Lessons From the History of Science 1896
1.43-125 G-c.1896-3
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LESSONS FROM THE HISTORY OF SCIENCE*
# 1. THE SCIENTIFIC ATTITUDE
43. If we endeavor to form our conceptions upon history
and life, we remark three classes of men. The first consists of
those for whom the chief thing is the qualities of feelings.
These men create art. The second consists of the practical
men, who carry on the business of the world. They respect
nothing but power, and respect power only so far as it [is]
exercized. The third class consists of men to whom nothing seems
great but reason. If force interests them, it is not in its
exertion, but in that it has a reason and a law. For men of the first
class, nature is a picture; for men of the second class, it is an
opportunity; for men of the third class, it is a cosmos, so
admirable, that to penetrate to its ways seems to them the
only thing that makes life worth living. These are the men
whom we see possessed by a passion to learn, just as other men
have a passion to teach and to disseminate their influence. If
they do not give themselves over completely to their passion to
learn, it is because they exercise self-control. Those are the
natural scientific men; and they are the only men that have any
real success in scientific research.
44. If we are to define science, not in the sense of stuffing
it into an artificial pigeon-hole where it may be found again by
some insignificant mark, but in the sense of characterizing it as
a living historic entity, we must conceive it as that about
which such men as I have described busy themselves. As such,
it does not consist so much in knowing, nor even in "organized
knowledge," as it does in diligent inquiry into truth for
truth's sake, without any sort of axe to grind, nor for the sake
of the delight of contemplating it, but from an impulse to
penetrate into the reason of things. This is the sense in which
* A manuscnpt of notes for a projected, but never completed, History of Scicnce,
c. 1896. |p20
this book is entitled a History of Science. Science and
philosophy seem to have been changed in their cradles. For it is not
knowing, but the love of learning, that characterizes the
scientific man; while the " philosopher " is a man with a system
which he thinks embodies all that is best worth knowing. If a
man burns to learn and sets himself to comparing his ideas
with experimental results in order that he may correct those
ideas, every scientific man will recognize him as a brother, no
matter how small his knowledge may be.
45. But if a man occupies himself with investigating the
truth of some question for some ulterior purpose, such as to
make money, or to amend his life, or to benefit his fellows, he
may be ever so much better than a scientific man, if you will
-- to discuss that would be aside from the question -- but he
is not a scientific man. For example, there are numbers of
chemists who occupy themselves exclusively with the study of
dyestuffs. They discover facts that are useful to scientific
chemistry; but they do not rank as genuine scientific men.
The genuine scientific chemist cares just as much to learn
about erbium -- the extreme rarity of which renders it
commercially unimportant -- as he does about iron. He is more
eager to learn about erbium if the knowledge of it would do
more to complete his conception of the Periodic Law, which
expresses the mutual relations of the elements.
# 2. THE SCIENTIFIC IMAGINATION
46. When a man desires ardently to know the truth, his
first effort will be to imagine what that truth can be. He
cannot prosecute his pursuit long without finding that imagination
unbridled is sure to carry him off the track. Yet nevertheless,
it remains true that there is, after all, nothing but imagination
that can ever supply him an inkling of the truth. He can stare
stupidly at phenomena; but in the absence of imagination they
will not connect themselves together in any rational way. Just
as for Peter Bell a cowslip was nothing but a cowslip, so for
thousands of men a falling apple was nothing but a falling
apple; and to compare it to the moon would by them be
deemed " fanciful. "
47. It is not too much to say that next after the passion to
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learn there is no quality so indispensable to the successful
prosecution of science as imagination. Find me a people whose
early medicine is not mixed up with magic and incantations,
and I will find you a people devoid of all scientific ability.
There is no magic in the medical Papyrus Ebers. The stolid
Egyptian saw nothing in disease but derangement of the
affected organ. There never was any true Egyptian science.
48. There are, no doubt, kinds of imagination of no value
in science, mere artistic imagination, mere dreaming of
opportunities for gain. The scientific imagination dreams of
explanations and laws.
# 3. SCIENCE AND MORALITY
49. A scientific man must be single-minded and sincere
with himself. Otherwise, his love of truth will melt away, at
once. He can, therefore, hardly be otherwise than an honest,
fair-minded man. True, a few naturalists have been accused of
purloining specimens; and some men have been far from
judicial in advocating their theories. Both of these faults must
be exceedingly deleterious to their scientific ability. But on the
whole, scientific men have been the best of men. It is quite
natural, therefore, that a young man who might develope into
a scientific man should be a well-conducted person.
50. Yet in more ways than one an exaggerated regard for
morality is unfavorable to scientific progress. I shall present
only one of those ways. It will no doubt shock some persons
that I should speak of morality as involving an element which
can become bad. To them good conduct and moral conduct
are one and the same -- and they will accuse me of hostility
to morality. I regard morality as highly necessary; but it
is a means to good life, not necessarily coextensive with good
conduct. Morality consists in the folklore of right conduct.
A man is brought up to think he ought to behave in certain
ways. If he behaves otherwise, he is uncomfortable. His
conscience pricks him. That system of morals is the
traditional wisdom of ages of experience. If a man cuts loose from
it, he will become the victim of his passions. It is not safe for
him even to reason about it, except in a purely speculative
way. Hence, morality is essentially conservative. Good
morals and good manners are identical, except that tradition
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attaches less importance to the latter. The gentleman is
imbued with conservatism. This conservatism is a habit, and it
is the law of habit that it tends to spread and extend itself over
more and more of the life. In this way, conservatism about
morals leads to conservatism about manners and finally
conservatism about opinions of a speculative kind. Besides, to
distinguish between speculative and practical opinions is the
mark of the most cultivated intellects. Go down below this
level and you come across reformers and rationalists at every
turn -- people who propose to remodel the ten
commandments on modern science. Hence it is that morality leads to
a conservatism which any new view, or even any free inquiry,
no matter how purely speculative, shocks. The whole moral
weight of such a community will be cast against science. To
inquire into nature is for a Turk very unbecoming to a good
Moslem; just as the family of Tycho Brahe regarded his
pursuit of astronomy as unbecoming to a nobleman. (See Thomas
Nash in Pierce Pennilesse for the character of a Danish
nobleman.)
51. This tendency is necessarily greatly exaggerated in a
country when the "gentleman," or recognized exponent of
good manners, is appointed to that place as the most learned
man. For then the inquiring spirit cannot say the gentlemen
are a lot of ignorant fools. To the moral weight cast against
progress in science is added the weight of superior learning.
Wherever there is a large class of academic professors who are
provided with good incomes and looked up to as gentlemen,
scientific inquiry must languish. Wherever the bureaucrats
are the more learned class, the case will be still worse.
# 4. MATHEMATICS
52. The first questions which men ask about the universe
are naturally the most general and abstract ones. Nor is it
true, as has so often been asserted, that these are the most
difficult questions to answer. Francis Bacon is largely
responsible for this error, he having represented -- having
nothing but his imagination and no acquaintance with actual science
to draw upon -- that the most general inductions must be
reached by successive steps. History does not at all bear out
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that theory. The errors about very general questions have
been due to a circumstance which I proceed to set forth.
