stone-age tools being really tools made by men. I had only seen a few
bad specimens, one or two of which I still think were just accidentally
broken flints which an old country clergyman took for stone-age tools.
This was to me then a mere guess, viz. that the cutting shape proved
{144} the flints to have been made by men. And obviously, if I had seen
hundreds of specimens no better than these, I should have treated it as
a mere guess all the same. But I happened to go to Salisbury, and there
I saw the famous Blackmore Museum, where there are not only hundreds
of specimens, but specimens arranged in series from the most beautiful
knives and arrow-heads to the rudest. There one’s eye caught the common
look of them at once, the better specimens helping one to interpret the
worse, and the guess was almost turned into a demonstration, because
one’s eyes were opened to the sort of handwork which these things
exhibit, and to the way in which they are chipped and flaked.
Now this very important operation of number of examples, in helping the
mind to an explanation, is always being confused with the effect of
mere repetition of examples, which does not help you to an explanation,
_i.e._ a repetition in which one tells you no more than another.
But these mere repetitions operate _prima facie_ in a different
way, viz. by making you think there is an _unknown_ cause in favour
of the combination of properties which recurs, and lead up to the
old-fashioned perfect Induction and the doctrine of chances, and not to
demonstration. [1]
[1] Ultimately the calculus of chances may be said to rest on
the same principle as Induction, in so far as the repetition of
examples derives its force from the (unspecified) variety of
contexts through which this repetition shows a certain result
to be persistent. But in such a calculus the presumption from
recurrence in such a variety of contexts is only estimated, and
not analysed.
On the road from guess-work to demonstration, and generally assisted
by great experience, we have _skilful_ {145} guess-work, the first
stage of discovery. This depends on the capacity for hitting upon
qualities which _are_ connected by causation, though the connection
remains to be proved. So a countryman or a sailor gets to judge of
the weather; it is not merely that he has seen so many instances, but
he has been taught by a great variety of instances to recognise the
essential points, and has formed probably a much more complex judgment
than he can put into words. So again a doctor or a nurse can see how
ill a patient is, though it does not follow that they could always say
why this appearance goes with this degree of illness. In proportion
as you merely _presume_ a causal connection, it is guess-work or pure
discovery. In as far as you can _analyse_ a causal connection it is
demonstration or proof; and for Logic, discovery cannot be treated
apart from proof, except as skilful guess-work. _In as far as_ there
is ground for the guess, so far it approaches to proof; _in as far as_
there is no ground, it gives nothing for Logic to get hold of--is mere
caprice. A good scientific guess really depends on a shrewd eye for the
essential points. I am not mathematician enough to give the history
of the discovery of Neptune by Leverrier and Adams, “calculating a
planet into existence by enormous heaps of algebra,” [1] but it must
have begun as a guess, I should suppose it was suggested before Adams
and Leverrier took it up, on the ground of the anomalous movements of
Uranus indicating an attraction unaccounted for by the known solar
system. And I suppose that this guess would gradually grow into
demonstration as it became clear that nothing but a new planet would
explain the anomalies of {146} the orbit of Uranus. And at last the
calculators were able to tell the telescopist almost exactly where
to look for the unknown planet. The proof in this case preceded the
observation or discovery by perception, and this makes it a very
dramatic example; but if the observation had come earlier, it would not
I suppose have dispensed with the precise proof of Neptune’s effect on
Uranus, though it might have made it easier.
[1] De Morgan, _Budget of Paradoxes_, p. 53.
_Figures of Syllogism_
6. In illustration of this progress from guess-work to science, [1]
I will give an example of the three Aristotelian figures of the
Syllogism. I omit the fourth. I assume that the heavier term, or the
term most like a “thing,” is fitted to be the Subject, and the term
more like an attribute to be the Predicate. The syllogistic rules
depend practically on the fact that common Logic, following common
speech and thought, treats the Predicate as wider than the Subject,
which corresponds to Mill’s view (also the common scientific view),
that the same effect may have several alternative causes (not a
compound cause, but different possible causes), and that consequent
is wider than antecedent. [2] It is this assumption that prevents
affirmative propositions from being simply convertible, _i.e._ prevents
“All men are mortal” from being identical with “All mortals are men,”
and but for it there would be no difference of figure at all, as there
is not for inference by equation.
