_ON CERTAIN CONSEQUENCES OF THE OBJECTIVE TREATMENT OF A SCIENCE OF
INFERENCE._[1]
1. In the previous edition a large part of this chapter was devoted to
the general consideration of the distinction between a Material and
a Conceptualist view of Logic. I have omitted most of this here, as
also a large part of a chapter devoted to the detailed discussion of
the Law of Causation, as I hope before very long to express my
opinions on these subjects more fully, and more appropriately, in a
treatise on the general principles of Inductive Logic.
1. Students of Logic are familiar with that broad
distinction between the two methods of treatment to which
the names of Material and Conceptualist may be applied.
The distinction was one which had been gradually growing
up under other names before it was emphasized, and treated
as a distinction within the field of Logic proper, by the publication
of Mill's well known work. No one, for instance,
can read Whewell's treatises on Induction, or Herschel's
Discourse, without seeing that they are treating of much the
same subject-matter, and regarding it in much the same
way, as that which Mill discussed under the name of Logic,
though they were not disposed to give it that name. That
is, these writers throughout took it for granted that what
they had to do was to systematise the facts of nature in
their objective form, and under their widest possible treatment,
and to expound the principal modes of inference and
the principal practical aids in the investigation of these
modes of inference, which reason could suggest and which
experience could justify. What Mill did was to bring these
methods into close relation with such portions of the old
scholastic Logic as he felt able to retain, to work them out
into much fuller detail, to systematize them by giving them
a certain philosophical and psychological foundation,--and
to entitle the result _Logic_.
The practical treatment of a science will seldom correspond
closely to the ideal which its supporters propose to
themselves, and still seldomer to that which its antagonists
insist upon demanding from the supporters. If we were to
take our account of the distinction between the two views of
Logic expounded respectively by Hamilton and by Mill,
from Mill and Hamilton respectively, we should certainly
not find it easy to bring them under one common definition.
By such a test, the material Logic would be regarded as
nothing more than a somewhat arbitrary selection from the
domain of Physical Science in general, and the conceptualist
Logic nothing more than a somewhat arbitrary selection from
the domain of Psychology. The former would omit all consideration
of the laws of thought and the latter all consideration
of the truth or falsehood of our conclusions.
Of course, in practice, such extremes as these are soon
seen to be avoidable, and in spite of all controversial exaggerations
the expounders of the opposite views do contrive to
retain a large area of speculation in common. I do not propose
here to examine in detail the restrictions by which this
accommodation is brought about, or the very real and important
distinctions of method, aim, tests, and limits which
in spite of all approach to agreement are still found to subsist.
To attempt this would be to open up rather too wide an
enquiry to be suitable in a treatise on one subdivision only
of the general science of Inference.
2. One subdivision of this enquiry is however really
forced upon our notice. It does become important to consider
the restrictions to which the ultra-material account of
the province of Logic has to be subjected, because we shall
thus have our attention drawn to an aspect of the subject
which, slight and fleeting as it is within the region of Induction
becomes very prominent and comparatively permanent
in that of Probability. According to this ultra-material view,
Inductive Logic would generally be considered to have nothing
to do with anything but objective facts: its duty is to
start from facts and to confine itself to such methods as will
yield nothing but facts. What is doubtful it either establishes
or it lets alone for the present, what is unattainable
it rejects, and in this way it proceeds to build up by slow
accretion a vast fabric of certain knowledge.
But of course all this is supposed to be done by human
minds, and therefore if we enquire whether notions or concepts,--call
them what we will,--have no place in such a
scheme it must necessarily be admitted that they _have_ some
place. The facts which form our starting point must be
grasped by an intelligent being before inference can be built
upon them; and the 'facts' which form the conclusion have
often, at any rate for some time, no place anywhere else than
in the mind of man. But no one can read Mill's treatise, for
instance, without noticing how slight is his reference to this
aspect of the question. He remarks, in almost contemptuous
indifference, that the man who digs must of course have a
notion of the ground he digs and of the spade he puts into
it, but he evidently considers that these 'notions' need not
much more occupy the attention of the speculative logician,
in so far as his mere inferences are concerned, than they
occupy that of the husbandman.
3. It must be admitted that there is some warrant
for this omission of all reference to the subjective side of
inference so long as we are dealing with Inductive Logic.