53. The most abstract of all the sciences is mathematics.
That this is so, has been made manifest in our day; because
all mathematicians now see clearly that mathematics is only
busied about purely hypothetical questions. As for what the
truth of existence may be the mathematician does not (qua
mathematician) care a straw. It is true that early
mathematicians could not clearly see that this was so. But for all their
not seeing it, it was just as true of the mathematics of early
days as of our own. The early mathematician might perhaps
be more inclined to assert roundly that two straight lines in a
plane cut by a third so as to make the sum of the internal
angles on one side less than two right angles would meet at
some finite distance on that side if sufficiently produced;
although, as a matter of fact, we observe no such tendency in
Euclid. But however that may have been, the early
mathematician had certainly no more tendency than the modern to
inquire into the truth of that postulate; but quite the reverse.
What he really did, therefore, was merely to deduce
consequences of unsupported assumptions, whether he recognized
that this was the nature of his business or not. Mathematics,
then, really was, for him as for us, the most abstract of the
sciences, cut off from all inquiry into existential truth.
Consequently, the tendency to attack the most abstract problems
first, not because they were recognized as such, but because such
they were, led to mathematics being the earliest field of inquiry.
54. We find some peoples drawn more toward arithmetic;
others more toward geometry. But in either case, a correct
method of reasoning was sure to be reached before many
centuries of real inquiry had elapsed. The reasoning would be at
first awkward, and one case would be needlessly split up into
several. But still all influences were pressing the reasoner to
make use of a diagram, and as soon as he did that he was
pursuing the correct method. For mathematical reasoning
consists in constructing a diagram according to a general precept,
in observing certain relations between parts of that diagram
not explicitly required by the precept, showing that these
relations will hold for all such diagrams, and in formulating this
conclusion in general terms. All valid necessary reasoning is in
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fact thus diagrammatic.* This, however, is far from being
obviously tme. There was nothing to draw the attention of the
early reasoners to the need of a diagram in such reasoning.
Finding that by their inward meditations they could deduce
the truth concerning, for example, the height of an inaccessible
pillar, they naturally concluded the same method could be
applied to positive inquiries.
In this way, early success in mathematics would naturally
lead to bad methods in the positive sciences, and especially in
metaphysics.
# 5. SCIENCE AS A GUIDE TO CONDUCT
55. We have seen how success in mathematics would
necessarily create a confidence altogether unfounded in man's power
of eliciting truth by inward meditation without any aid from
experience. Both its confidence in what is within and the
absolute certainty of its conclusions lead to the confusion of a
priori reason with conscience. For conscience, also, refuses to
submit its dicta to experiment, and makes an absolute dual
distinction between right and wrong. One result of this is that
men begin to rationalize about questions of purity and
integrity, which in the long run, through moral decay, is unfavorable
to science. But what is worse, from our point of view, they
begin to look upon science as a guide to conduct, that is, no
longer as pure science but as an instrument for a practical end.
One result of this is that all probable reasoning is despised. If
a proposition is to be applied to action, it has to be embraced,
or believed without reservation. There is no room for doubt,
which can only paralyze action. But the scientific spirit
requires a man to be at all times ready to dump his whole
cart-load of beliefs, the moment experience is against them. The
desire to learn forbids him to be perfectly cocksure that he
knows already. Besides positive science can only rest on
experience; and experience can never result in absolute certainty,
exactitude, necessity, or universality. But it is precisely with
the universal and necessary, that is, with Law, that [con]science
concerns itself. Thus the real character of science is destroyed
as soon as it is made an adjunct to conduct; and especially all
progress in the inductive sciences is brought to a standstill.
* See 66, 240, 369 and vol. 4, bk. II.
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# 6. MORALITY AND SHAM REASONING
56. The effect of mixing speculative inquiry with questions
of conduct results finally in a sort of half make-believe
reasoning which deceives itself in regard to its real character.
Conscience really belongs to the subconscious man, to that part of
the soul which is hardly distinct in different individuals, a sort
of community-consciousness, or public spirit, not absolutely
one and the same in different citizens, and yet not by any
means independent in them. Conscience has been created by
experience just as any knowledge is; but it is modified by
further experience only with secular* slowness.
57. When men begin to rationalize about their conduct,
the first effect is to deliver them over to their passions and
produce the most frightful demoralization, especially in sexual
matters. Thus, among the Greeks, it brought about pederasty
and a precedence of public women over private wives. But
ultimately the subconscious part of the soul, being stronger,
regains its predominance and insists on setting matters right.
Men, then, continue to tell themselves they regulate their
conduct by reason; but they learn to look forward and see what
conclusions a given method will lead to before they give their
adhesion to it. In short, it is no longer the reasoning which
determines what the conclusion shall be, but it is the conclusion
which determines what the reasoning shall be. This is sham
reasoning. In short, as morality supposes self-control, men
learn that they must not surrender themselves unreservedly to
any method, without considering to what conclusions it will
lead them. But this is utterly contrary to the single-mindedness
that is requisite in science. In order that science may be
successful, its votaries must hasten to surrender themselves at
discretion to experimental inquiry, in advance of knowing what
its decisions may be. There must be no reservations.
58. The effect of this shamming is that men come to look
upon reasoning as mainly decorative, or at most, as a secondary
aid in minor matters -- a view not altogether unjust, if
questions of conduct are alone to interest us. They, therefore,
demand that it shall be plain and facile. If, in special cases,
complicated reasoning is indispensable, they hire a specialist to
perform it. The result of this state of things is, of course, a rapid
* On this use of "secular" see 176.
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deterioration of intellectual vigor, very perceptible from one
generation to the next. This is just what is taking place among
us before our eyes; and to judge from the history of
Constantinople, it is likely to go on until the race comes to a
despicable end.
# 7. THE METHOD OF AUTHORITY
59. When society is broken into bands, now warring, now
allied, now for a time subordinated one to another, man loses
his conceptions of truth and of reason. If he sees one man
assert what another denies, he will, if he is concerned, choose
his side and set to work by all means in his power to silence his
adversaries. The truth for him is that for which he fights.
60. The next step which is to be expected in a logical
development not interrupted by accidental occurrences will consist
in the recognition that a central authority ought to deterrnine
the beliefs of the entire community. As far as morals and
religion go, this plan admirably fulfills its purpose of producing
uniformity. But in order that it may do this, it is desirable
that there should be another less absolute authority which
shall dedare, not infallibly but yet with a weight of collective
learning, the propositions which science from time to time puts
out of reasonable doubt, and which shall aid the researches of
competent investigators. The value of such services in the
development of science is immense; though they are
accompanied by very serious disadvantages in not allowing to
unofficial studies the weight which ought to be accorded to them.
The history of science is full of examples of this sort.