[1] Cf. Plato’s _Republic_, Bk. VI., end. [2] See p. 141, note.
This progression is here merely meant to illustrate the universal or
systematic connection of particulars in process of disengaging itself.
But I do _not_ say that the first {147} figure with a major premise is
a natural form for all arguments.
I take the scheme of the first three figures from Jevons, and suggest
their meaning as follows:--
X denotes the major term.
Y denotes the middle term.
Z denotes the minor term.
1st Fig. 2nd Fig. 3rd Fig.
Major Premise YX XY YX
Minor Premise ZY ZY YZ
Conclusion ZX ZX ZX
Fig. 3. _An observation and a guess._
Yesterday it rained in the evening.
All yesterday the smoke tended to sink.
∴ The smoke sinking ( may be ) a sign of rain.
( is sometimes )
The conclusion cannot be general in this figure, because nothing
general has been said in the premisses about the subject of the
conclusion. So it is very suitable for a mere suggested connection
given in a single content--that of the time “yesterday,” implying
moreover that both the points in question have something to do with the
state of the atmosphere on that single day.
Fig. 2. _A tentative justification_.
Smoke that goes downwards is heavier than air
Particles of moisture are heavier than air.
∴ Particles of moisture may be in the descending smoke.
A universal conclusion in this figure would be formally bad. But we
do not care for that, because we only mean it to be tentative, and we
do not draw a universal affirmative {148} conclusion. We express its
badness by querying it, or by saying “may be.” The reason why it is
formally bad is that nothing general has been said in the premisses
about the middle term or reason, so that it is possible that the two
Subjects do not touch each other within it, _i.e._ that the suggested
special cause, moisture, is not connected with the special effect, the
sinking of the smoke. The general reason “heavier than air” may include
both special suggested cause and special suggested effect without their
touching. Smoke and moisture may both sink in air, but for different
and unconnected reasons. Still, when a special cause is suggested which
is probably present in part, and which would act in the way required
by the general character of the effect, there is a certain probability
that it _is_ the operative cause, subject to further analysis; and
the argument has substantive value, though bad in form. The only good
arguments in this figure have negative conclusions, _e.g._--
Smoke that is heavier than air goes downwards.
Smoke on dry days does not go downwards.
∴ Smoke on dry days is not heavier than air.
This conclusion _is_ formal, because the negative throws the second
Subject altogether outside the Predicate, and so outside the first
Subject. The one content always has a characteristic which can never
attach to the other, and consequently it is clear that some genuine
underlying difference keeps them apart. Such an inference would
corroborate the suggestion previously obtained that the presence of
moisture was the active cause of the descending smoke on days when rain
was coming.
Fig. 1. _A completely reasoned judgment_.
{149}
All particles that sink in the air in damp weather more
than in dry, are loaded with moisture when they sink.
Smoke that descends before rain is an example of particles
that sink in the air in damp weather more than in dry.
∴ Smoke that descends before rain is loaded with moisture
when it descends (and therefore its sinking is not
accidentally a sign of rain, but is really connected with
the cause of rain).
