says he, “in our time attempts to explain the particular
specific gravity of each substance or of each structure. Why should it be
otherwise as to the specific color, the notion of which is undoubtedly no
less primordial?”(160)
Now although, as he elsewhere observes, a color must always remain a
different thing from a weight or a sound, varieties of color might
nevertheless follow, or correspond to, given varieties of weight, or
sound, or some other phenomenon as different as these are from color
itself. It is one question what a thing is, and another what it depends
on; and though to ascertain the conditions of an elementary phenomenon is
not to obtain any new insight into the nature of the phenomenon itself,
that is no reason against attempting to discover the conditions. The
interdict against endeavoring to reduce distinctions of color to any
common principle, would have held equally good against a like attempt on
the subject of distinctions of sound; which nevertheless have been found
to be immediately preceded and caused by distinguishable varieties in the
vibrations of elastic bodies; though a sound, no doubt, is quite as
different as a color is from any motion of particles, vibratory or
otherwise. We might add, that, in the case of colors, there are strong
positive indications that they are not ultimate properties of the
different kinds of substances, but depend on conditions capable of being
superinduced upon all substances; since there is no substance which can
not, according to the kind of light thrown upon it, be made to assume
almost any color; and since almost every change in the mode of aggregation
of the particles of the same substance is attended with alterations in its
color, and in its optical properties generally.
The really weak point in the attempts which have been made to account for
colors by the vibrations of a fluid, is not that the attempt itself is
unphilosophical, but that the existence of the fluid, and the fact of its
vibratory motion, are not proved, but are assumed, on no other ground than
the facility they are supposed to afford of explaining the phenomena. And
this consideration leads to the important question of the proper use of
scientific hypotheses, the connection of which with the subject of the
explanation of the phenomena of nature, and of the necessary limits to
that explanation, need not be pointed out.
§ 4. An hypothesis is any supposition which we make (either without actual
evidence, or on evidence avowedly insufficient) in order to endeavor to
deduce from it conclusions in accordance with facts which are known to be
real; under the idea that if the conclusions to which the hypothesis leads
are known truths, the hypothesis itself either must be, or at least is
likely to be, true. If the hypothesis relates to the cause or mode of
production of a phenomenon, it will serve, if admitted, to explain such
facts as are found capable of being deduced from it. And this explanation
is the purpose of many, if not most hypotheses. Since explaining, in the
scientific sense, means resolving a uniformity which is not a law of
causation, into the laws of causation from which it results, or a complex
law of causation into simpler and more general ones from which it is
capable of being deductively inferred, if there do not exist any known
laws which fulfill this requirement, we may feign or imagine some which
would fulfill it; and this is making an hypothesis.
An hypothesis being a mere supposition, there are no other limits to
hypotheses than those of the human imagination; we may, if we please,
imagine, by way of accounting for an effect, some cause of a kind utterly
unknown, and acting according to a law altogether fictitious. But as
hypotheses of this sort would not have any of the plausibility belonging
to those which ally themselves by analogy with known laws of nature, and
besides would not supply the want which arbitrary hypotheses are generally
invented to satisfy, by enabling the imagination to represent to itself an
obscure phenomenon in a familiar light, there is probably no hypothesis in
the history of science in which both the agent itself and the law of its
operation were fictitious. Either the phenomenon assigned as the cause is
real, but the law according to which it acts merely supposed; or the cause
is fictitious, but is supposed to produce its effects according to laws
similar to those of some known class of phenomena. An instance of the
first kind is afforded by the different suppositions made respecting the
law of the planetary central force, anterior to the discovery of the true
law, that the force varies as the inverse square of the distance; which
also suggested itself to Newton, in the first instance, as an hypothesis,
and was verified by proving that it led deductively to Kepler’s laws.
Hypotheses of the second kind are such as the vortices of Descartes, which
were fictitious, but were supposed to obey the known laws of rotatory
motion; or the two rival hypotheses respecting the nature of light, the
one ascribing the phenomena to a fluid emitted from all luminous bodies,
the other (now generally received) attributing them to vibratory motions
among the particles of an ether pervading all space. Of the existence of
either fluid there is no evidence, save the explanation they are
calculated to afford of some of the phenomena; but they are supposed to
produce their effects according to known laws: the ordinary laws of
continued locomotion in the one case, and in the other those of the
propagation of undulatory movements among the particles of an elastic
fluid.