# 8. SCIENCE AND CONTINUITY
61. One of the worst effects of the influence of moral and
religious reasonings upon science lies in this, that the
distinctions upon which both insist as fundamental are dual
distinctions, and that their tendency is toward an ignoring of all
distinctions that are not dual and especially of the conception
of continuity. Religion recognizes the saints and the damned.
It will not readily admit any third fate. Morality insists that
a motive is either good or bad. That the gulf between them is
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bridged over and that most motives are somewhere near the
middle of the bridge, is quite contrary to the teachings of any
moral system which ever lived in the hearts and consciences of
a people.
62. It is not necessary to read far in almost any work of
philosophy written by a man whose training is that of a
theologian, in order to see how helpless such minds are in
attempting to deal with continuity. Now continuity, it is not too much
to say, is the leading conception of science. The complexity of
the conception of continuity is so great as to render it
important wherever it occurs. Now it enters into every fundamental
and exact law of physics or of psychics that is known. The
few laws of chemistry which do not involve continuity seem
for the most part to be very roughly true. It seems not
unlikely that if the veritable laws were known continuity would
be found to be involved in them....*
# 9. THE ANALYTIC METHOD
63. The first problems to suggest themselves to the
inquirer into nature are far too complex and difficult for any
early solution, even if any satisfactorily secure conclusion can
ever be drawn concerning them. What ought to be done,
therefore, and what in fact is done, is at first to substitute for
those problems others much simpler, much more abstract, of
which there is a good prospect of finding probable solutions.
Then, the reasonably certain solutions of these last problems
will throw a light more or less clear upon more concrete
problems which are in certain respects more interesting.
64. This method of procedure is that Analytic Method to
which modern physics owes all its triumphs. It has been
applied with great success in psychical sciences also. (Thus,
the classical political economists, especially Ricardo, pursued
this method.) ** It is reprobated by the whole Hegelian army,
who think it ought to be replaced by the " Historic Method, "
which studies complex problems in all their complexity, but
which cannot boast any distinguished successes.
* See vol. 6, bk. I
** Cf. 4.115.
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# 10. KINDS OF REASONING*
65. There are in science three fundamentally different
kinds of reasoning, Deduction (called by Aristotle {...}
or {...} ), Induction (Aristotle's and Plato's {...})
and Retroduction (Aristotle's {...}, but misunderstood
because of corrupt text, and as misunderstood usually
translated abduction). ** Besides these three, Analogy (Aristotle's
{...}) combines the characters of Induction and
Retroduction.
66. Deduction is that mode of reasoning which examines
the state of things asserted in the premisses, forms a diagram
of that state of things, perceives in the parts of that diagram
relations not explicitly mentioned in the premisses, satisfies
itself by mental experiments upon the diagram that these
relations would always subsist, or at least would do so in a
certain proportion of cases, and concludes their necessary, or
probable, truth. For example, let the premiss be that there are
four marked points upon a line which has neither extremity nor
furcation. Then, by means of a diagram,
{DIAGRAM}
we may conclude that there are two pairs of points such that
in passing along the line in any way from one to the other
point of either pair, one point of the second pair will be passed
an odd number of times and the other point an even (or zero)
number of times. This is deduction.
67. Induction is that mode of reasoning which adopts a
conclusion as approximate, because it results from a method of
inference which must generally lead to the truth in the long
run. For example, a ship enters port laden with coffee. I go
aboard and sample the coffee. Perhaps I do not examine over
a hundred beans, but they have been taken from the middle,
top, and bottom of bags in every part of the hold. I conclude
by induction that the whole cargo has approximately the same
value per bean as the hundred beans of my sample. All that
induction can do is to ascertain the value of a ratio.
* Cf. vol. 2, bk. III.
** Peirce usually calls it abduction; sometimes hypothesis.
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68. Retroduction is the provisional adoption of a
hypothesis, because every possible consequence of it is capable of
experimental verification, so that the persevering application of
the same method may be expected to revea,. its disagreement
with facts, if it does so disagree. For example, all the
operations of chemistry fail to decompose hydrogen, lithium,
glucinum, boron, carbon, nitrogen, oxygen, fluorine, sodium,...
gold, mercury, thallium, lead, bismuth, thorium, and uranium.
We provisionally suppose these bodies to be simple; for if not,
similar experimentation will detect their compound nature, if
it can be detected at all. That I term retroduction.
69. Analogy is the inference that a not very large collection
of objects which agree in various respects may very likely
agree in another respect. For instance, the earth and Mars
agree in so many respects that it seems not unlikely they may
agree in being inhabited.
70. The methods of reasoning of science have been studied
in various ways and with results which disagree in important
particulars. The followers of Laplace treat the subject from
the point of view of the theory of probabilities. After
corrections due to Boole* and others ** that method yields
substantially the results stated above. Whewell *** described the
reasoning just as it appeared to a man deeply conversant with several
branches of science as only a genuine researcher can know
them, and adding to that knowledge a full acquaintance with
the history of science. These results, as might be expected, are
of the highest value, although there are important distinctions
and reasons which he overlooked. John Stuart Mill endeavored
to explain the reasonings of science by the nominalistic
metaphysics of his father. The superficial perspicuity of that kind
of metaphysics rendered his logic extremely popular with
those who think, but do not think profoundly; who know
something of science, but more from the outside than the
inside, and who for one reason or another delight in the
simplest theories even if they fail to cover the facts.
71. Mill denies that there was any reasoning in Kepler's
* Laws of Thought, chs. 16-21.
** Including C. S. Peirce. See Paper No. 1, vol. 3.
*** The Philosophy of the Inductive Sciences, 1890.
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procedure. He says it is merely a description of the facts.* He
seems to imagine that Kepler had all the places of Mars in
space given him by Tycho's observations; and that all he did
was to generalize and so obtain a general expression for them.
Even had that been all, it would certainly have been inference.
Had Mill had even so much practical acquaintance with
astronomy as to have practised discussions of the motions of
double stars, he would have seen that. But so to characterize
Kepler's work is to betray total ignorance of it. Mill certainly
never read the De Motu [Motibus] Stellae Martis, which is not
easy reading. The reason it is not easy is that it calls for the
most vigorous exercise of all the powers of reasoning from
beginning to end.
72. What Kepler had given was a large collection of
observations of the apparent places of Mars at different times. He
also knew that, in a general way, the Ptolemaic theory agrees
with the appearances, although there were various difficulties
in making it fit exactly. He was furthermore convinced that
the hypothesis of Copernicus ought to be accepted. Now this
hypothesis, as Copernicus himself understood its first outline,
merely modifies the theory of Ptolemy so far as [to] impart to
all the bodies of the solar system one common motion, just
what is required to annul the mean motion of the sun. It
would seem, therefore, at first sight, that it ought not to affect
the appearances at all. If Mill had called the work of
Copernicus mere description he would not have been so very f ar from
the truth as he was. But Kepler did not understand the matter
quite as Copernicus did. Because the sun was so near the
centre of the system, and was of vast size (even Kepler knew
its diameter must be at least fifteen times that of the earth),
Kepler, looking at the matter dynamically, thought it must
have something to do with causing the planets to move in their
orbits. This retroduction, vague as it was, cost great
intellectual labor, and was most important in its bearings upon all
Kepler's work. Now Kepler remarked that the lines of apsides
of the orbits of Mars and of the earth are not parallel; and he
utilized various observations most ingeniously to infer that
they probably intersected in the sun. Consequently, it must
be supposed that a general description of the motion would be
* Ibid., bk. III, Ch. 2, #3.
