calculable probability (if I may so call it) has its only application,
or its only assured application, within groups whose character is
either postulated, or is independently arrived at by inference and
observation. These groups, be they natural or conventional, provide a
framework, marking out a region wherein prevails the kind of ignorance
which is the subjective reflection of objective “randomness.” This is
the kind of ignorance which the calculus of probabilities can most
successfully transmute into knowledge: and herein lies the reason why
the discoverers of the calculus found their original inspiration in
the hazards of the gambling-table, and why their successors still find
in games of chance its happiest illustrations. For in games of chance
the group framework is provided by convention; perfect “randomness”
is secured by fitting devices; and he who attempts to modify it is
expelled from society as a cheat.
None of these observations apply to the kind of probability on
whose importance I am now insisting. If calculable probability be
indeed “common sense reduced to calculation,” intuitive probability
lies deeper. It supports common sense, and it supplies the ultimate
ground—be it secure or insecure—of all work-a-day practice and all
scientific theory. It has nothing to do with “randomness”; it knows
nothing of averages; it obeys no formal laws; no light is thrown on it
by cards or dice; it cannot be reduced to calculation. How, then, is it
to be treated? What place is it to occupy in our general scheme?
These are all important questions. But no answer to them can be given
till we have pressed somewhat further the line of thought which the
discussion in this present lecture has for a moment interrupted. Before
I began this long parenthesis on the theory of chance, I was occupied
with a most important example of a belief which possesses the highest
degree of intuitive probability, but no calculable probability at all.
I mean the belief in an independent physical universe. In the next
lecture I shall resume the general thread of my argument, and consider
another belief of the same kind which is not less—some would say even
more—essential to natural science than the one with which I have
already dealt. I mean a belief in the regularity of nature.
FOOTNOTES:
[9] Although, as a matter of fact, I do speak of it in the next lecture.
[10] Maxwell, as all who interest themselves in physics are aware,
arrived at very interesting conclusions by considering what would
happen if little demons interfered with the random motions of the
molecules constituting a gas.
LECTURE VIII
UNIFORMITY AND CAUSATION
I
In my last lecture but one I dwelt upon the interplay of causes and
reasons in one special case—the case of our immediate experiences of
the external world, the world in which we move, the world investigated
by the physical sciences. No case can indeed be more important; for
these immediate experiences are deemed by every man to be his guide
through all the hours of his waking life, and by every man of science
to supply the evidence on which depends all our knowledge of natural
laws.
Yet this very statement suggests the existence of another series of
problems not less important and not less closely connected with my
general argument. For, how do we get from particular experiences to
general laws—from beliefs about individual occurrences to beliefs
about the ordering of the universe? These beliefs, looked at from the
scientific point of view, are, as I have so often observed, a natural
product. They have a history like other natural products. They are the
effects of a long train of causes; and among those causes are some
which claim, rightly or wrongly, to be reasons, an uncounted multitude
which make no such claim, and others, again, which occupy a doubtful
position between the two.
Imagine an external intelligence studying the methods by which
earth-born creatures of various types adjust themselves to future
circumstances. The most primitive method is, I suppose, no more than
simple nervous reaction. The most developed method involves reasoned
expectation. And between these two extremes our supposed observer would
see a long series of intermediate forms melting into one another by
insensible gradation.
From the point of view of the argument I am endeavouring to present
to you, this development is of the greatest interest. The creation
of a capacity for expectation, and of an inclination to expect a
future similar to the past, must be deemed one of the most remarkable
triumphs of selection—if to selection it indeed be due. Here we have
this irrational mimic of reason, starting from the simplest forms of
response to external stimulus, improving them into such excellent
imitations of inductive reasoning as those which lead a chick, no more
than a few hours old, to reject food which it has once found nasty[11];
and finally evolving out of these humble beginnings a mode of inference
which, according to empirical philosophy, is the true and only source
of all our general knowledge, whether of nature or of man.
It must be owned, indeed, that the attempt to treat instinctive
expectation as a form of rational inference has been a lamentable
failure. By no exercise of ingenuity can beliefs about what is not
experienced be logically extracted from particular experiences,
multiply them as you will. It is in vain that empirical philosophers
attempt to give an air of rationality to this leap from the known to
the unknown by the use of high-sounding logical titles. “Induction
by simple enumeration” is doubtless an imposing name. But those who
practise the thing are in no wise improving on their predecessor, the
chick. Indeed they lag behind it. For the chick expects—but gives no
reason; the empirical philosopher expects—and gives a bad one.
II
Expectation, then, if it is to be rational, can only be rationally
extracted from experiences by the aid of one or more general
principles. What principles are they?
One of them, at all events, must be the regularity of nature. In some
form or other, and to some degree or other, this is assumed in every
scientific speculation and in every purposeful action reflectively
performed. It is, as you may recollect, one of the “inevitable beliefs
of common sense” to which I referred in my first lecture.
But you may also recollect that in the same lecture I pointed out that
inevitable beliefs, though we cannot avoid holding them in some shape,
are, and have been, held in many shapes; shapes which vary with the
changes in our general outlook on men and things. In what shape, then,
should our belief in regularity now be held?
The shape in which it is very commonly formulated is something of
this kind: “everything is caused; and the same causes are always
followed by the same effects.” This is the so-called “law of universal
causation.” It has been treated as an assured truth by philosophers of
many different schools, though not always for the same reasons; and, so
far as the physical universe is concerned, the modern world accepts it
without demur. It is, nevertheless, open to criticism from two points
of view. It asserts somewhat more about the course of nature than
experience suggests, and somewhat less than science requires. Let me
take the two points separately.
When I was dealing with ethics I had occasion to point out that if
the primitive manifestations of loyalty and love are products of
selection, they have developed by a kind of internal momentum, to a
point far beyond that to which selection can possibly have carried
them. Something of the same kind has happened in the case of the causal
postulate. Selection, we must suppose, has produced the capacity for
acquiring habitual expectations; and habitual expectation is induction
without reasoning. Like induction, it would not only be useless, but
harmful, if no regularity existed; if at any moment the future ceased
to bear some resemblance to the past. But the regularity asserted by
the law of universal causation is far in excess of this requirement.