According to the foregoing remarks, hypotheses are invented to enable the
Deductive Method to be earlier applied to phenomena. But(161) in order to
discover the cause of any phenomenon by the Deductive Method, the process
must consist of three parts: induction, ratiocination, and verification.
Induction (the place of which, however, may be supplied by a prior
deduction), to ascertain the laws of the causes; ratiocination, to compute
from those laws how the causes will operate in the particular combination
known to exist in the case in hand; verification, by comparing this
calculated effect with the actual phenomenon. No one of these three parts
of the process can be dispensed with. In the deduction which proves the
identity of gravity with the central force of the solar system, all the
three are found. First, it is proved from the moon’s motions, that the
earth attracts her with a force varying as the inverse square of the
distance. This (though partly dependent on prior deductions) corresponds
to the first, or purely inductive, step: the ascertainment of the law of
the cause. Secondly, from this law, and from the knowledge previously
obtained of the moon’s mean distance from the earth, and of the actual
amount of her deflection from the tangent, it is ascertained with what
rapidity the earth’s attraction would cause the moon to fall, if she were
no further off, and no more acted upon by extraneous forces, than
terrestrial bodies are: that is the second step, the ratiocination.
Finally, this calculated velocity being compared with the observed
velocity with which all heavy bodies fall, by mere gravity, toward the
surface of the earth (sixteen feet in the first second, forty-eight in the
second, and so forth, in the ratio of the odd numbers, 1, 3, 5, etc.), the
two quantities are found to agree. The order in which the steps are here
presented was not that of their discovery; but it is their correct logical
order, as portions of the proof that the same attraction of the earth
which causes the moon’s motion causes also the fall of heavy bodies to the
earth: a proof which is thus complete in all its parts.
Now, the Hypothetical Method suppresses the first of the three steps, the
induction to ascertain the law; and contents itself with the other two
operations, ratiocination and verification; the law which is reasoned from
being assumed instead of proved.
This process may evidently be legitimate on one supposition, namely, if
the nature of the case be such that the final step, the verification,
shall amount to, and fulfill the conditions of, a complete induction. We
want to be assured that the law we have hypothetically assumed is a true
one; and its leading deductively to true results will afford this
assurance, provided the case be such that a false law can not lead to a
true result; provided no law, except the very one which we have assumed,
can lead deductively to the same conclusions which that leads to. And this
proviso is often realized. For example, in the very complete specimen of
deduction which we just cited, the original major premise of the
ratiocination, the law of the attractive force, was ascertained in this
mode; by this legitimate employment of the Hypothetical Method. Newton
began by an assumption that the force which at each instant deflects a
planet from its rectilineal course, and makes it describe a curve round
the sun, is a force tending directly toward the sun. He then proved that
if this be so, the planet will describe, as we know by Kepler’s first law
that it does describe, equal areas in equal times; and, lastly, he proved
that if the force acted in any other direction whatever, the planet would
not describe equal areas in equal times. It being thus shown that no other
hypothesis would accord with the facts, the assumption was proved; the
hypothesis became an inductive truth. Not only did Newton ascertain by
this hypothetical process the direction of the deflecting force; he
proceeded in exactly the same manner to ascertain the law of variation of
the quantity of that force. He assumed that the force varied inversely as
the square of the distance; showed that from this assumption the remaining
two of Kepler’s laws might be deduced; and, finally, that any other law of
variation would give results inconsistent with those laws, and
inconsistent, therefore, with the real motions of the planets, of which
Kepler’s laws were known to be a correct expression.
I have said that in this case the verification fulfills the conditions of
an induction; but an induction of what sort? On examination we find that
it conforms to the canon of the Method of Difference. It affords the two
instances, A B C, _a b c_, and B C, _b c_. A represents central force; A B
C, the planets _plus_ a central force; B C, the planets apart from a
central force. The planets with a central force give _a_, areas
proportional to the times; the planets without a central force give _b c_
(a set of motions) without _a_, or with something else instead of _a_.