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simpler when referred to the sun as a fixed point of reference
than when referred to any other point. Thence it followed that
the proper times at which to take the observations of Mars for
deterrnining its orbit were when it appeared just opposite the
sun -- the true sun -- instead of when it was opposite the
mean sun, as had been the practice. Carrying out this idea, he
obtained a theory of Mars which satisfied the longitudes at all
the oppositions observed by Tycho and himself, thirteen in
number, to perfection. But unfortunately, it did not satisfy
the latitudes at all and was totally irreconcilable with
observations of Mars when far from opposition.
73. At each stage of his long investigation, Kepler has a
theory which is approximately true, since it approximately
satisfies the observations (that is, within 8', which is less than
any but Tycho's observations could decisively pronounce an
error), and he proceeds to modify this theory, after the most
careful and judicious reflection, in such a way as to render it
more rational or closer to the observed fact. Thus, having
found that the centre of the orbit bisects the eccentricity, he
finds in this an indication of the falsity of the theory of the
equant and substitutes, for this artificial device, the principle
of the equable description of areas. Subsequently, finding that
the planet moves faster at ninety degrees from its apsides than
it ought to do, the question is whether this is owing to an error
in the law of areas or to a compression of the orbit. He
ingeniously proves that the latter is the case.
74. Thus, never modifying his theory capriciously, but
always with a sound and rational motive for just the
modification he makes, it follows that when he finally reaches a
modification -- of most striking simplicity and rationality -- which
exactly satisfies the observations, it stands upon a totally
different logical footing from what it would if it had been struck
out at random, or the reader knows not how, and had been
found to satisfy the observation. Kepler shows his keen logical
sense in detailing the whole process by which he finally arrived
at the true orbit. This is the greatest piece of Retroductive
reasoning ever performed.
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# 11. THE STUDY OF THE USELESS
75....The old-fashioned political economist adored, as alone
capable of redeeming the human race, the glorious principle of
individual greed, although, as this principle requires for its
action hypocrisy and fraud, he generally threw in some dash
of inconsistent concessions to virtue, as a sop to the vulgar
Cerberus. But it is easy to see that the only kind of science
this principle would favor would be such as is immediately
remunerative with a great preference for such as can be kept
secret, like the modern sciences of dyeing and perfumery.
Kepler's discovery rendered Newton possible, and Newton
rendered modern physics possible, with the steam engine,
electricity, and all the other sources of the stupendous fortunes of
our age. But Kepler's discovery would not have been possible
without the doctrine of conics. Now contemporaries of Kepler
-- such penetrating minds as Descartes and Pascal -- were
abandoning the study of geometry (in which they included what
we now call the differential ca,culus, so far as that had at that
time any existence) because they said it was so UTTERLY
USELESS. There was the future of the human race almost
trembling in the balance; for had not the geometry of conic
sections already been worked out in large measure, and had their
opinion that only sciences apparently useful ought to be
pursued, [prevailed] the nineteenth century would have had none
of those characters which distinguish it from the ancien regime.
76. True science is distinctively the study of useless things.
For the useful things will get studied without the aid of
scientific men. To employ these rare minds on such work is like
running a steam engine by burning diamonds.
77. The University of Paris encouraged useless studies in
the most effective way possible, by training so many men as to
be almost sure of getting a large proportion of all the minds
that could be very serviceable in such studies. At the same
time, it provided a sure living not only for such as were really
successful, but even for those whose talents were of a somewhat
inferior kind. On the other hand, like all universities, it set up
an official standard of truth, and frowned on all who questioned
it. Just so, the German universities for a whole generation
turned the cold shoulder to every man who did not extol their
stale Hegelianism, until it became a stench in the nostrils of
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every man of common sense. Then the official fashion shifted,
and a Hegelian is today treated in Germany with the same
arrogant stupidity with which an anti-Hegelian formerly was.
Of course, so-called "universities," whose purpose is not the
solution of great problems, but merely the fitting of a selection
of young men to earn more money than their fellow citizens
not so favored, have for the interests of science none of the
vaiue of the medieval and German universities, although they
exercise the same baleful influence to about the same degree.
78. The small academies of continental Europe are
reasonably free from the gravest fault of the universities. Their
defect is that while they indirectly do much for their few
members they extend little aid to the younger men, except that of
giving a general tone of respectability to pure science.
79. The larger bodies give much less aid to individuals; but
they begin to aid them sooner. They have a distinct though
limited use when they are specialized, like the Union of
German chemists. But whether the Royal Society has been as
serviceable to science as the French Academie des Sciences may
be doubted.
# 12. IL LUME NATURALE
80. In examining the reasonings of those physicists who
gave to modern science the initial propulsion which has insured
its healthful life ever since, we are struck with the great,
though not absolutely decisive, weight they allowed to
instinctive judgments. Galileo appeals to il lume naturale at the most
critical stages of his reasoning. Kepler, Gilbert, and Harvey
-- not to speak of Copernicus -- substantially rely upon an
inward power, not sufficient to reach the truth by itself, but
yet supplying an essential factor to the inf,uences carrying
their minds to the truth.
81. It is certain that the only hope of retroductive
reasoning ever reaching the truth is that there may be some natural
tendency toward an agreement between the ideas which suggest
themselves to the human mind and those which are concemed
in the laws of nature.
|p34
# 13. GENERALIZATION AND ABSTRACTION
82. The most important operation of the mind is that of
generalization. There are some exceedingly difficult questions
of theoretical logic connected with generalization. On the
other hand, there are some valuable lessons which evade those
puzzles. If we look at any earlier work upon mathematics as
compared with a later one upon the same subject, that which
most astonishes us is to see the difficulty men had in first
seizing upon general conceptions which after we become a little
familiarized to them are quite matters of course. That an
Egyptian should have been able to think of adding one-fifth
and one-fifth, and yet should not have been content to call the
sum two-fifths, but must call it one-third plus one-fifteenth, as
if he could not conceive of a sum of fractions unless their
denominators were different, seems perverse stupidity. That decimals
should have been so slow in coming in, and that, when they did
come, the so-called decimal point should be written as if the
relation of units to tenths were somehow peculiar, while what
was logically called for was simply some mark attached to the
units place, so that instead of 3.14159 [what] should have been
written [was] ^314159, seems very surprising. That Descartes
should have thought it necessary to work problems in
analytical geometry four times over, according to the different
quadrants between the axes of coordinates in which the point to be
determined might occur, is astonishing. That which the early
mathematicians failed to see in all these cases was that some
feature which they were accustomed to insert into their
theorems was quite irrelevant and could perfectly well be omitted
without affecting in the slightest degree the cogency of any
step of the demonstrations.