The major premise belongs only to this figure. In the other it is mere
tradition to call it so, and their two premisses are the same in kind,
and contribute equally to the conclusion, and for that reason the
affirmative conclusion was not general or not formal. If your general
conclusion is to follow by mere form, you must show your principle
as explicitly covering your conclusion. But if you do this, then of
course you are charged with begging the question. And, in a sense,
that is what you mean to do, when you set out to make your argument
complete by its mere form. If you have _bonâ fide_ to construct a
combination of your data, you cannot predict whether the conclusion
will take this form or that form. Using a major premise meant, “We
have got a principle that covers the conclusion, and so explains the
case before us.” Granting that the major premise involves the minor
premise and conclusion, that is just the reason why it is imperative
to express them. The meaning of the Syllogism is that it analyses the
whole actual thought; the fault is to suppose that novelty is the
point of inference. The Syllogism shows you how you must understand
either premise in order that it may cover {150} the conclusion. Or,
starting from the conclusion as a current popular belief, or as an
isolated observation or suggestion by an individual observer (and this
is practically the way in which our science on any subject as a rule
takes its rise), the characteristic process through the three stages
described above consists in first noting the given circumstances under
which, according to the _prima facie_ belief or observation, the
conjunction in question takes place (“yesterday,” _i.e._ “in the state
of the atmosphere yesterday”); secondly in analysing or considering
those given circumstances, to find within them something which looks
like a general property, a law, or causal operation, which may attach
the conjunction in question to the systematic whole of our experience
(the presence of something heavier than air in the atmosphere); and
thirdly, in the exhibition of this ground or reason as a principle, in
the light of which the primary belief or observation (probably a good
deal modified) becomes a part of our systematic intelligible world.
{151}
LECTURE X INDUCTION, DEDUCTION, AND CAUSATION
_Induction_ [1]
1. Induction has always meant some process that starts from instances;
the Greek word for it is used by Aristotle both in his own Logic and
in describing the method of Socrates. It meant either “bringing up
instance after instance,” or “carrying the hearer on by instances.” And
still in speaking of Induction we think of some process that consists
in doing something with a number of instances. But we find that this
notion really breaks down, and the contradiction between Mill and other
writers (Jevons, ch. i.) shows exactly how it breaks down. The question
is whether one experiment will establish an inductive truth. We will
review the meanings of the term, and show how they change.
[1] Read N. Lockyer’s _Elements of Astronomy_; Abney’s _Colour
Measurement_; Introduction to _Bain on Induction_; Jevons’s
_Elementary Lessons on “Observation and Experiment”_ p. 228, and
on _Induction_, p. 214 (about Mill).
_Induction by simple Enumeration_
(_a_) Induction by simple enumeration was what Bacon was always
attacking, and saying, quite rightly, that it was not scientific. It is
the method which I stated in the Third Figure of the syllogism, almost
a conversational method; the mere beginning of observation. “I am sure
the influenza is a serious illness; all my friends who have had it have
been dreadfully pulled down.”
{152}
A B C have been seriously ill.
ABC have had influenza.
∴ Influenza is a serious illness.
Now this popular kind of inference, as Bacon says, “Precarie concludit,
et periculo exponitur ab instantia contradictoria.” Suppose you come
across one slight case of influenza, the conclusion is upset. This
type of reasoning really appeals to two quite opposite principles;
one the principle of counting, which leads up to statistics and the
old-fashioned perfect Induction or the theory of chance, the other the
principle of scientific system.
_Enumeration always has a ground_
(_b_) In counting, we do not think of the reason why we count, but
there always is a reason, which is given in the nature of the whole
whose parts we are counting. If I count the members of this audience,
it is because I want to know how many units the whole audience consists
of. I do not ask why each unit is there; counting is different from
scientific analysis; but yet the connection between whole and part is
present in _my reason for counting_. So really, though I only say,
“One, two, three, four, etc.,” each unit demands a judgment, “This is
one member--that makes two members, that makes three members,” etc.
Counting is the construction of a total of units sharing a common
nature; measurement is a form of counting in which the units are also
referred to some other standard besides the whole in question, _e.g._
the standard pound or inch.
_Perfect Induction_
(_c_) _Mere_ counting or “enumeration” only helps you in induction by
comparison with some other numerical result, and, if imperfect, only to
the extent of suggesting that there {153} is a common cause or there is
not a common cause. _E.g._ if you throw a six with one die fifty times
running, you infer that the die is probably loaded. This is because
you compare the result with that which you expect if the die is fair,
viz. a six once in every six throws. You infer that there is a special
cause favouring one side. The principle is that ignorance is impartial.