The inductive _discoverer_ is of course in a very different
position. If he is worthy of the name his mind at every
moment will be teeming with notions which he would be as
far as any one from calling facts: he is busy making them
such to the best of his power. But the logician who follows
in his steps, and whose business it is to explain and justify
what his leader has discovered, is rather apt to overlook this
mental or uncertain stage. What he mostly deals in are the
'complete inductions' and 'well-grounded generalizations'
and so forth, or the exploded errors which contradict them:
the prisoners and the corpses respectively, which the real
discoverer leaves on the field behind him whilst he presses
on to complete his victory. The whole method of science,--expository
as contrasted with militant,--is to emphasize the
distinction between fact and non-fact, and to treat of little
else but these two. In other words a treatise on Inductive
Logic _can_ be written without any occasion being found to
define what is meant by a notion or concept, or even to employ
such terms.
4. And yet, when we come to look more closely, signs
may be detected even within the field of Inductive Logic,
of an occasional breaking down of the sharp distinction in
question; we may meet now and then with entities (to use
the widest term attainable) in reference to which it would
be hard to say that they are either facts or conceptions.
For instance, Inductive Logic has often occasion to make use
of Hypotheses: to which of the above two classes are these
to be referred? They do not seem in strictness to belong to
either; nor are they, as will presently be pointed out, by any
means a solitary instance of the kind.
It is true that within the province of Inductive Logic
these hypotheses do not give much trouble on this score.
However vague may be the form in which they first present
themselves to the philosopher's mind, they have not much
business to come before us in our capacity of logicians until
they are well on their way, so to say, towards becoming
facts: until they are beginning to harden into that firm
tangible shape in which they will eventually appear. We
generally have some such recommendations given to us as
that our hypotheses shall be well-grounded and reasonable.
This seems only another way of telling us that however
freely the philosopher may make his guesses in the privacy
of his own study, he had better not bring them out into
public until they can with fair propriety be termed facts,
even though the name be given with some qualification, as
by terming them 'probable facts.' The reason, therefore,
why we do not take much account of this intermediate state
in the hypothesis, when we are dealing with the inductive
processes, is that here at any rate it plays only a temporary
part; its appearance in that guise is but very fugitive. If
the hypothesis be a sound one, it will soon take its place as
an admitted fact; if not, it will soon be rejected altogether.
Its state as a hypothesis is not a normal one, and therefore
we have not much occasion to scrutinize its characteristics.
In so saying, it must of course be understood that we are
speaking as inductive logicians; the philosopher in his workshop
ought, as already remarked, to be familiar enough with
the hypothesis in every stage of its existence from its origin;
but the logician's duty is different, dealing as he does with
proof rather than with the processes of original investigation
and discovery.
We might indeed even go further, and say that in many
cases the hypothesis does not present itself to the reader,
that is to the recipient of the knowledge, until it has ceased
to deserve that name at all. It may be first suggested to
him along with the proof which establishes it, he not having
had occasion to think of it before. It thus comes at a single
step out of the obscurity of the unknown into the full possession
of its rights as a fact, skipping practically the intermediate
or hypothetical stage altogether. The original investigator
himself may have long pondered over it, and kept
it present to his mind, in this its dubious stage, but finally
have given it to the world with that amount of evidence
which raises it at once in the minds of others to the level of
commonly accepted facts.
Still this doubtful stage exists in every hypothesis,
though for logical purposes, and to most minds, it exists
in a very fugitive way only. When attention has been
directed to it, it may be also detected elsewhere in Logic.
Take the case, for instance, of the reference of names.
Mill gives the examples of the sun, and a battle, as distinguished
from the ideas of them which we, or children,
may entertain. Here the distinction is plain and obvious
enough. But if, on the other hand, we take the case of
things whose existence is doubtful or disputed, the difficulty
above mentioned begins to show itself. The case of merely
extinct things, or such as have not yet come into existence,
offers indeed no trouble, since of course actually _present_
existence is not necessary to constitute a fact. The usual
distinction may even be retained also in the case of mythical
existences. Centaur and Griffin have as universally recognised
a significance amongst the poets, painters, and heralds
as lion and leopard have. Hence we may claim, even here,
that our conceptions shall be 'truthful,' 'consistent with
fact,' and so on, by which we mean that they are to be in
accordance with universal convention upon such subjects.