83. Another operation closely allied to generalization is
abstraction; and the use of it is perhaps even more
characteristic of mathematical reasoning than is generalization. This
consists of seizing upon something which has been conceived
as {...}, a meaning not dwelt upon but through
which something else is discerned, and converting it into an
{...}, a meaning upon which we rest as the
principal subject of discourse. Thus, the mathematician conceives
an operation as something itself to be operated upon. He
conceives the collection of places of a moving particle as itself a
|p35
place which can at one instant be totally occupied by a
filament,which can again move, and the aggregate of all its places,
considered as possibly occupied in one instant, is a surface,
and so forth.
84. The intimate connection between generalization and
continuity is to be pointed out.*
# 14. THE EVALUATION OF EXACTITDE
85. For every line of scientific research there is in any given
stage of its development, an appropriate standard of certitude
and exactitude, such that it is useless to require more, and
unsatisfactory to have less. This is a part of the doctrine of the
Economy of Research. When Phoenix ** made his celebrated
survey of the route from San Francisco to the Mission of
Dolores, the distance required was the sum of two parts, one
of them resting on the guess of a driver, while the other was
determined at great expense to a transcendental precision. As
long as one part of the distance was extremely uncertain, there
was no use in spending much money in ascertaining the other
part precisely. For there is a relation between the value of an
increased certainty of an item of knowledge and the cost of
such increase of certainty, which enables us to determine
whether it is better to expend our genius, energy, time, and
money upon one investigation or upon another.
86. If a result is to be used merely to confirm the result of
an independent investigation, it may have a high value even
though its probability is not very high. But if it is only to be
used in combination with other results, very little will be gained
by increasing its probability far beyond the probabilities of
those others. Of course, knowledge that is to be put to special
purposes may need to be more precise than other knowledge.
Thus, it pays to determine the places of a thousand stars with
the utmost accuracy, leaving hundreds of thousands only
roughly located, and others only recorded upon photographs.
But where a high degree of exactitude and probability is
unattainable, that is no reason for refusing to accept such
knowledge as we can attain. Because we cannot reach great
certainty aboutthelife and teachings of Pythagorasis no reason
* See vol. 6, bk. I, ch. 7.
** In his Phoenixiana "Official Report."
|p36
for sulkily dismissing the subject as one we know nothing
about, as Dr. Ed. Zeller* would have us do.
# 15. SCIENCE AND
EXTRAORDINARY PHENOMENA
87. Science is from the nature of its procedure confined to
the investigation of the ordinary course of nature. I do not
mean that it cannot investigate individual objects, such as the
earth. But all its explanations of such objects must be limited
to the supposition that they have come about in the ordinary
course of nature. A statistical result may be obtained.
88. We may find that such and such a proportion of calves
have five legs. But we never can conclude with any
probability that the ratio is strictly zero; and even if we knew that the
proportion of men with golden thighsis exactlyzero, that would
be no argument at all against Pythagoras having had a golden
thigh. For something might be true of one man, or any
number of men, and yet might occur in the long run in a finite
number of cases out of an infinite series. Now a finite number
divided by infinity is exactly zero. That Pythagoras had a
golden thigh is the testimony of history. It is asserted by
Aristotle, of all possible authorities the highest, by both
Porphyry and Jamblichus after Nicomachus, by Herodotus, by
Plutarch, Diogenes Laertius, Aelian, Apollonius, ** etc. This
is far stronger testimony than we have for the resurrection of
Jesus. Are we then to admit as a part of the science of history
that Pythagoras had a golden thigh?
89. To do so would be to make a retroductive inference.
Now a retroductive conclusion is only justified by its
explaining an observed fact. An explanation is a syllogism of which
the major premiss, or rule, is a known law or rule of nature, or
other general truth; the minor premiss, or case, is the
hypothesis or retroductive conclusion, and the conclusion, or result, is
the observed (or otherwise established) fact. Such an
explanation, in this case, would be like this:
* Der Philosophie der Griechen, 5. 279.
** Peirce seems to have secured his authorities from Zeller's A History of Greek
Phtiosophy 1881, vol. 1, p. 328, n. 4. Zeller's references are not all accurate, and
the authorities quoted are not independent. Peirce's annotated copy of this book
is now, through the gift of his wife, the property of the Harvard College Library.
|p37
Every fact about Pythagoras (unless kept secret or
insignificant) would be reported by his ancient biographers.
That Pythagoras had a golden thighwas a fact about
Pythagoras neither secret nor insignificant.
.-. That Pythagoras had a golden thigh would be reported by all
his ancient biographers.
90. But this syllogism may be condemned at once on the
ground that it supposes we have statistical knowledge about
such kinds of facts as are quite contrary to the usual course of
nature. If the reply be made that it could make in regard to
the reporting of the fact no difference whether it were a natural
one or not, I rejoin, that granting that, it is not to the purpose.
It only goes to show that there is no difference between natural
and supernatural facts in this respect; from which the only just
inference is that no such proposition can be known even in
respect to natural facts. This, indeed, is the case. We cannot
say that evry remarkable public fact about Pythagoras would
be reported, but only that every phenomenon would be told as
it appeared to people in an almost primitive state of
civilization. Nobody can think that the golden thigh was treated as a
modern assayer would treat a gold brick. It was probably
flexible and therefore its golden appearance was superficial.
One of these days, we may find out something about the
ancient Persians, Chorasmians, or Brahmins which may make
this story significant. At present, it only illustrates the
impossibility of science making any assertion about a fact out of
the course of nature. Pythagoras was certainly a wonderful
man. We have no right, at all, to say that supernal powers had
not put a physical mark upon him as extraordinary as his
personality. Science can no more deny a miracle than it can
assert one.
91. But although science cannot infer any particular
violation of the ordinary course of nature, it may very well be that
it should find evidence that such violations are so frequent and
usual that this fact is itself z part of the ordinary course of
nature. For that reason, it is perfectly proper that science
should inquire, for example, into the evidences of the
fulfillment of prayers, etc. That is something open to experimental
inquiry; and until such inquiry has been instituted nobody is
entitled to any opinion whatever, or any bias, as to its result.