If you know no reason for one case more than another, you take them
as equal fractions of reality; if results are not equal fractions
of reality, you infer a special reason favouring one case. [1] Pure
counting cannot help you in Induction in any way but this. _Perfect
Induction_ simply means that the total is limited and the limit is
reached; you have counted 100 per cent, of the possible cases, and the
chance becomes certainty. The result is a mere collective judgment.
[1] See Lecture IX, p. 144, note.
_System_
(_d_) The principle of scientific system is quite a different thing.
Essentially, it has nothing to do with number or with a generalised
conclusion. It is merely this, “What is once true is always true, and
what is not true never was true.” The aim of scientific induction is
to find out “What _is_ true,” _i.e._ what is consistent with the given
system. We never doubt this principle; if we did we could have no
science. If observation contradicts our best-established scientific
laws, and we cannot suppose an error in the observation, we must
infer that the law was wrongly, _i.e._ untruly stated. Therefore, as
Mill says, one case is enough, _if_ you can find the truth about it.
People object that you cannot make a whole science out of one case,
and therefore you must have a number of instances. That is a {154}
_practical_ point to be borne in mind, but it has no real scientific
meaning. “Instance” cannot be defined except as one observation, which
is a purely accidental limitation. The point is, that you use your
instances not by counting cases of given terms, but by ascertaining
what the terms really are (_i.e._ modifying them), and what is their
real connection. This is the simple secret of Mill’s struggle to base
scientific Induction, on Induction by simple Enumeration; the latter is
not the evidence, but the beginning of eliciting the evidence--so that
the Scientific Induction is far more certain than that on which Mill
bases it. Aristotle’s statement is the clearest and profoundest that
has ever been made. [1]
“Nor is it possible to obtain scientific knowledge by way
sense-perception. For even if sense-perception reveals a certain
character in its object, yet we necessarily perceive _this_, _here_,
and _now_. The universal, which is throughout all, it is impossible to
perceive; for it is not a this-now; if it had been it would not have
been universal, for what is always and everywhere we call universal.
Since then demonstration (science) is universal, and such elements it
is impossible to perceive by sense, it is plain that we cannot obtain
scientific knowledge by way of sense. But it is clear that even if we
had been able to perceive by sense [_e.g._ by measurement] that the
three angles of a triangle are equal to two right angles, we should
still have had to search for a demonstration, and should not, as some
say, have known it scientifically (without one); for we necessarily
perceive in particular cases only, but science comes by knowing the
universal. Wherefore if we could have been on the moon, and seen the
earth coming between it and the {155} sun, we should not (by that mere
perception) have _known_ the cause of the eclipse. Not but what by
seeing this frequently happen we should have grasped the universal,
and obtained a demonstration; for the universal becomes evident out
of a plurality of particulars, and the universal is valuable because
it reveals the cause;” and again, [2] “And that the search of science
is for the middle term is made plain in those cases in which the
middle term is perceptible to sense. For we search where we have had
no perception,--as for the reason (or middle term) of an eclipse,--to
know if there is a reason or not. But if we had been upon the moon, we
should not have had to inquire if the process (of an eclipse as such,
and not some other kind of darkness) takes place, or for what reason,
but both would have been plain at once. The perception would have been,
‘The earth is now coming between,’ carrying with it the obvious fact,
‘The moon is now suffering an eclipse,’ and _out of this_ the universal
(connection) would have arisen.”
[1] Aristotle, _An. Post._ 87, b. 28. [2] _Ibid._ 90, a. 24.
_Analogy_
(_e_) I showed you a method on the way to this in the shape of
Aristotle’s second figure, which we may call _analogy_. The plain sign
of it is, that you give up counting the instances and begin to weigh
them, so that the attributes which are predicates fall into the middle
term or reason. In the former inference about influenza we did not
suppose that you had any idea _why_ influenza was a serious illness;
but in analogy there is some suggestion of this kind, so that the
connection is examined into. Here at once you begin to get suggested
explanations and confirmation from the {156} system of knowledge. You
cannot have analogy by merely counting attributes.