The law applies to regions which never come within the range of finite
experience; and, as regards regions which do come within that range,
experience hardly confirms it. We may, of course, attribute the
apparent irregularities in nature to our ignorance or our errors; and
this, in fact, is what we always do. We must (we think) have observed
wrongly or insufficiently; or it may be that a clearer insight would
show how apparent aberrations really illustrate some larger law, or
depend on conditions at present beyond our ken. Such explanations
are easy; and, what is more, they are true. There is no complaint to
be made of a verdict in favour of absolute uniformity except that it
outruns the evidence. None surely, who understand the meaning of the
words they use, will dare to assert that nature _appears_ regular. What
they _may_ assert is, that the more you examine it, the more regular
it appears. The reign of law is always extending. New provinces are
always being added to its domains. Anomalies vanish as knowledge grows;
and the absolute uniformity which we now only know by faith, we may
some day know by sight.
To this “credo” (with reservations) I readily subscribe. But it sounds
a little strange in the mouths of some who preach it. Does it not imply
that we interpret our experiences in the light of a preconceived scheme
of things; that we force our observations into a mould which they do
not naturally fit? If, in unravelling a cypher, I come across passages
which are unintelligible, I attribute the check to my own ignorance
or dullness. Why? Because I know independently that the cypher has a
meaning, if only I could find it. But the empirical agnostic professes
to know nothing about the world, except what he has observed himself or
what other people have observed for him. Why, then, should he suppose
perfect regularity to exist when no perfect regularity appears? Why is
he not content to accept what he finds, namely, a regularity which is
real but incomplete?
It is no reply to say that patient genius is constantly detecting order
in apparent chaos. So it is. And when this happens, by all means
rearrange your map of the universe accordingly. But do not argue that
chaos is therefore non-existent. The belief in universal causation is
not based on argument, nor yet on observation. It depends on what I
have described as intuitive probability. And if we refuse to regard
nature as liable to lapses from perfect uniformity, this is not because
such a theory is unthinkable, not because it is contrary to experience,
not because it is incompatible with knowledge, not because it is fatal
to purposeful action; for it is none of these things. We reject it
because it is out of harmony with the ideal we have formed of what the
material universe ought to be and is: and so strong is this speculative
prepossession that there is no experimental evidence which would
convince a man of science that, when physical causes were the same,
physical consequences could be different.
III
But this observation brings me to my second commentary on the formula
of universal causation. If, as I have contended, it goes beyond what
mere experience suggests, it also falls short of what scientific
inference requires. The uniformity it postulates lacks a certain kind
of “structure” which is absolutely necessary if the past is to be
explained and the future foreseen. It is not enough for this purpose
that the course of Nature should be determined. It must be determined
after a particular pattern; its uniformity must conform to a particular
type.
At first sight this statement may seem rather obscure. What (you
will ask) is this “structure” or pattern whose absence would be so
disastrous to knowledge? It is a structure (I reply) which makes it
possible to break up the flow of events into intelligible repetitions.
It is not enough that the condition of the world at any moment should
be strictly determined by its condition at the preceding moment.
Such a world would, I suppose, completely conform to the doctrine of
uniformity, and obey both in spirit and in letter the law of universal
causation. Yet, unless it also conformed to the additional canon I
have just laid down, it would provide no basis either for scientific
knowledge or for practical decision. The same consequent would always
succeed the same antecedent, if and when it recurred. But, unless we
accept the cyclic theories of the Stoics, it never would recur. The
completest knowledge of the past would tell us nothing about the
future; not because the succession of events was arbitrary or (as the
word is commonly misused) miraculous; but because each cross-section
of the stream of Time (that is to say, the sum of all contemporaneous
facts and events) had to be considered as a single cause, completely
determining the whole cross-sections immediately in front of it; and,
as a single effect, completely determined by the whole cross-section
immediately behind it. Such a world might have a history, but it could
never have a science.
The reason is plain. Science requires uniformities even more than
uniformity; and a universe such as I have just described has uniformity
but no uniformities. The very phrase “laws of nature” shows that it is
these subordinate uniformities for which we look. The whole efforts
of the skilled investigator are directed towards so isolating the
sequences he is examining that his experiments shall become (as the
phrase goes) _crucial_. If no such isolation could be effected, it
would never be possible to point to some “phenomenon” and say of it
“Here is a cause,” and to some other “phenomenon” and say of it “Here
is its effect.” The world, in short, must have a structure which
connects its successive phases in such a way that definite parts of all
that exists or happens are knit with peculiar closeness to definite
parts of what existed or happened before. It is on these connecting
strands that we mainly fix our gaze; they are often difficult to trace,
they are sometimes hopelessly entangled; but when we can bring them
into clear vision, then, and not till then, we triumphantly say that we
have discovered a law of nature.
We are so familiar with this “fibrous” structure of the natural world
that it seems almost a matter of course. Mill, for example, assumes
it, unconsciously no doubt, through all his exposition of inductive
methods: and if he had not assumed it, these methods would have come
tumbling about his ears in irreparable ruin. But assuredly neither
he nor any other logician has a right to make such an assumption
in silence. In spite of many speculative difficulties, there is no
principle more vital to knowledge, practical and theoretical, than
the principle of “negligibility”; the principle which asserts that
sequences can be isolated and repeated, and that vast bodies of
contemporaneous facts and happenings may be wholly neglected. It is
much more important than the principle of causation, if by causation
is meant, not a working, though possibly imperfect, regularity, but the
speculative completeness implied by the phrase “universal causation” as
commonly interpreted.
It may be said, and I think with truth, that these observations
scarcely apply to a material world conceived in a purely mechanical
fashion. In such a world negligibility is theoretically measurable.
The mass of Sirius, without doubt, modifies the weight of the pen with
which I am writing. But the effect is demonstrably infinitesimal,
and negligibility is not assumed, but proved. Laplace’s calculator,
surveying the universe, would have no difficulty either in fixing
his attention on particular repetitions which exemplify the “laws of
nature,” or in regarding them as integral parts of a single mechanical
whole, whose successive phases (if the law of energy dissipation be
universal) can never be repeated.
But this does not lighten the difficulty. The world may, or may not,
be a single mechanical system; but, if it is, the fact can only be
empirically known to us through induction: and induction assumes
negligibility, and cannot, so far as I can see, move a step without it.
Choose the most perfect experiment on record, idealise its conditions
to your heart’s content; for greater security, suppose it repeated
even to weariness, how will you be advanced? There are, I suppose,
millions of circumstances, for the most part utterly unknown, which
have co-existed with all the experiments already tried, but will have
vanished before the next experiment is undertaken. Does this disturb
you? Do you ask yourself whether, among the unnumbered circumstances in
which the world of to-day differs from the world of yesterday, there
may not be one which is necessary to the expected effect? Not at all.