|p38
# 16. REASONING FROM SAMPLES
92. Many persons seem to suppose that the state of things
asserted in the premisses of an induction renders the state of
things asserted in the conclusion probable. The fact that
Macaulay's essay on Bacon was admired in its day shows how
little the absurdity of such a position was perceived. Even
John Stuart Mill holds that the uniformity of nature makes
the one state of things follow from the other. He overlooks the
circumstance that if so it ought to follow necessarily, while in
truth no definite probability can be assigned to it without
absurd consequences. He also overlooks the fact that
inductive reasoning does not invariably infer a uniformity; it may
infer a diversity. I watch the throws of a die, I notice that
about half are odd and half are even, and that they follow one
another with the utmost irregularity. I conclude that about
half of all the throws of that die are odd and that the odd and
even follow one another with great irregularity. How can any
principle of uniforrnity account for the truth of such an
induction? Mill never made up his mind in what sense he took
the phrase " uniformity of nature " when he spoke of it as the
basis of induction. In some passages he clearly means any
special uniformity by which a given character is likely to
belong to the whole of a species, a genus, a family, or a class if it
belongs to any members of that group. In this sense, as well
as in others, overlooked by Mill, there is no doubt the
knowledge of a uniformity strengthens an inductive conclusion; but
it is equally free from doubt that such knowledge is not
essential to induction. But in other passages Mill holds that it is
not the knowledge of the uniformity, but the uniformity itself
that supports induction, and furthermore that it is no special
uniformity but a general uniformity in nature. Mill's mind
was certainly acute and vigorous, but it was not
mathematically accurate; and it is by that trait that I am forced to
explain his not seeing that this general uniformity could not be
so defined as not on the one hand to appear manifestly false
or on the other hand to render no support to induction, or
both. He says it means that under similar circumstances
similar events will occur. But this is vague. Does he mean that
objects alike in all respects but one are alike in that one?
But plainly no two different real objects are alike in all respects
|p39
but one. Does he mean that objects sufficiently alike in other
respects are alike in any given respect? But that would be
but another way of saying that no two different. objects are
alike in all respects but one. It is obviously true; but it has no
bearing on induction, where we deal with objects which we well
know are, like all existing things, alike in numberless respects
and unlike in numberless other respects.*
93. The truth is that induction is reasoning from a sample
taken at random to the whole lot sampled. A sample is a
random one, provided it is drawn by such machinery, artificial
or physiological, that in the long run any one individual of the
whole lot would get taken as often as any other. Therefore,
judging of the statistical composition of a whole lot from a
sample is judging by a method which will be right on the
average in the long run, and, by the reasoning of the doctrine of
chances, will be nearly right oftener than it will be far from
right.
94. That this does justify induction is a mathematical
proposition beyond dispute. It has been objected that the sampling
cannot be random in this sense. But this is an idea which fiies
far away from the plain facts. Thirty throws of a die
constitute an approximately random sample of all the throws of that
die; and that the randomness should be approximate is all that
is required.
95. This account of the rationale of induction is
distinguished from others in that it has as its consequences two rules
of inductive inference which are very frequently violated,
although they have sometimes been insisted upon. The first of
these is that the sample must be a random one. Upon that I
shall not dwell here. The other rule is that the character,
toward the ascertainment of the proportionate frequency of
which in the lot sampled [the sampling is done], must not be
determined by the character of the particular sample taken.
For example, we must not take a sample of eminent men, and
studying over them, find that they have certain characters and
conclude that all eminent men will have those characters. We
must first decide for what character we propose to examine the
sample, and only after that decision examine the sample. The
reason is that any sample will be peculiar and unlike the average
* Mill's views on induction are exarnined in more detail in vol. 2, bk. III, ch. 9.
|p40
of the lot sampled in innumerable respects. At the same
time it will be approximately like the average of the whole lot
in the great majority of respects.
96. In order to illustrate the necessity of this rule I ta,"e a
random sample of eminent persons. It is quite a random one,
for it consists of the first names on pages 100, 300, 500, 700,
900, of Phillips's Great Index of Biography [Biographical
Reference, second edition, 1881]. The names are as follows:
Born Died
Francis Baring 1740 1810 Sept. 12
Vicomte de Custine 1760 1794 Jan 3
Hippostrates (of uncertain age)
Marquis d'O . 1535 1594 Oct. 24
Theocrenes 1480 1536 Oct. 18
Now I might, in violation of the above rule of
predesignation, draw the following inductions:
1. Three-fourths of these men were born in a year whose
date ends in a cipher. Hence about three-fourths of all eminent
men are probably so born. But, in fact, only one in ten is so
born.
2. Three eminent men out of four die in autumn. In fact,
only one out of four.
3. All eminent men die on a day of the month divisible
by three. In fact, one out of three.
4. All eminent men die in years whose date doubled and
increased by one gives a number whose last figure is the same
as that in the tens' place of the date itself. In fact, only one
in ten.
5. All eminent men who were living in any year ending in
forty-four died at an age which after subtracting four becomes
divisible by eleven. All others die at an age which increased
by ten is divisible by eleven.
97. This rule is recognized in the requirement of physicists
that a theory shall furnish predictions which shall be verified
before any particular weight is accorded to it. The medical
men, too, who deserve special mention for the reason that they
have had since Galen a logical tradition of their own, recognize
this rule, however dimly, in their working against reasoning
" post hoc, ergo propter hoc.". . .
|p41
# 17 THE METHOD OF RESIDUAL PHENOMENA
98. The so-called "method of residual phenomena" is so
simple that it hardly calls for any remark. At any early stage
of science when there are few observations of a given matter,
and those rough ones, a law is made out which, when the
observations come to be increased in number and made more
accurate, is found not to hold exactly. The departures from
this law are found themselves to follow a law which may now
be shown to be true. But at a still later date it is found that
this law again is interfered with, that there are still more
minute departures from it, and these departures are again
found to follow a law. All the successive laws so found may be
real, or they may be merely empirical formulae....
# 18. OBSERVATION
99. I have already remarked that a definition of science in
general which shall express a really intelligent conception of it
as a living historic entity must regard it as the occupation of
that peculiar class of men, the scientific men. The same remark
may be extended to definitions of the different branches of
science. The men who pursue a given branch herd together.
They understand one another; they live in the same world,
while those who pursue another branch are for them foreigners.
100. It will be found upon close examination that that
which renders the modes of thought of the students of a special
branch of science peculiar is that their experience lies in a
peculiar region. And the cause of this is that they are trained
and equipped to make a peculiar kind of observations. The
man who is continually making chemical analyses lives in a
different region of nature from other men. The same thing is
even more true of men who are constantly using a microscope.
101. It comes to this, that sciences must be classified
according to the peculiar means of observation they employ.
102. So too the great landmarks in the history of science
are to be placed at the points where new instruments, or other
means of observation, are introduced. Astronomy before the
telescope and astronomy after the telescope. Prephotographic
astronomy and photographic astronomy. Chemistry before
the exact analytic balance, and after.
|p42
# 19. EVOLUTION
103. The evolutionary theory in general throws great light
upon history and especially upon the history of science -- both
its public history and the account of its development in an
individual intellect. As great a light is thrown upon the theory
of evolution in general by the evolution of history, especially
that of science -- whether public or private.
104. The main theories of the evolution of organic species
are three. First, the theory of Darwin, according to which the
entire interval from Moner to Man has been traversed by
successive purely fortuitous and insensible variations in
reproduction. The changes on the whole follow a determinate course
simply because a certain amount of change in certain directions
destroys the species altogether, as the final result of successive
weakenings of its reproductive power. Second, the theory of
Lamarck, according to which the whole interval has been
traversed by a succession of very minute changes. But these
have not taken place in reproduction, which has absolutely
nothing to do with the business, except to keep the average
individuals plastic by their youth. The changes have not been
fortuitous but wholly the result of strivings of the individuals.