This is the Method of Difference in all its strictness. It is true, the
two instances which the method requires are obtained in this case, not by
experiment, but by a prior deduction. But that is of no consequence. It is
immaterial what is the nature of the evidence from which we derive the
assurance that A B C will produce _a b c_, and B C only _b c_; it is
enough that we have that assurance. In the present case, a process of
reasoning furnished Newton with the very instances which, if the nature of
the case had admitted of it, he would have sought by experiment.
It is thus perfectly possible, and indeed is a very common occurrence,
that what was an hypothesis at the beginning of the inquiry becomes a
proved law of nature before its close. But in order that this should
happen, we must be able, either by deduction or experiment, to obtain
_both_ the instances which the Method of Difference requires. That we are
able from the hypothesis to deduce the known facts, gives only the
affirmative instance, A B C, _a b c_. It is equally necessary that we
should be able to obtain, as Newton did, the negative instance B C, _b c_;
by showing that no antecedent, except the one assumed in the hypothesis,
would in conjunction with B C produce _a_.
Now it appears to me that this assurance can not be obtained, when the
cause assumed in the hypothesis is an unknown cause imagined solely to
account for _a_. When we are only seeking to determine the precise law of
a cause already ascertained, or to distinguish the particular agent which
is in fact the cause, among several agents of the same kind, one or other
of which it is already known to be, we may then obtain the negative
instance. An inquiry which of the bodies of the solar system causes by its
attraction some particular irregularity in the orbit or periodic time of
some satellite or comet, would be a case of the second description.
Newton’s was a case of the first. If it had not been previously known that
the planets were hindered from moving in straight lines by some force
tending toward the interior of their orbit, though the exact direction was
doubtful; or if it had not been known that the force increased in some
proportion or other as the distance diminished, and diminished as it
increased, Newton’s argument would not have proved his conclusion. These
facts, however, being already certain, the range of admissible
suppositions was limited to the various possible directions of a line, and
the various possible numerical relations between the variations of the
distance, and the variations of the attractive force. Now among these it
was easily shown that different suppositions could not lead to identical
consequences.
Accordingly, Newton could not have performed his second great scientific
operation: that of identifying terrestrial gravity with the central force
of the solar system by the same hypothetical method. When the law of the
moon’s attraction had been proved from the data of the moon itself, then,
on finding the same law to accord with the phenomena of terrestrial
gravity, he was warranted in adopting it as the law of those phenomena
likewise; but it would not have been allowable for him, without any lunar
data, to assume that the moon was attracted toward the earth with a force
as the inverse square of the distance, merely because that ratio would
enable him to account for terrestrial gravity; for it would have been
impossible for him to prove that the observed law of the fall of heavy
bodies to the earth could not result from any force, save one extending to
the moon, and proportional to the inverse square.
It appears, then, to be a condition of the most genuinely scientific
hypothesis, that it be not destined always to remain an hypothesis, but be
of such a nature as to be either proved or disproved by comparison with
observed facts. This condition is fulfilled when the effect is already
known to depend on the very cause supposed, and the hypothesis relates
only to the precise mode of dependence; the law of the variation of the
effect according to the variations in the quantity or in the relations of
the cause. With these may be classed the hypotheses which do not make any
supposition with regard to causation, but only with regard to the law of
correspondence between facts which accompany each other in their
variations, though there may be no relation of cause and effect between
them. Such were the different false hypotheses which Kepler made
respecting the law of the refraction of light. It was known that the
direction of the line of refraction varied with every variation in the
direction of the line of incidence, but it was not known how; that is,
what changes of the one corresponded to the different changes of the
other. In this case any law different from the true one must have led to
false results. And, lastly, we must add to these all hypothetical modes of
merely representing or _describing_ phenomena; such as the hypothesis of
the ancient astronomers that the heavenly bodies moved in circles; the
various hypotheses of eccentrics, deferents, and epicycles, which were
added to that original hypothesis; the nineteen false hypotheses which
Kepler made and abandoned respecting the form of the planetary orbits; and
even the doctrine in which he finally rested, that those orbits are
ellipses, which was but an hypothesis like the rest until verified by
facts.