You brush them aside. You say they may be neglected. And doubtless you
do well. But why? Not on any grounds which observation or reasoning can
supply, not on any grounds formulated in the logic of induction, or
the calculus of chances. You trust yourself to a feeling of antecedent
probability;—the intuitive probability on whose importance I dwelt
in the last lecture, which is not the flower of experience but its
root;—and your trust will sometimes be betrayed.
The principle of negligibility, or (in terms of belief) the belief that
observed regularities may often be treated as if they were complete and
self-contained cases of cause and effect, separable from contemporary
events, is thus a necessary presupposition of concrete science; and,
like other presuppositions, it is incapable of scientific proof.
We often hear it said, indeed, that principles of this kind should
be regarded as hypotheses verified by an ever-increasing volume of
experimental proof. They are found to work; what more can be desired?
But it is not accurate to say that these and other fundamental
principles are, or ever have been, regarded either by common sense
or science as inferences from experience or as hypotheses requiring
verification. Nor is it accurate to suggest that verification differs
essentially from any other kind of experimental evidence except in
the date of its occurrence. If evidence follows conjecture, but not
otherwise, it is called verification; and though, from the point of
view of method, this chronological order is of immense importance, from
the point of view of logic it is nothing. A doubtful conjecture (let
us suppose) is “verified” by experiment. If the experiment had come
earlier there would have been no conjecture, but there would have been
equal evidence, indeed the same evidence. It is true that without the
conjecture there might have been no experiment, and that without the
experiment there might have been no proof. But, though the conjecture
occasioned the proof, it certainly adds nothing to its force, and we
therefore come back to the question already discussed—namely, whether
principles without which no inference from experiences is possible,
can be themselves inferred from experiences?—a question to which, as I
conceive, only one answer is possible. Experiences may produce habit,
and habit may produce expectation, and this process may masquerade
as induction. But expectations thus engendered belong to the causal
series, not the cognitive. Physiology and psychology may explain them.
But they can neither be proved nor treated as axiomatic.
Axiomatic they certainly are not; nor do they possess the universality
and precision of outline which we are accustomed to associate
with axioms. It is curious, in this connection, to note that the
philosophers who are most firmly resolved to root the principle of
regularity (they ignore negligibility) in experience always insist on
giving it that absolute character which our inferences from experience
rarely possess. The notion that fundamental beliefs should be liable to
exception, should be capable of degrees, and should apply unequally
in different fields of observation, is as abhorrent to them as to any
metaphysician out of the opposite camp. One would suppose, to hear them
talk, that, unless causation be universal, experience is worthless.
IV
The region where these uncompromising doctrines show to least advantage
is human character. I do not propose to discuss causation and free
will; but I may with advantage say something on a less hackneyed
theme, namely, negligibility and foreknowledge. The thesis I desire to
maintain is that, in dealing with a human character, full foreknowledge
is theoretically impossible, even though free will be wholly absent,
and the succession of psychic states be completely determined.
Practically impossible we know it to be. But most determinists would
hold that this impossibility is due partly to our ignorance and partly
to our incapacity. We know too little either of the general laws of
mind, or of individual character, or of surrounding circumstances,
to make accurate forecasts; and, even if we possessed the requisite
information, we could not use it, owing to the irremediable
weakness of our powers of calculation. It is this contention that
I wish to traverse. I hold that, had we the supernatural powers of
Laplace’s calculator, armed with a knowledge of the human heart which
supernatural powers of observation could alone supply, we should
still fail, because we are face to face with that which is inherently
incalculable.
The contrary opinion is due, I think, to an imperfect comprehension
of the doctrines I have touched on in this lecture. All human
foreknowledge depends on detecting old sequences in a new context. The
context, of course, is always new. There is never full or complete
repetition. But, unless there be partial repetitions embedded in the
universal flux, prescience is impossible. This is the doctrine of
“negligibility.”
Now consider two illustrative examples.
First, imagine yourself standing on the edge of a valley down which
a landslip has just let loose the waters of some great reservoir
in the hills. The catastrophe is sudden in its onset, brief in its
duration, wildly irregular in its character. Even the most tumultuous
cataract retains a certain steadiness of outline: and few sights are
more impressive than the stationary waves in a great rapid. But there
is here no trace of order imposed on disorder, fixity on motion. The
rushing wall of water, spouting into foam over every obstacle it
encounters, the tossing flood that follows furiously behind, seem
in their brief violence to present the very ideal of incalculable
confusion. But we know it is not so. In the presence of such a
spectacle our calculator would not feel a moment’s embarrassment. He
could forecast without difficulty the whole scene down to its minutest
eddy; the motions of each drop obey laws with which he was perfectly
familiar; and the total effect, catastrophic though it be, is but the
sum of all these component examples of natural uniformity.
Turn now and contemplate a calmer scene. Consider the commonplace life
of a commonplace man as it develops in the untroubled prosperity of a
steady business and a quiet home. Such a career seems as orderly and
uniform as the flood I have been describing is terrible and strange.
Surely no supernatural calculator is required to cast the horoscope
of its hero: for he does, and leaves undone, the same actions, he
thinks and leaves unthought the same ideas, as thousands of his
contemporaries; and, so far as outward appearance goes, he is an
indistinguishable member of an undistinguished crowd.
Yet, in spite of this, we know him to be unique. There never has been
before, nor will there ever be again, another individual exactly like
him. A similar statement, it may be urged, can be made about our
catastrophic flood. Though this has plenty of parallels, none of them,
strictly speaking, are exact. Where, then, lies the distinction on
which I am trying to insist? Let me endeavour to mark the contrast.
If the material world be conceived as a mechanical system, the flood
in my illustration may be regarded as a piece arbitrarily cut out
of it at the whim of the spectator. It possesses no natural unity;
and, like the whole of which it is a fraction, the moving particles
which compose it do each obey laws which are (we assume) perfectly
well known, and have been endlessly exemplified. Its behaviour is the
sum of the behaviour of these several parts: and it is by estimating
their movements that our imaginary calculator can prophesy its course
with absolute exactness. He is never perplexed by the problem of
negligibility; for negligibility in such a case can be accurately
measured, and our calculator possesses all the data required for its
measurement. In short, the principle of regularity may here be applied
in its most uncompromising form; it requires no qualification, nor can
it be pressed too boldly or too far.