Third, the theory of cataclysmal evolution, according to which
the changes have not been small and have not been fortuitous;
but they have taken place chiefly in reproduction. According
to this view, sudden changes of the environment have taken
place from time to time. These changes have put certain
organs at a disadvantage, and there has been an effort to use
them in new ways. Such organs are particularly apt to sport
in reproduction and to change in the way which adapts them
better to their recent mode of exercise.
105. Notwithstanding the teachings of Weismann, it
seems altogether probable that all three of these modes of
evolution have acted. It is probable that the last has been the
most efficient. These three modes of organic evolution have
their parallels in other departments of evolution.
106. Let us consider, for example, the evolution of
standards of weights and measures. In order to define the word
"pound" in the Century Dictionary,* I made a list of about
* See 209. Peirce wrote the definitions of terms in mechanics, mathematics
astronomy, astrology, weights and measures, logic, metaphysics, all those
relating to universities, and many on psychology for the Century Dictionary, edition
of 1889.
|p43
four hundred pounds which had been in use in different parts
of Europe -- undoubtedly a very incomplete list, for it was
confined in great measure to certain provinces concerning
which I was able to obtain information. Each individual
pound or measuring stick is from time to time copied; and at
length the old one becomes destroyed. The measure of each
copy is imperceptibly larger or smaller than its immediate
prototype. If then these variations cannot, by gradual
summation, produce a standard much smaller without that standard
being destroyed as inconvenient while no such destruction
would follow upon an increase of the standard, the average of
the standards will slowly grow larger by Darwinian evolution.
If there were a disposition on the part of owners of pounds to
file them down, so as to make them lighter, though not enough
to be noticed, then these filed pounds being copied, and the
copies filed, there would be a gradual lightening of the pound
by Lamarckian evolution. But it is very unlikely that either of
these two modes has been a considerable factor in the actual
evolution of weights and measures. As long as their
circumstances are unchanged, human communities are exceedingly
conservative. Nothing short of the despotism of a modern
government with a modern police can cause a change in
weights and measures. But from time to time changes occur
which cause trade to take new routes. Business has to be
adapted to new conditions; and under such influences we find
all those habits of communities which are rendered unsuitable
by the change become plastic enough. Then it is that a new
pound or a new yard may be made which is a compromise
between a desire to retain old ways and a desire to please
new-comers.
107. In the evolution of science, a Darwinian mode of
evolution might, for example, consist in this, that at every
recall of a judgment to the mind -- say, for example, a judgment
in regard to some such delicate question as the marriage of the
dergy -- a slight fortuitous modification of the judgment
might take place; the modified judgment would cause a
corresponding modification of the belief-habit, so that the next recall
would be influenced by this fortuitous modification, though it
would depart more or less from it by a new fortuitous
modification. If, however, by such summation of modifications an
|p44
opinion quite untenable were reached, it would either be
violently changed or would be associationally weak and not apt
to be recalled. The effect of this would be in the long run that
belief would move away from such untenable positions. It is
possible that such a mode of influence may affect our
instinctive feelings; but there can be nothing of this sort in science,
which is controlled and exact. But another sort of Darwinian
evolution undoubtedly does take place. We are studying over
phenomena of which we have been unable to acquire any
satisfactory account. Various tentative explanations recur to our
minds from time to time, and at each occurrence are modified
by omission, insertion, or change in the point of view, in an
almost fortuitous way. Finally, one of these takes such an
aspect that we are led to dismiss it as impossible. Then, all
the energy of thought which had previously gone to the
consideration of that becomes distributed among the other
explanations, until finally one of them becomes greatly strengthened
in our minds.
108. Lamarckian evolution might, for example, take the
form of perpetually modifying our opinion in the effort to
make that opinion represent the known facts as more and more
observations came to be collected. This is all the time going
on in regard, for example, to our estimate of the danger of
infection of phthisis. Yet, after all, it does not play a
prominent part in the evolution of science. The physical journals --
say, for example, Poggendorff's [Annalen der Physik] and
Beiblatter -- publish each month a great number of new
researches. Each of these is a distinct contribution to science.
It represents some good, solid, well-trained labor of
observation and inference. But as modifying what is already known,
the average effect of the ordinary research may be said to be
insignificant. Nevertheless, as these modifications are not
fortuitous but are for the most part movements toward the
truth -- could they be rightly understood, all of them would
be so -- there is no doubt that from decade to decade, even
without any splendid discoveries or great studies, science would
advance very perceptibly. We see that it is so in branches of
physics which remain for a long time without any decisive
conquests. It was so, for example, in regard to the classification
of the chemical elements in the lapse of time from Berzelius to
|p45
Mendeleeff, as the valuable history of Venable * shows. This
is an evolution of the Lamarckian type.
109. But this is not the way in which science mainly
progresses. It advances by leaps; and the impulse for each leap is
either some new observational resource, or some novel way of
reasoning about the observations. Such novel way of reasoning
might, perhaps, be considered as a new observational means,
since it draws attention to relations between facts which would
previously have been passed by unperceived.
[I] illustrate by the discoveries of Pasteur, ** who began by
applying the microscope to chemistry. He picked out the
right- and left-handed crystals of tartaric acid. The two kinds
have absolutely the same properties except in regard to
direction of rotation of the plane of polarization and in their chemical
relations to other " optically active " bodies. Since this method
of picking out individual crystals was so slow, Pasteur looked
for other means. Ferments of appropriate kinds were found to
have the same effect. The microscope showed these were due
to living organisms, which Pasteur began studying. At that
time the medical world was dominated by Claude Bernard's
dictum that a disease is not an entity but merely a sum of
symptoms. *** This was pure metaphysics which only barricaded
inquiry in that direction. But that was a generation which
attached great value to nominalistic metaphysics. Pasteur
began with the phylloxera. He found it influenced the "optical
activity " of the sugar. This pointed to a ferment and therefore
to an entity. He began to extend the doctrine to other diseases.
The medical men, dominated by the metaphysics of Claude
Bernard, raised all sorts of sophistical objections. But the
method of cultures and inoculation proved the thing, and here
we see new ideas connected with new observational methods
and a fine example of the usual process of scientific evolution.
It is not by insensible steps.
# 20. SOME A PRIORI DICTA
110. The last fifty years have taught the lesson of not
trifling with facts and not trusting to principles and methodswhich
* The Development of the Periodic Law, Easton, Pa., 1896.
** See Oevres de Pasteur, vol. 1, p. 83, Paris, 1922.
*** Lefons de Pathologie experimental, 2me le‡on, Paris, 1872.
|p46
are not logically founded upon facts and which serve only to
exclude testimony from consideration.