In all these cases, verification is proof; if the supposition accords with
the phenomena there needs no other evidence of it. But in order that this
may be the case, I conceive it to be necessary, when the hypothesis
relates to causation, that the supposed cause should not only be a real
phenomenon, something actually existing in nature, but should be already
known to exercise, or at least to be capable of exercising, an influence
of some sort over the effect. In any other case, it is no sufficient
evidence of the truth of the hypothesis that we are able to deduce the
real phenomena from it.
Is it, then, never allowable, in a scientific hypothesis, to assume a
cause, but only to ascribe an assumed law to a known cause? I do not
assert this. I only say, that in the latter case alone can the hypothesis
be received as true merely because it explains the phenomena. In the
former case it may be very useful by suggesting a line of investigation
which may possibly terminate in obtaining real proof. But for this
purpose, as is justly remarked by M. Comte, it is indispensable that the
cause suggested by the hypothesis should be in its own nature susceptible
of being proved by other evidence. This seems to be the philosophical
import of Newton’s maxim, (so often cited with approbation by subsequent
writers), that the cause assigned for any phenomenon must not only be such
as if admitted would explain the phenomenon, but must also be a _vera
causa_. What he meant by a _vera causa_ Newton did not indeed very
explicitly define; and Dr. Whewell, who dissents from the propriety of any
such restriction upon the latitude of framing hypotheses, has had little
difficulty in showing(162) that his conception of it was neither precise
nor consistent with itself; accordingly his optical theory was a signal
instance of the violation of his own rule. It is certainly not necessary
that the cause assigned should be a cause already known; otherwise we
should sacrifice our best opportunities of becoming acquainted with new
causes. But what is true in the maxim is, that the cause, though not known
previously, should be capable of being known thereafter; that its
existence should be capable of being detected, and its connection with the
effect ascribed to it should be susceptible of being proved, by
independent evidence. The hypothesis, by suggesting observations and
experiments, puts us on the road to that independent evidence, if it be
really attainable; and till it be attained, the hypothesis ought only to
count for a more or less plausible conjecture.
§ 5. This function, however, of hypotheses, is one which must be reckoned
absolutely indispensable in science. When Newton said, “Hypotheses non
fingo,” he did not mean that he deprived himself of the facilities of
investigation afforded by assuming in the first instance what he hoped
ultimately to be able to prove. Without such assumptions, science could
never have attained its present state; they are necessary steps in the
progress to something more certain; and nearly every thing which is now
theory was once hypothesis. Even in purely experimental science, some
inducement is necessary for trying one experiment rather than another; and
though it is abstractedly possible that all the experiments which have
been tried, might have been produced by the mere desire to ascertain what
would happen in certain circumstances, without any previous conjecture as
to the result; yet, in point of fact, those unobvious, delicate, and often
cumbrous and tedious processes of experiment, which have thrown most light
upon the general constitution of nature, would hardly ever have been
undertaken by the persons or at the time they were, unless it had seemed
to depend on them whether some general doctrine or theory which had been
suggested, but not yet proved, should be admitted or not. If this be true
even of merely experimental inquiry, the conversion of experimental into
deductive truths could still less have been effected without large
temporary assistance from hypotheses. The process of tracing regularity in
any complicated, and at first sight confused, set of appearances, is
necessarily tentative; we begin by making any supposition, even a false
one, to see what consequences will follow from it; and by observing how
these differ from the real phenomena, we learn what corrections to make in
our assumption. The simplest supposition which accords with the more
obvious facts is the best to begin with; because its consequences are the
most easily traced. This rude hypothesis is then rudely corrected, and the
operation repeated; and the comparison of the consequences deducible from
the corrected hypothesis, with the observed facts, suggests still further
correction, until the deductive results are at last made to tally with the