But the case is otherwise when we have to abandon the strictly
mechanical point of view, and investigate regions where negligibility
has a small and uncertain application. Such a region is individual
consciousness. This possesses a natural or intrinsic unity. Its phases
are never precisely repeated; nor can it be regarded as a collection
of independent elements, the sequences of which may be separately
examined, verified, and repeated. Not only is the whole unique, but the
parts are unique also. Or, perhaps it would be more accurate to say
that there _are_ no parts possessing a fixed character of their own
apart from the whole. Not only is everything qualified by everything
else, but few of these qualifications are negligible. Perfect
repetition is therefore impossible, and our calculator, whatever his
powers, could never feel at home with his premises, or secure in his
conclusions. The present would always be new, and the future would
always be doubtful.
If this seems paradoxical it is, I think, mainly for two reasons. In
the first place, such a doctrine seems inconsistent with the fact that,
whatever Laplace’s calculator could do, humbler beings like ourselves
manage somehow or other to forecast the behaviour of our neighbours
with some small measure of success. This, no doubt, is true. But it
is in part because the alternatives of behaviour are very few and
very definite compared with the infinitely graduated variations of
thought, will, and feeling. Action is “canalised.” It can flow only
along channels engineered for it by circumstances, and among these the
choice is commonly small. But the character which lies behind action is
complex beyond all power of analysis, and variable beyond all powers
of anticipation. The routine which is unwaveringly pursued from month
to month and year to year is pursued each day in a different spirit:
and often a critical hour strikes when some well-drilled creature of
custom, to his own surprise and the scandal of his friends, deserts the
ancient ways and wanders suddenly forth into the unknown.
Of course, these violent aberrations are the exception. The more
familiar experience is that, in an orderly society, the alternatives of
action which need be taken into account are few, and the “limits of
deviation” narrow. Often, therefore, we can anticipate conduct without
any real insight into the depths of character or the complexities of
motive from which the conduct springs. And truly this is fortunate;
for, if mutual comprehension were necessary to social intercourse, how
could society exist?
But there is another reason why we take little note of the distinction
I am endeavouring to draw between the calculable uniformities of a
material world and the incalculable regularities of psychic life.
The distinction is rather speculative than practical. It does not
affect the routine of daily existence. For, although the course of
the material world is calculable, we mortals have neither the time
nor the knowledge nor the mental powers required to calculate it. We
behave, therefore, towards nature as we behave towards man. We content
ourselves with approximations, with analogies, with resemblances.
Even if we had the power, we should not have the time to resolve the
movement of all the bits of matter with which we have to deal from
minute to minute into the exact sequences of which they are composed.
We would not if we could. We apply rough methods; we are satisfied
with imperfect results. Nor are these results always more imperfect in
the psychic than in the material sphere of observation. The ways (for
example) of British weather are even more mysterious than the ways of
British men. Why, then, should we interest ourselves in a speculation
which tells us, however truly, that perfect foreknowledge is
theoretically possible in the first case, but theoretically impossible
in the second? In practice it is impossible in both. And with this we
must be content.
And yet the speculation is interesting. For the distinction between the
two cases lies deep. It has nothing (let me say again) to do with free
will. It has nothing to do with our ignorance of facts. It has nothing
to do with our intellectual insufficiency. It is due to a fundamental
difference between the uniformities of matter and the regularities of
mind. Perfect foresight requires perfect repetition, and in the psychic
sphere perfect repetition can never happen. Every self is unique; all
its experiences are unique; and these unique wholes are not compounded
of interchangeable elements obeying identical laws. They do not alter
by mere addition, subtraction, or rearrangement of parts. They grow.
And the sequence of one phase upon another faintly resembles that
which would prevail in the imaginary universe of which I spoke just
now, the universe where all contemporaneous events were treated as
the single effect of the immediate past and the single cause of the
immediate future. Of such a universe I observed that it would have a
history, but could have no science. And though we cannot go so far when
speaking of psychic unities, though we cannot rule out psychology or
sociology, it must be admitted that no regularities which observation
discloses can ever possess the precision which we theoretically
attribute to material mechanism. Instructive likenesses we shall find
in abundance, complete determination we may assume if we please; but
“laws,” in the full and strict sense of the term, we shall not find,
for they are not there.
NOTE
The shortcomings of mechanism have been discussed by M. Bergson in a
manner which no other thinker is likely to rival. He has, however,
usually dealt with the subject in connection with _freedom_; whereas
in this section I have only dealt with it in connection with
foreknowledge, repetition, and what I have termed the doctrine of
“negligibility.” He approaches it from the side of reality. I approach
it from the side of inductive inference and the law of universal
causation.
FOOTNOTES:
[11] Extract from Morgan’s “Habit and Instinct,” page 40. “A young
chick two days old, for example, had learnt to pick out pieces of
yolk from others of white of egg. I cut little bits of orange-peel of
about the same size as the pieces of yolk, and one of these was soon
seized, but at once relinquished, the chick shaking his head. Seizing
another, he held it for a moment in the bill, but then dropped it and
scratched at the base of his beak. That was enough; he could not again
be induced to seize a piece of orange-peel. The obnoxious material
was now removed, and pieces of yolk of egg substituted, but they were
left untouched, being probably taken for orange-peel. Subsequently, he
looked at the yolk with hesitation, but presently pecked doubtfully,
not seizing, but merely touching. Then he pecked again, seized, and
swallowed.”
LECTURE IX
TENDENCIES OF SCIENTIFIC BELIEF
I
In the sixth and eighth lectures of this course I dealt with two
inevitable beliefs which lie at the root of all science and all
practice—the beliefs that an independent, or, as it is commonly called,
an “external” world exists, and the belief that the world, whether
external or internal, has at least a measure of regularity. In the
seventh lecture I interpolated a discussion upon probability; and
showed, or attempted to show, that we must take account of a kind of
probability other than that which, in the hands of mathematicians, has
so greatly contributed to knowledge.
If, now, we consider these subjects in their mutual relation, we
perceive that an “inevitable” belief is one which possesses the highest
degree of this intuitive probability. These are two descriptions of the
same quality—one emphasising the objective, the other the subjective,
aspects of a single fact.
But this at once suggests a further inquiry. Probability is evidently
a matter of degree. A belief may be more probable or less probable.
Inevitableness, on the other hand, seems at first sight to be
insusceptible of gradation. It is, or it is not. Yet this extreme
definiteness vanishes if we regard it as a limiting case—as the last
term of a series whose earlier members represent varying degrees of
plausibility. On this view we should regard our beliefs about the
universe as moulded by formative forces, which vary from irresistible
coercion to faint and doubtful inclination. Beliefs in the reality of
the external world and in its regularity are important products of the
first. I now propose to call attention to some beliefs which are due
to the less obvious action of the second. Both kinds, whether capable
of proof or not, are more or less independent of it. Both are to be
regarded rather as the results of tendencies than as the conclusions of
logic.