111. Such, for example, was the dictum of Claude Bernard
that a disease is not an entity -- a purely metaphysical
doctrine. But the observation of facts has taught us that a disease
is in many, if not most, serious cases, just as much an entity
as a human family consisting of father, mother, and children.
112. Such was the dictum of the old psychology which
identified the soul with the ego, declared its absolute simplicity
and held that its faculties were mere names for logical divisions
of human activity. This was all unadulterated fancy. The
observation of facts has now taught us that the ego is a mere
wave in the soul, a superficial and small feature, that the soul
may contain several personalities and is as complex as the brain
itself, and that the faculties, while not exactly definable and not
absolutely fixed, are as real as are the different convolutions of
the cortex.
113. Such were the dicta by means of which the internal
criticism of historical documents was carried to such a height
that it often amounted to the rejection of all the testimony that
bas come down to us, and the substitution for it of a dream
spun out of the critic's brain. But archeological researches
have shown that ancient testimony ought to be trusted in the
main, with a small allowance for the changes in the meanings
of words. When we are told that Pythagoras had a golden
thigh, we are to remember that to the ancients gold did not
mean a chemical element of atomic weight 197.5 and specific
gravity 19.3, melting at 1045ø C. and forming saline
compounds of the types AuX and AuX3. It meant something of
metallic lustre, warmer in color than electrum and cooler than
copper. Dr. Schliemann's discoveries were the first socdolager
that " higher criticism " received. It has since got many others.
114. Such was the dictum of Laplace that stones do not
come from heaven.
115. Such were the dicta by which everything of the nature
of extraordinary powers connected with psychological states of
which the hypnotic trance is an example were set down as
tricks. At present, while the existence of telepathy cannot be
said to be established, all scientific men are obliged by observed
facts to admit that it presents at least a very serious problem
requiring respectful treatment.
|p47
# 21. THE PAUCITY OF
SCIENTIFIC KNOWLEDGE
116. Persons who know science chiefly by its results --
that is to say, have no acquaintance with it at all as a living
inquiry -- are apt to acquire the notion that the universe is
now entirely explained in all its leading features; and that it is
only here and there that the fabric of scientific knowledge
betrays any rents.
117. But in point of fact, notwithstanding all that has been
discovered since Newton's time, his saying that we are little
children picking up pretty pebbles on the beach while the whole
ocean lies before us unexplored remains substantially as true as
ever, and will do so though we shovel up the pebbles by steam
shovels and carry them off in carloads. An infinitesimal ratio
may be multiplied indefinitely and remain infinitesimal still.
118. In the first place all that science has done is to study
those relations between objects which were brought into
prominence and conceiving which we had been endowed with some
original knowledge in two instincts -- the instinct of feeding,
which brought with it elementary knowledge of mechanical
forces, space, etc., and the instinct of breeding, which brought
with it elementary knowledge of psychical motives, of time, etc.
All the other relations of things concerning which we must
suppose there is vast store of truth are for us merely the object of
such false sciences as judicial astrology, palmistry, the doctrine
of signatures, the doctrine of correspondences, magic, and the
like.
119. In the next place, even within the very bounds to
which our science is confined, it is altogether superficial and
fragmentary. Want of knowledge of the constitution of matter
and of electricity. The conservation of forces, as Helmholtz
first enunciated it, untenable; whether it can be universally
true in any sense is a difficult problem. To strengthen it
Helmholtz greatly insisted on discontinuities -- a most
objectionable theory from every point of view. Mind quite as little
understood as matter, and the relations between the two an
enigma. The forces we know can be but a small part of all
those that are operative. Our ignorance of small things and
great, of distant times and of very slow operations. We are
equally ignorant of very rapid performances which nevertheless |p48
we know to take place. Our science is altogether
middle-sized and mediocre. Its insignificance compared with the
universe cannot be exaggerated.
# 22. THE UNCERTAINTY OF
SCIENTIFIC RESULTS
120. It is a great mistake to suppose that the mind of the
active scientist is filled with propositions which, if not proved
beyond all reasonable cavil, are at least extremely probable.
On the contrary, he entertains hypotheses which are almost
wildly incredible, and treats them with respect for the time
being. Why does he do this? Simply because any scientific
proposition whatever is always liable to be refuted and
dropped at short notice. A hypothesis is something which
looks as if it might be true and were true, and which is capable
of verification or refutation by comparison with facts. The
best hypothesis, in the sense of the one most recommending
itself to the inquirer, is the one which can be the most readily
refuted if it is false. This far outweighs the trifling merit of
being likely. For after all, what is a likely hypothesis? It is
one which falls in with our preconceived ideas. But these may
be wrong. Their errors are just what the scientific man is out
gunning for more particularly. But if a hypothesis can quickly
and easily be cleared away so as to go toward leaving the field
free for the main struggle, this is an immense advantage.
121. Retroduction goes upon the hope that there is
sufficient affinity between the reasoner's mind and nature's to
render guessing not altogether hopeless, provided each guess is
checked by comparison with observation. It is true that
agreement does not show the guess is right; but if it is wrong it must
ultimately get found out. The effort should therefore be to
make each hypothesis, which is practically no more than a
question, as near an even bet as possible.
# 23. THE ECONOMY OF RESEARCH
122. Dr. Ernst Mach, who has one of the best faults a
philosopher can have, that of riding his horse to death, does
just this with his principle of Economy in science.* But of
* See, e.g., the lecture on the " Econornical Nature of Physical Inquiry" in the
Popular Scientific Lectures (1895).
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course there is a doctrine of the Economies of Research. One
or two of its principles are easily made out. The value of
knowledge is, for the purposes of science, in one sense absolute.
It is not to be measured, it may be said, in money; in one sense
that is true. But knowledge that leads to other knowledge is
more valuable in proportion to the trouble it saves in the way
of expenditure to get that other knowledge. Having a certain
fund of energy, time, money, etc., all of which are merchantable
artides to spend upon research, the question is how much is to
be allowed to each investigation; and for us the value of that
investigation is the amount of money it will pay us to spend
upon it. Relatively, therefore, knowledge, even of a purely
scientific kind, has a money value.
This value increases with the fullness and precision of the
information, but plainly it increases slower and slower as the
knowledge becomes fuller and more precise. The cost of the
information also increases with its fullness and accuracy, and
increases faster and faster the more accurate and full it is. It
therefore may be the case that it does not pay to get any
information on a given subject; but, at any rate, it must be true
that it does not pay (in any given state of science) to push the
investigation beyond a certain pomt in fullness or precision.
123. If we have a number of studies in which we are
interested, we should commence with the most remunerative and
carry that forward until it becomes no more than equally
remunerative with the commencement of another; carry both
forward at such rates that they are equally remunerative until
each is no more remunerative than a third, and so on.
124. If two or more kinds of knowledge are so related that
one can replace the other so that the possession of one renders
the other less profitable, this will diminish the investigation of
either while increasing the investigation of all.
125. If two or more kinds of information are of use only as
supplementing one another, that is, only when combined
together, this will increase the investigations until there is little
or no profit from the least profitable kind of research.