phenomena. “Some fact is as yet little understood, or some law is unknown;
we frame on the subject an hypothesis as accordant as possible with the
whole of the data already possessed; and the science, being thus enabled
to move forward freely, always ends by leading to new consequences capable
of observation, which either confirm or refute, unequivocally, the first
supposition.” Neither induction nor deduction would enable us to
understand even the simplest phenomena, “if we did not often commence by
anticipating on the results; by making a provisional supposition, at first
essentially conjectural, as to some of the very notions which constitute
the final object of the inquiry.”(163) Let any one watch the manner in
which he himself unravels a complicated mass of evidence; let him observe
how, for instance, he elicits the true history of any occurrence from the
involved statements of one or of many witnesses; he will find that he does
not take all the items of evidence into his mind at once, and attempt to
weave them together; he extemporizes, from a few of the particulars, a
first rude theory of the mode in which the facts took place, and then
looks at the other statements one by one, to try whether they can be
reconciled with that provisional theory, or what alterations or additions
it requires to make it square with them. In this way, which has been
justly compared to the Methods of Approximation of mathematicians, we
arrive, by means of hypotheses, at conclusions not hypothetical.(164)
§ 6. It is perfectly consistent with the spirit of the method, to assume
in this provisional manner not only an hypothesis respecting the law of
what we already know to be the cause, but an hypothesis respecting the
cause itself. It is allowable, useful, and often even necessary, to begin
by asking ourselves what cause _may_ have produced the effect, in order
that we may know in what direction to look out for evidence to determine
whether it actually _did_. The vortices of Descartes would have been a
perfectly legitimate hypothesis, if it had been possible, by any mode of
exploration which we could entertain the hope of ever possessing, to bring
the reality of the vortices, as a fact in nature, conclusively to the test
of observation. The vice of the hypothesis was that it could not lead to
any course of investigation capable of converting it from an hypothesis
into a proved fact. It might chance to be _dis_proved, either by some want
of correspondence with the phenomena it purported to explain, or (as
actually happened) by some extraneous fact. “The free passage of comets
through the spaces in which these vortices should have been, convinced men
that these vortices did not exist.”(165) But the hypothesis would have
been false, though no such direct evidence of its falsity had been
procurable. Direct evidence of its truth there could not be.
The prevailing hypothesis of a luminiferous ether, in other respects not
without analogy to that of Descartes, is not in its own nature entirely
cut off from the possibility of direct evidence in its favor. It is well
known that the difference between the calculated and the observed times of
the periodical return of Encke’s comet, has led to a conjecture that a
medium capable of opposing resistance to motion is diffused through space.
If this surmise should be confirmed, in the course of ages, by the gradual
accumulation of a similar variance in the case of the other bodies of the
solar system, the luminiferous ether would have made a considerable
advance toward the character of a _vera causa_, since the existence would
have been ascertained of a great cosmical agent, possessing some of the
attributes which the hypothesis assumes; though there would still remain
many difficulties, and the identification of the ether with the resisting
medium would even, I imagine, give rise to new ones. At present, however,
this supposition can not be looked upon as more than a conjecture; the
existence of the ether still rests on the possibility of deducing from its
assumed laws a considerable number of actual phenomena; and this evidence
I can not regard as conclusive, because we can not have, in the case of
such an hypothesis, the assurance that if the hypothesis be false it must
lead to results at variance with the true facts.
Accordingly, most thinkers of any degree of sobriety allow that an
hypothesis of this kind is not to be received as probably true because it
accounts for all the known phenomena; since this is a condition sometimes
fulfilled tolerably well by two conflicting hypotheses; while there are
probably many others which are equally possible, but which, for want of
any thing analogous in our experience, our minds are unfitted to conceive.