I am well aware that a doctrine like this will find few admirers among
systematic thinkers. Inevitable beliefs which are fundamental without
being axiomatic; which lack definiteness and precision; which do not
seem equally applicable to every field of experience; which do not
claim to be of the essence of our understanding, like the categories
of the critical philosophy, or the so-called laws of thought, have
little to recommend them to philosophers. And when inevitableness is
treated as merely an extreme form of plausibility, when guidance is
discovered in tendencies which are weak and of uncertain application,
leading to error as well as to truth, their objections will scarcely be
mitigated.
Many of those who look at these problems from (what they deem to
be) a strictly scientific point of view are not likely to be more
favourable. Their loyalty to experience takes the form of supposing
that men accumulate knowledge by peering about for “sequences” among
“phenomena,” as a child looks for shells upon the beach—equally ready
to go north or south, east or west, as the humour of the moment moves
him. They would regard any antecedent preference for this or that
sort of explanation as a sin against the categorical imperatives of
intellectual morals. Science, they think, should have no partialities:
and as the honest investigator “entertains no belief with a conviction
the least in excess of the evidence,”[12] so he will resist any leaning
toward one kind of conclusion rather than another. Such is their view
of scientific duty. Scientific practice, however, has been otherwise.
That the practice of ordinary humanity has been otherwise seems indeed
sufficiently plain. The folk-lore, the magic, and the religions of
primitive races, with all their unborrowed resemblances, are there to
attest it. But these (you will say) are superstitions. The objection
is not, I think, relevant; yet, for the sake of peace, let us pass to
what is not regarded as a superstition, namely, morality. Here you
have the singular spectacle of a close agreement among moralists as
to the contents of the moral law, and a profound disagreement as to
the grounds on which the moral law is to be accepted. Can the power of
“tendency” be better shown? Can there be a clearer illustration of the
way in which it may guide belief and anticipate proof?
II
But our business to-day is neither with magic nor morality. It is
with physical science. When we survey man’s strivings to understand
the world in which he lives, can we detect any secular leanings
towards certain types of belief, any deep-lying inclination to guess
by preference in one direction rather than another? We surely can.
There are some answers, for example, which we refuse to take from
experiment and observation. I have already referred to one such case
in connection with causation. No man of science can be provoked, by
any seeming irregularities, into supposing that the course of nature
is subject to lapses from the rule of perfect uniformity. Consider,
again, another case, where the tendency is far less strong, but where
few can doubt that it is real. I refer to the deep-seated reluctance
felt by most physicists to accept as final any scientific explanation
which involves a belief in “action at a distance”—a reluctance which is
the more remarkable since action at a distance seems a familiar fact of
experience, while action by contact, when you attempt to work it out in
detail, seems hard to comprehend.
But there are tendencies feebler and less general than these which
give much food for reflection. Consider, for example, the familiar
history of atomism. At least as far back as Democritus we find the
confident assertion that the world consists of atoms, and that its
infinite variety is due to the motions and positions of immutable
and imperceptible units, which, if they are not exactly alike, at
least differ less among themselves than do the visible objects into
which they are compounded. Through successive centuries this theory
never died. With the revival of learning and the beginning of modern
science it burst into fresh life. It was believed in firmly by Bacon,
the prophet of the new era. It was treated as almost self-evident
by philosophers like Gassendi and Hobbes. Boyle held it in its most
uncompromising form. Newton assumed it without question. After a period
of varying fortunes in the eighteenth century, a modification of it in
the hands of Dalton started a new era in chemistry. Taken over by the
physicists, it now lies at the root of the modern theory of gases and
liquids; the modern theory of matter, the modern theory of heat, and
the modern theory of electricity.
This is a very strange story; and it is not really made less strange by
those who emphasise the differences between the atoms of Democritus,
which are the theme of its first chapter, and the electrons of Sir
Joseph Thomson, which appear in its last. Different indeed they are;
but, though the difference be great, the agreement is fundamental.
There are some who think that the achievement sung by Lucretius is
lessened by showing that the ancients who believed in atoms had no
experimental warrant for their convictions. And this is perfectly true.
They had not. Nor had Bacon, nor Gassendi, nor Hobbes, nor Boyle, nor
Newton. But this only brings into clearer relief the point I desire to
emphasise. If experience did not establish the belief, whence came it?
If it represents nothing better than an individual guess, why did it
appeal so persistently to leaders of scientific thought, and by what
strange hazard does it turn out to be true? It is certainly curious
that Tyndal, in a once famous address to the British Association at
Belfast, should have sketched the story from Democritus to Lucretius,
and from Lucretius to 1874, without ever putting these questions to his
audience, or, so far as I know, to himself.
But the Atomic Theory is by no means the only example of tendencies
which have played an important part in the evolution of science. There
are other beliefs, or kinds of beliefs, of the most far-reaching
importance which have almost exactly similar characteristics. They
anticipate evidence, they guide research, and in some shape or other
they turn out to be true.
Consider, for example, the group of beliefs which may be described
generally as beliefs in persistence, or beliefs in conservation—the
kind of belief which has been applied at different periods, and by
different schools of scientific thought, to matter, mass, bulk, weight,
motion, force, heat, and energy. As every one knows, these ascriptions
have not always been correct. But this only emphasises the strength of
the tendency. Weight was at one time supposed to be invariable. We know
now that the weight of a body varies with its position relatively to
other bodies. It is different, for example, at the poles from what it
is at the Equator. But how was the error discovered? Not by experiment.
There were experiments, no doubt. But those who undertook them already
believed in the law of gravitation; and the law of gravitation made it
necessary to distinguish the mass of any given fragment of matter both
from its weight and from the occult quality of gravity, which is one
of the factors on which its weight in any given situation depends. The
desire for conservation was not, however, defeated; since physicists,
till within the last few years, regarded both mass and gravity as
unalterable characteristics of all material bodies.
Again, consider the case of heat. This also has been regarded by
powerful schools of scientific thought as a substance that was
“conserved.” It is so regarded no longer. But is the inclination to
believe in conservation thereby defeated? Not at all. Though heat may
vanish, energy remains, and heat is a form of energy.