I begin from _Enumerative Suggestion_ drawn from observation of
Butterflies.
1. Three species of genus _x_ closely resemble three species of _y_.
2. The species of _x_ would be protected by resembling _y_ (because _y_
is distasteful to birds).
∴ The resemblance may be a “protective resemblance,” _i.e._ a
resemblance brought about by survival of those thus protected.
On this there naturally follows _Analogy_.
1. Protective resemblances naturally increase through series of species
from slighter to closer resemblances.
2. The resemblances in question increase in genus _x_ through series of
species from slighter to closer resemblance to _y_.
∴ The resemblances in question show important signs of being protective
resemblances.
When we get thus far, a single syllogism will not really represent
the argument. It can only analyse with convenience a single step in
inference. But now we have connected the reason of the resemblances
with the whole doctrine of natural selection, the gradual approximation
of the species is most striking, and we could set up a corroborative
analogy on the basis of every feature and detail of these resemblances,
the tendency of which would be to show that no cause or combination of
causes other than that suggested is likely to account for the observed
resemblances.
{157} I give a confirmatory negative analogy.
1. No protective resemblance can grow up where there is no initial
tendency to resemblance.
2. The non-resembling species in the genus _x_ show no initial tendency
towards _y_.
∴ The non-resemblances observed are such as could not produce
protective resemblances. This is a formally bad argument from two
negative premisses justified by its positive meaning, which implies
that _just where_ the alleged effect ceases, the alleged cause ceases
too.
If you look at the case in the Natural History Museum [1] you see the
normal Pierinae down one side, not approaching Euploinae. They are the
positive examples, negatively confirming the explanation of those which
do approach Euploinae. These latter all start from some form which
varied slightly, by accident we presume, towards Euploinae, and then
this partially resembling series splits into three sets, each leading
up to a different and complete protective resemblance.
[1] These cases in the entrance-hall of the Natural History
Museum at South Kensington afford excellent practical
illustrations of Inductive Method. I strongly urge the London
student to try his hand at formulating them.
I said _mere_ number was no help in scientific Induction. But do not
these three sets of resemblances make a stronger proof than any one
would? Yes, because we need a presumption against accident. You would
not want this if you could unveil what really happens in one case,
but as infinite conditions are operative in such matters, and it is
impossible to experiment accurately, [1] this cannot be done; {158}
and it might be said that _one_ such resemblance was an accident,
_i.e._ that it was owing to causes independent of the protection. But
as the cases become more numerous it becomes more improbable that
different circumstances produce the same effect, which would then be
a mere coincidence, in so many different cases. If, however, we knew
by positive and negative analysis what circumstance did produce the
effect, this confirmation would be useless.
[1] Ultimately, no experiments are absolutely accurate. There is
always an unexhausted background in which unsuspected causes of
error may be latent.
_Negative Instance_
(_f_) In order to show _exactly_ what circumstance produces a given
effect, a system must be brought to bear on the phenomenon through
negation. The only test of truth is that it is that which enables you
to organise your thought and perception.
The first means of doing this is Observation, then Experiment, then
Classification and Hypothesis, which takes us into Deduction.
Observation is inaccurate, until you begin to distinguish what is
connected from what is not connected. When you do this, you are very
near experiment, the use of which is to introduce perfectly definite
and measurable changes into what you are observing. [1] There is no
absolute distinction between observation and experiment. Looking at a
tissue through a microscope is observation; putting on a polariscope,
though it changes the _image_ altogether, is observation; if you
warm the stage, or put an acid on the object, that, I suppose, is
experiment, because you interfere with the object {159} itself. What
should we say, for example, as to spectroscopic analysis of the Sun’s
corona?
[1] Jevons, _loc. cit_., esp. quot. from Herschel (p. 234).