But it seems to be thought that an hypothesis of the sort in question is
entitled to a more favorable reception, if, besides accounting for all the
facts previously known, it has led to the anticipation and prediction of
others which experience afterward verified; as the undulatory theory of
light led to the prediction, subsequently realized by experiment, that two
luminous rays might meet each other in such a manner as to produce
darkness. Such predictions and their fulfillment are, indeed, well
calculated to impress the uninformed, whose faith in science rests solely
on similar coincidences between its prophecies and what comes to pass. But
it is strange that any considerable stress should be laid upon such a
coincidence by persons of scientific attainments. If the laws of the
propagation of light accord with those of the vibrations of an elastic
fluid in as many respects as is necessary to make the hypothesis afford a
correct expression of all or most of the phenomena known at the time, it
is nothing strange that they should accord with each other in one respect
more. Though twenty such coincidences should occur, they would not prove
the reality of the undulatory ether; it would not follow that the
phenomena of light were results of the laws of elastic fluids, but at most
that they are governed by laws partially identical with these; which, we
may observe, is already certain, from the fact that the hypothesis in
question could be for a moment tenable.(166) Cases may be cited, even in
our imperfect acquaintance with nature, where agencies that we have good
reason to consider as radically distinct produce their effects, or some of
their effects, according to laws which are identical. The law, for
example, of the inverse square of the distance, is the measure of the
intensity not only of gravitation, but (it is believed) of illumination,
and of heat diffused from a centre. Yet no one looks upon this identity as
proving similarity in the mechanism by which the three kinds of phenomena
are produced.
According to Dr. Whewell, the coincidence of results predicted from an
hypothesis with facts afterward observed, amounts to a conclusive proof of
the truth of the theory. “If I copy a long series of letters, of which the
last half-dozen are concealed, and if I guess these aright, as is found to
be the case when they are afterward uncovered, this must be because I have
made out the import of the inscription. To say that because I have copied
all that I could see, it is nothing strange that I should guess those
which I can not see, would be absurd, without supposing such a ground for
guessing.”(167) If any one, from examining the greater part of a long
inscription, can interpret the characters so that the inscription gives a
rational meaning in a known language, there is a strong presumption that
his interpretation is correct; but I do not think the presumption much
increased by his being able to guess the few remaining letters without
seeing them; for we should naturally expect (when the nature of the case
excludes chance) that even an erroneous interpretation which accorded with
all the visible parts of the inscription would accord also with the small
remainder; as would be the case, for example, if the inscription had been
designedly so contrived as to admit of a double sense. I assume that the
uncovered characters afford an amount of coincidence too great to be
merely casual; otherwise the illustration is not a fair one. No one
supposes the agreement of the phenomena of light with the theory of
undulations to be merely fortuitous. It must arise from the actual
identity of some of the laws of undulations with some of those of light;
and if there be that identity, it is reasonable to suppose that its
consequences would not end with the phenomena which first suggested the
identification, nor be even confined to such phenomena as were known at
the time. But it does not follow, because some of the laws agree with
those of undulations, that there are any actual undulations; no more than
it followed because some (though not so many) of the same laws agreed with
those of the projection of particles, that there was actual emission of
particles. Even the undulatory hypothesis does not account for all the
phenomena of light. The natural colors of objects, the compound nature of
the solar ray, the absorption of light, and its chemical and vital action,
the hypothesis leaves as mysterious as it found them; and some of these
facts are, at least apparently, more reconcilable with the emission theory
than with that of Young and Fresnel. Who knows but that some third
hypothesis, including all these phenomena, may in time leave the
undulatory theory as far behind as that has left the theory of Newton and
his successors?
To the statement, that the condition of accounting for all the known
phenomena is often fulfilled equally well by two conflicting hypotheses,
Dr. Whewell makes answer that he knows “of no such case in the history of
science, where the phenomena are at all numerous and complicated.”(168)
Such an affirmation, by a writer of Dr. Whewell’s minute acquaintance with
the history of science, would carry great authority, if he had not, a few
pages before, taken pains to refute it,(169) by maintaining that even the
exploded scientific hypotheses might always, or almost always, have been
so modified as to make them correct representations of the phenomena. The
hypothesis of vortices, he tells us, was, by successive modifications,
brought to coincide in its results with the Newtonian theory and with the
facts. The vortices did not, indeed, explain all the phenomena which the
Newtonian theory was ultimately found to account for, such as the
precession of the equinoxes; but this phenomenon was not, at the time, in
the contemplation of either party, as one of the facts to be accounted
for. All the facts which they did contemplate, we may believe on Dr.