This doctrine of the conservation of energy is indeed the crowning
triumph of the tendency I am discussing, and provides the best
illustrations of its strength. For natural philosophers, intent on
finding conservation wherever they could, started too boldly on their
quest. Descartes regarded the conservation of motion as a self-evident
inference from the rationality of God. It is true that he neither
had experimental evidence of his doctrine, nor could he, under any
circumstances, have obtained it; for the energy of motion, as he
incorrectly described it, is not conserved. Leibnitz described it
correctly, and had as great a confidence as his predecessor in its
conservation, and as little proof to support him. So confident indeed
was he, and so independent of experimental evidence was his faith, that
he dogmatically asserted that, when motion seemed to disappear, what
was lost by the bodies which we see, was exactly taken up by their
component elements which we do not see; so that nothing in the nature
of what he called _vis viva_ was either lost or created. That this
transformation of energy from molar to molecular motion is constantly
occurring we now have sufficient proof. But Leibnitz had no proof; and
apparently thought none was required other than the Cartesian deduction
from the rationality of God. He made a bold anticipation of experience,
with nothing to support him but _a priori_ inclination.
His anticipation, however, was not only bold; it was fortunate. Kinetic
energy may really be transformed from molar to molecular motion, and
suffer no variation. It is conserved. On the other hand, it may not. It
may altogether cease, and what becomes of conservation then?
The scientific formula which satisfies both the facts of the case and
our desire for conservation is well known.[13] Energy, we are taught,
is of two kinds: kinetic and potential energy—energy in act and energy
in possibility. Each may turn into the other, and is continually so
turning. Each, therefore, may vary in quantity, and does vary in
quantity. It is only their sum which is indestructible.
Few scientific generalisations have been more fruitful; few have been
accepted on more slender evidence; none are more certain; none more
clearly illustrate our natural appetite for beliefs of conservation.
For, indeed, to the over-critical this sort of conservation must needs
leave something to be desired. When we assert the indestructibility of
matter we mean that a real entity continues through time unchanged in
quantity. But the word has a less obvious meaning when it is applied
to energy. The propriety of describing motion as energy seems indeed
clear enough; and if all energy were energy of motion, and if energy of
motion were always conserved, the conservation of energy would be on
all fours with the conservation of matter. But this is not the case.
In spite of Leibnitz, the amount of _vis viva_ is not indestructible.
What, then, happens when some of it is destroyed? In that case, says
science, energy changes its form but not its quantity. Energy of
motion becomes energy of position. What was kinetic becomes potential;
and, as the transformation is effected without loss, the principle of
conservation is saved.
When, however, energy thus becomes potential, in what sense does it
still exist, and why do we still call it energy? Energy suggests
“doings” and “happenings.” In the case of “potential” energy there are
no “doings” and no “happenings.” It is “stored”; and stored it may for
ever remain, hibernating (as it were) to all eternity, neither changing
nor causing change.
I do not quarrel with this; but I ask myself why “energy” should be
treated more leniently than “force.” Though force is now known not to
be “conserved,” ordinary thought attributes to it a certain continuity
of existence even when it does not show itself in motion. Force may be
exerted though nothing moves; as, for example, by a book pressing on a
table. But this view is profoundly unsatisfactory to many scientific
thinkers. For them force is nothing apart from “acceleration”; it
does not represent a cause, it only measures an effect. And if
in our ordinary moments we think otherwise, this (they think) is
simply because we illegitimately attribute to matter something which
corresponds to muscular effort in man.
It is not, perhaps, so easy as these critics suppose to extrude from
scientific thought (I say nothing of scientific language) this notion
of latent force—force which would produce movement if it could; and is
actively, though imperceptibly, striving to show itself in motion. But
why should they try? They welcome potential energy—why should they
anathematise latent force?
I think the answer is to be found in the fact that, whether force has,
or has not, any being apart from acceleration, it is certainly _not_
conserved; while, if energy be as real when it is potential as when it
is kinetic, it certainly _is_ conserved. A lapse into anthropomorphism,
therefore, is without excuse in the first case, while a lapse into
metaphysics is justified in the second. Any heresy may be forgiven, and
any evidence is worth respectful attention when conservation is the
thing to be proved.
I have sometimes amused myself by wondering what would have happened
about the year 1842 if the conservation of energy had been a
theological dogma instead of a scientific guess. Descartes, as I
mentioned just now, inferred the conservation of motion from the
attributes of God. Colding and Joule used the same argument in favour
of the conservation of energy. Now, if a belief in the conservation of
energy had been an integral part of religious orthodoxy in the early
forties of the last century surely some positivist philosopher would
have used Joule’s first investigation on Work and Heat to upset the
very dogma they were intended to establish. “Here” (he would have
said) “you have a believer in these metaphysico-theological methods
of discovering the laws of nature; and mark what happens. In true
medieval fashion he begins with some fanciful deductions from the
way in which he thinks God must have made the world. Fortunately,
however, though his principles are medieval, his methods are modern.
Not only is he a most brilliant experimenter, but he has the courage
to put his own speculations to an experimental test. He takes the
minutest precautions, he chooses the most favourable conditions, and
what happens? Does he prove his case? Do his results square with
his theories? Does he find a fixed relation between work and heat?
Does he justify his views of God? Not at all. Between his lowest
determination of the mechanical equivalent of heat, and his highest,
there is an immense and lamentable gap. What does he do? He takes their
mean value:—a very proper method if he knew there _was_ a mechanical
equivalent of heat; a very improper method if the reality of such an
equivalent was the thing to be proved. Clearly, if he had not put his
theological opinions into his scientific premises when he began his
experiment, he never would have got them out again as scientific
conclusions when he had reached its end.”
For my own part, I think this imaginary critic would, at that date,
have had something to say for himself—supposing always we are prepared
to accept his presuppositions about scientific method. If sound
reason and intellectual integrity require us to follow the lead of
observation and experiment with no antecedent preference for one class
of conclusions rather than another, then no doubt Joule and a long line
of distinguished predecessors were the spoilt children of fortune. They
made their discoveries in advance of their evidence, and in spite of
their methods. If they turned out to be right, or, at least, on the
right road, what can we do but criticise their credulity and wonder at
their luck? unless, indeed, their luck be a form of inspiration.
Before leaving beliefs of conservation, I must say one more word
about the most famous of them all—the belief in the conservation of
matter. This was an important article in the scientific creed of the
early atomists, who had no better evidence for it than they had for
the Atomic Theory itself. The material “substance” of the medieval
Aristotelians was, I imagine, also conserved; though as all that could
be known about it were its qualities, and as these were not necessarily
conserved, the doctrine in practice did not, perhaps, amount to
much. Then came the theory which, chiefly in the hands of Boyle[14]
at the end of the seventeenth century, initiated modern chemistry.