Whewell’s authority to have accorded as accurately with the Cartesian
hypothesis, in its finally improved state, as with Newton’s.
But it is not, I conceive, a valid reason for accepting any given
hypothesis, that we are unable to imagine any other which will account for
the facts. There is no necessity for supposing that the true explanation
must be one which, with only our present experience, we could imagine.
Among the natural agents with which we are acquainted, the vibrations of
an elastic fluid may be the only one whose laws bear a close resemblance
to those of light; but we can not tell that there does not exist an
unknown cause, other than an elastic ether diffused through space, yet
producing effects identical in some respects with those which would result
from the undulations of such an ether. To assume that no such cause can
exist, appears to me an extreme case of assumption without evidence. And
at the risk of being charged with want of modesty, I can not help
expressing astonishment that a philosopher of Dr. Whewell’s abilities and
attainments should have written an elaborate treatise on the philosophy of
induction, in which he recognizes absolutely no mode of induction except
that of trying hypothesis after hypothesis until one is found which fits
the phenomena; which one, when found, is to be assumed as true, with no
other reservation than that if, on re-examination, it should appear to
assume more than is needful for explaining the phenomena, the superfluous
part of the assumption should be cut off. And this without the slightest
distinction between the cases in which it may be known beforehand that two
different hypotheses can not lead to the same result, and those in which,
for aught we can ever know, the range of suppositions, all equally
consistent with the phenomena, may be infinite.(170)
Nevertheless, I do not agree with M. Comte in condemning those who employ
themselves in working out into detail the application of these hypotheses
to the explanation of ascertained facts, provided they bear in mind that
the utmost they can prove is, not that the hypothesis is, but that it
_may_ be true. The ether hypothesis has a very strong claim to be so
followed out, a claim greatly strengthened since it has been shown to
afford a mechanism which would explain the mode of production, not of
light only, but also of heat. Indeed, the speculation has a smaller
element of hypothesis in its application to heat, than in the case for
which it was originally framed. We have proof by our senses of the
existence of molecular movement among the particles of all heated bodies;
while we have no similar experience in the case of light. When, therefore,
heat is communicated from the sun to the earth across apparently empty
space, the chain of causation has molecular motion both at the beginning
and end. The hypothesis only makes the motion continuous by extending it
to the middle. Now, motion in a body is known to be capable of being
imparted to another body contiguous to it; and the intervention of a
hypothetical elastic fluid occupying the space between the sun and the
earth, supplies the contiguity which is the only condition wanting, and
which can be supplied by no supposition but that of an intervening medium.
The supposition, notwithstanding, is at best a probable conjecture, not a
proved truth. For there is no proof that contiguity is absolutely required
for the communication of motion from one body to another. Contiguity does
not always exist, to our senses at least, in the cases in which motion
produces motion. The forces which go under the name of attraction,
especially the greatest of all, gravitation, are examples of motion
producing motion without apparent contiguity. When a planet moves, its
distant satellites accompany its motion. The sun carries the whole solar
system along with it in the progress which it is ascertained to be
executing through space. And even if we were to accept as conclusive the
geometrical reasonings (strikingly similar to those by which the
Cartesians defended their vortices) by which it has been attempted to show
that the motions of the ether may account for gravitation itself, even
then it would only have been proved that the supposed mode of production
may be, but not that no other mode can be, the true one.
§ 7. It is necessary, before quitting the subject of hypotheses, to guard
against the appearance of reflecting upon the scientific value of several
branches of physical inquiry, which, though only in their infancy, I hold
to be strictly inductive. There is a great difference between inventing
agencies to account for classes of phenomena, and endeavoring, in
conformity with known laws, to conjecture what former collocations of
known agents may have given birth to individual facts still in existence.