What was conserved, according to this view, was not a metaphysical
substance with detachable qualities, but elementary kinds of matter
with inseparable qualities; and out of these qualified entities was
compounded the whole material universe. I may incidentally observe
that a company promoter who should issue a prospectus based on no
better evidence than Boyle could advance for this tremendous theory
would certainly be in peril of the law. Yet Boyle was right: and,
notwithstanding subsequent developments, his conjecture remains the
corner-stone of modern chemical research.
Now, what is it that we intend to assert when we say that matter is
conserved, or is indestructible? We certainly do not mean that its
qualities never suffer change: for most of those which are obvious
and striking are always liable to change. If you sufficiently
vary temperature or pressure; if you effect chemical composition
or decomposition, the old characteristics will vanish and new
characteristics will take their place. What, then, is conserved?
In the first place, the lost qualities can (in theory) always be
restored, though not always without the expenditure of energy. Water
never ceases to be convertible into steam, nor steam into water. The
characteristics may vanish, but in appropriate conditions they will
always reappear.
Now science, as we have just seen, is tolerant of this notion of
latency or potentiality, and is ready enough to use it in aid of
beliefs in conservation. It was so used in connection with heat when
heat was regarded as a material substance. It is still so used in
connection with energy, which is sometimes described as an immaterial
substance. But (as I have already noted) it has never been so used
in connection with matter. The reason, I suppose, is that the
conservation of matter is much more a belief of common sense than the
conservation of energy. Energy is a conception which has but recently
been disengaged from other conceptions, like force and momentum, and
has but recently been associated with heat, with chemical reactions,
with changes of physical phase, and with electro-magnetic phenomena.
It is, therefore, a remote and somewhat abstract product of scientific
reflection; and science may do what it will with its own.
The notion of matter, on the other hand, is the common possession of
mankind. Whatever difficulties it may present to reflective analysis,
it presents none to our work-a-day beliefs. We are quite ready to
regard it as indestructible; but we are not ready to combine this
conviction with the view that it possesses no single characteristic
which may not be temporarily etherealised into a “potentiality.” On
such terms the eternal and unchanging identity of this or that parcel
of matter would seem a difficult and elusive doctrine, inappropriate
to the familiar and substantial world in which we suppose ourselves to
live. A belief in the conservation of matter has therefore always, or
almost always, carried with it a belief in the unchanging continuity of
at least _some_ material qualities; though as to what these qualities
are there has been much dispute.
Descartes, though not consistent, found unchanging continuity in the
attribute of size; so also did Hobbes. I presume that the older
atomists, who explained the appearances of matter by the shape of its
constituent atoms, would have regarded both atomic form and atomic
magnitude as persistent. But it was the assumption that the same piece
of ponderable matter always possessed the same gravitating power, and
that the same gravitating power was always associated with the same
mass, which, in the hands of Lavoisier, made so great a revolution in
eighteenth-century chemistry. Matter might change its size, its shape,
its colour, its phase, its power of acting and reacting; but its mass
and the quality which caused its weight it could not change; these
characteristics were always associated with each other, and were never
in abeyance.
To Lavoisier this double principle seemed self-evident. It was not
a hypothesis that required testing, but a touchstone by which other
hypotheses might safely be tested. If, in the course of some chemical
operation, weight increased, then no further proof was required to show
that mass had increased also, and that matter had been added. If, on
the other hand, weight diminished, then no further proof was required
to show that mass had diminished also, and that matter had been
subtracted. Whatever other qualities matter might gain or lose, mass
and gravity were indestructible and unchanging.
Men of science seemed, on the whole, content silently to assume these
principles of conservation without inconveniently raising the question
of evidence. Philosophers have not always been so cautious. Kant
supposed himself to have demonstrated them _a priori_. Schopenhauer
followed suit. Spencer declared their contraries to be inconceivable.
Mill said they were proved by experience. In short, all these eminent
thinkers vied with each other in conferring upon this doctrine the
highest honours permitted by their respective philosophies. But
apparently they were hasty. Recent discoveries have changed our point
of view. Mass (it seems) is no longer to be regarded as unchanging.
When bodies move at speeds approaching the velocity of light their
mass rapidly increases; so that this quality, which is peculiarly
characteristic of matter, must be removed from the category of those
which persist unchanged, and placed in the category of those which
change but can always be restored. Are we so to class gravitation?
Would the weight of a body moving nearly at the speed of light increase
as, in like circumstances, its inertia increases? If the answer is
“no,” then the link is broken which has for long been thought to
connect gravity and mass. If the answer is “yes,” then what Kant
regarded as certain _a priori_ is false; what Spencer regarded as
“inconceivable” is true; another carrier of “persistence” is lost, and
some fresh characteristic must be found which will remain unchanged
through all time, and under all conditions.
If this characteristic should turn out to be electric charge, what
a curious light it will throw upon our tendency to “beliefs of
conservation”[15]. After long seeking for some indestructible attribute
of matter; after taking up and rejecting size, shape, weight, mass,
and (perhaps) impenetrability, we shall at last find the object of our
quest in a conception which has (I suppose) been clearly realised only
within the last hundred years, about which our senses tell us nothing,
and of which the general run of educated mankind are still completely
ignorant!
III
It is possible, but not, I hope, probable, that some hasty reader may
suppose that in this and the preceding lectures I am recommending a
new method or instrument of discovery. “If you want to reach truth,
follow your unreasoned inclination,” may be his summary of my doctrine:
brief—but also unjust.
Of the manner in which discoveries are going to be made I say nothing,
for I know nothing. I am dealing with the past: and in the historic
movements of scientific thought I see, or think I see, drifts and
currents such as astronomers detect among the stars of heaven. And,
as the law of gravitation will hardly (I suppose) explain the last,
so observation, experiment, and reasoning will hardly explain the
first. They belong to the causal, not to the cognitive, series; and the
beliefs in which they issue are effects rather than conclusions.
Those who feel little sympathy for such a view may be inclined to
regard the relatively faint inclinations dealt with in this lecture
as ordinary scientific hypotheses confirmed by ordinary scientific
methods. This view, as I have already observed, is not applicable
to the inevitable beliefs dealt with in earlier lectures. Whatever
philosophers may say after the event the conviction that we live in an
external world of things and persons, where events are more or less
regularly repeated, has never been treated as a speculative conjecture
about which doubt was a duty till truth was proved. Beliefs like these
are not scientific hypotheses, but scientific presuppositions, and all
criticism of their validity is a speculative after-thought. The same
may be said, though with less emphasis and some qualification, about
beliefs fostered by the intellectual tendencies considered in this
chapter. These, as we have seen, are many. They are often inconsistent;
they are never inevitable; and they perpetually change their form under
the pressure of scientific discovery. Atomism in one shape follows
atomism in another; doctrines of conservation rise, fall, and rise
again; incredulity about “action at a distance” breeds explanations
whose failure (in the case of gravity) leaves the hope of final success
untouched.