The latter is the legitimate operation of inferring from an observed
effect the existence, in time past, of a cause similar to that by which we
know it to be produced in all cases in which we have actual experience of
its origin. This, for example, is the scope of the inquiries of geology;
and they are no more illogical or visionary than judicial inquiries, which
also aim at discovering a past event by inference from those of its
effects which still subsist. As we can ascertain whether a man was
murdered or died a natural death, from the indications exhibited by the
corpse, the presence or absence of signs of struggling on the ground or on
the adjacent objects, the marks of blood, the footsteps of the supposed
murderers, and so on, proceeding throughout on uniformities ascertained by
a perfect induction without any mixture of hypothesis; so if we find, on
and beneath the surface of our planet, masses exactly similar to deposits
from water, or to results of the cooling of matter melted by fire, we may
justly conclude that such has been their origin; and if the effects,
though similar in kind, are on a far larger scale than any which are now
produced, we may rationally, and without hypothesis, conclude either that
the causes existed formerly with greater intensity, or that they have
operated during an enormous length of time. Further than this no geologist
of authority has, since the rise of the present enlightened school of
geological speculation, attempted to go.
In many geological inquiries it doubtless happens that though the laws to
which the phenomena are ascribed are known laws, and the agents known
agents, those agents are not known to have been present in the particular
case. In the speculation respecting the igneous origin of trap or granite,
the fact does not admit of direct proof that those substances have been
actually subjected to intense heat. But the same thing might be said of
all judicial inquiries which proceed on circumstantial evidence. We can
conclude that a man was murdered, though it is not proved by the testimony
of eye-witnesses that some person who had the intention of murdering him
was present on the spot. It is enough for most purposes, if no other known
cause could have generated the effects shown to have been produced.
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The celebrated speculation of Laplace concerning the origin of the earth
and planets, participates essentially in the inductive character of modern
geological theory. The speculation is, that the atmosphere of the sun
originally extended to the present limits of the solar system; from which,
by the process of cooling, it has contracted to its present dimensions;
and since, by the general principles of mechanics the rotation of the sun
and of its accompanying atmosphere must increase in rapidity as its volume
diminishes, the increased centrifugal force generated by the more rapid
rotation, overbalancing the action of gravitation, has caused the sun to
abandon successive rings of vaporous matter, which are supposed to have
condensed by cooling, and to have become the planets. There is in this
theory no unknown substance introduced on supposition, nor any unknown
property or law ascribed to a known substance. The known laws of matter
authorize us to suppose that a body which is constantly giving out so
large an amount of heat as the sun is, must be progressively cooling, and
that, by the process of cooling it must contract; if, therefore, we
endeavor, from the present state of that luminary, to infer its state in a
time long past, we must necessarily suppose that its atmosphere extended
much farther than at present, and we are entitled to suppose that it
extended as far as we can trace effects such as it might naturally leave
behind it on retiring; and such the planets are. These suppositions being
made, it follows from known laws that successive zones of the solar
atmosphere might be abandoned; that these would continue to revolve round
the sun with the same velocity as when they formed part of its substance;
and that they would cool down, long before the sun itself, to any given
temperature, and consequently to that at which the greater part of the
vaporous matter of which they consisted would become liquid or solid. The
known law of gravitation would then cause them to agglomerate in masses,
which would assume the shape our planets actually exhibit; would acquire,
each about its own axis, a rotatory movement; and would in that state
revolve, as the planets actually do, about the sun, in the same direction
with the sun’s rotation, but with less velocity, because in the same
periodic time which the sun’s rotation occupied when his atmosphere
extended to that point. There is thus, in Laplace’s theory, nothing,
strictly speaking, hypothetical; it is an example of legitimate reasoning
from a present effect to a possible past cause, according to the known
laws of that cause. The theory, therefore, is, as I have said, of a
similar character to the theories of geologists; but considerably inferior
to them in point of evidence. Even if it were proved (which it is not)
that the conditions necessary for determining the breaking off of
successive rings would certainly occur, there would still be a much
greater chance of error in assuming that the existing laws of nature are
the same which existed at the origin of the solar system, than in merely
presuming (with geologists) that those laws have lasted through a few
revolutions and transformations of a single one among the bodies of which
that system is composed.