Now, it would be an error to say that science does not, when it can,
apply to these various theories its ordinary methods of verification.
They are in a different position from inevitable beliefs, which can
hardly be verified because the process of verification assumes them.
Yet they must not be confounded with ordinary scientific hypotheses,
for they are something more and something different. Like these, they
are guesses, but they are guesses directed, not by the immediate
suggestion of particular experiences (which indeed they sometimes
contradict), but by general tendencies which are enduring though
sometimes feeble. Those who make them do not attempt the interrogation
of Nature wholly free from certain forms of bias. In cross-examining
that most stubborn and recalcitrant of witnesses they never hesitate
to ply her with leading questions; and, whether this procedure be
logically defensible or not, no lover of truth need regret its results.
Readers of M. Bergson’s “Creative Evolution” may remember the picture
he draws of the _élan vital_—the principle of life—forcing its way
along different paths of organic evolution, some without issue or
promise of progress; others leading on through regions hitherto
untraversed to ends remote and unforeseen. The secular movements of
science, as I conceive them, somewhat resemble this process, even
though it be faintly and at a distance. There is in both a striving
towards some imperfectly foreshadowed end; and in both the advance is
irregular, tentative, precarious, with many changes of direction, and
some reversals. Yet I would not press the parallel over-far or plunge
too deeply into metaphor. It is enough to say that as, according to M.
Bergson, the course followed by organic evolution cannot be wholly due
to Selection, so the course followed by scientific discovery, as I read
its history, cannot be wholly due to reasoning and experience. In both
cases we seem forced to assume something in the nature of a directing
influence, and (as I should add, though perhaps M. Bergson would
not) of supramundane design. And if “a Power that makes for truth”
be required to justify our scientific faith, we must surely count
ourselves as theists.
NOTE
_Extracts from a letter from Sir Oliver Lodge on certain passages in
this lecture relating to Energy and its transformations._
* * * * *
You say, on page 226, “Energy, we are taught, is of two kinds: kinetic
and potential energy—energy in act and energy in possibility.”
So long as emphasis is laid upon the words “we are taught,” I have
no objection. People _have_ taught that, though I strongly object to
such teaching, because I object to the idea “Energy in possibility” or
“possible Energy” of any kind. I teach the identity of Energy in much
the same terms as the identity of Matter; not merely the conservation,
with the idea that one quantity can disappear and another quantity
reappear. It is not another quantity, but the same; though it may
have been locked up for any length of time. But then it has not been
usually taught so, and I think you are dealing with what is usual.
* * * * *
Again, you say on page 227, “Energy suggests ‘doings’ and
‘happenings.’” No, say I, _activity_ suggests doings and happenings,
and activity is Energy in transformation. Energy alone is something
stored, like Capital. The earth’s rotational energy, for instance, is
stored just as really as, and for a longer time than, the vegetation
of the carboniferous epoch.
Lower down you observe that “Force may be exerted though nothing
moves.” Certainly it may, when resisted by an equal opposite force.
But I fully admit that a lot of nonsense has been talked about the
acceleration measure of force, as if it were the only measure, and
that some criticism on this procedure is useful. But I should not
speak of “latent” force; it is real force you have in mind, or at
least real stress—_i.e._ two equal and opposite forces. It is latent
Activity which becomes active when the other factor, viz. Motion,
is supplied or allowed—_e.g._ by the release of a bent bow, or a
wound-up spring, or a raised weight.
So it is also with the Energy of a fly-wheel. That, too, is latent
Activity until the other factor, viz. Force, is supplied, _i.e._
when it is employed to overcome resistance, and therefore do work.
Otherwise its Motion will be stored to all eternity.
In short, activity, or doing of work, has two factors, Force and
Motion. When both are present, work is done; when either is present
alone, Energy is stored. Static Energy is the Force factor, with the
possibility of a certain range of effectiveness understood; like a
head of water, for instance, a certain height above the sea. Kinetic
Energy is the Motion factor, with a certain inertia or possibility of
Force understood; not Motion alone, but a mass in motion, so that it
may be able to overcome resistance.
There is no real reason why one form of Energy should be considered
more “actual” or real than another; our eyes appreciate the one form,
our muscles could appreciate the other.
* * * * *
In considering cases of Potential Energy, it is wise to realise that
our knowledge about Gravitation is altogether too vague to make the
case of a raised weight useful. And our knowledge of solid elasticity,
though not so insignificant, is small enough to make the case of a
bent bow or wound spring not very easy for fundamental contemplation.
A case of chemical Energy, like gun-cotton, is in much the same
predicament.
But a typical and satisfactory example of Potential Energy is the
case of a vessel of compressed air. Here is Energy stagnant enough,
and violent enough when released, and one that can be locked up
apparently to all eternity, and yet released by the pulling of a
trigger. It represents, however, a case of which we know something
concerning the internal mechanism; and we have learnt that in this
case the force statically exerted on the walls of a vessel is really
a kinetic bombardment of the molecules. In other words, we recognise
in this case that Potential Energy is ultimately resolvable into
Kinetic. It may be so in the other cases. And on Kelvin’s Kinetic
Theory of Elasticity, which he showed a tendency in later life to
abandon, all strain or stress in Ether may be ultimately due to its
ultramicroscopic vortex circulation.
But none of this is yet proven.
* * * * *
The general argument of your lecture deals with the ease with which
certain general propositions are accepted as it were intuitively,
without real conclusive evidence. I am entirely with you. And the way
we feel secure about general laws, when adequate evidence for them is
really impossible, has often struck me as remarkable. Even when facts
appear to go against them, we question the facts, and find after all
that in so doing we have been right.
FOOTNOTES:
[12] See Lecture VI.
[13] See note at the end of the Lecture.
[14] I got this view of Boyle’s relation to modern chemistry from
Ostwald’s work.
[15] In this chapter, especially in that part of it which deals with
beliefs of conservation, I am greatly indebted to Meyerson’s “Identité
et Réalité.” This acute and learned work is not written from the
same point of view as that which I have adopted; but this in no way
diminishes the amount of my obligation to its author.