Necessary and universal accordance is sometimes claimed
to be all that is meant by 'objective,' and since universal
accordance is attainable in the case of the notoriously fictitious,
our fundamental distinction between fact and conception,
and our determination that our terms shall refer to
what is objective rather than to what is subjective, may with
some degree of strain be still conceived to be tenable even here.
5. But when we come to the case of disputed phenomena
the difficulty re-emerges. A supposed planet or
new mineral, a doubtful fact in history, a disputed theological
doctrine, are but a few examples out of many that might be
offered. What some persons strenuously assert, others as
strenuously deny, and whatever hope there may be of speedy
agreement in the case of physical phenomena, experience
shows that there is not much prospect of this in the case of
those which are moral and historical, to say nothing of theological.
So long as those who are in agreement confine their
intercourse to themselves, their 'facts' are accepted as such,
but as soon as they come to communicate with others all
distinction between fact and conception is lost at once, the
'facts' of one party being mere groundless 'conceptions' to
their opponents. There is therefore, I think, in these cases
a real difficulty in carrying out distinctly and consistently
the account which the Materialist logician offers as to the
reference of names. It need hardly be pointed out that
what thus applies to names or terms applies equally to
propositions in which particular or general statements are
made involving names.
6. But when we step into Probability, and treat this
from the same material or Phenomenal point of view, we can
no longer neglect the question which is thus presented to us.
The difficulty cannot here be rejected, as referring to what is
merely temporary or occasional. The intermediate condition
between conjecture and fact, so far from being temporary
or occasional only, is here normal. It is just the condition
which is specially characteristic of Probability. Hence it
follows that however decidedly we may reject the Conceptualist
theory we cannot altogether reject the use of
Conceptualist language. If we can prove that a given man
will die next year, or attain sufficiently near to proof to
leave us practically certain on the point, we may speak of
his death as a (future) fact. But if we merely contemplate
his death as probable? This is the sort of inference, or
substitute for inference, with which Probability is specially
concerned. We may, if we so please, speak of 'probable
facts,' but if we examine the meaning of the words we
may find them not merely obscure, but self-contradictory.
Doubtless there are facts here, in the fullest sense of the
term, namely the statistics upon which our opinion is ultimately
based, for these are known and admitted by all who
have looked into the matter. The same language may also
be applied to that extension of these statistics by induction
which is involved in the assertion that similar statistics
will be found to prevail elsewhere, for these also may rightfully
claim universal acceptance. But these statements, as
was abundantly shown in the earlier chapters, stand on a
very different footing from a statement concerning the individual
event; the establishment and discussion of the
former belong by rights to Induction, and only the latter
to Probability.
7. It is true that for want of appropriate terms to
express such things we are often induced, indeed compelled,
to apply the same name of 'facts' to such individual contingencies.
We should not, for instance, hesitate to speak of
the fact of the man dying being probable, possible, unlikely,
or whatever it might be. But I cannot help regarding such
expressions as a strictly incorrect usage arising out of a
deficiency of appropriate technical terms. It is doubtless
certain that one or other of the two alternatives must happen,
but this alternative certainty is not the subject of our contemplation;
what we have before us is the _single_ alternative,
which is notoriously uncertain. It is this, and this only,
which is at present under notice, and whose occurrence has
to be estimated. We have surely no right to dignify this
with the name of a fact, under any qualifications, when the
opposite alternative has claims, not perhaps actually equal to,
but at any rate not much inferior to its own. Such language,
as already remarked, may be quite right in Inductive logic,
where we are only concerned with conjectures of such a high
degree of likelihood that their non-occurrence need not be
taken into practical account, and which are moreover regarded
as merely temporary. But in Probability the conjecture
may have any degree of likelihood about it; it may be just
as likely as the other alternative, nay it may be much less
likely. In these latter cases, for instance, if the chances are
very much against the man's death, it is surely an abuse of
language to speak of the 'fact' of his dying, even though we
qualify it by declaring it to be highly improbable. The
subject-matter essential to Probability being the uncertain,
we can never with propriety employ upon it language which
in its original and correct application is only appropriate to
what is actually or approximately certain.
8. It should be remembered also that this state of
things, thus characteristic of Probability, is _permanent_ there.
So long as they remain under the treatment of that science
our conjectures, or whatever we like to call them, never
develop into facts. I calculate, for instance, the chance that
a die will give ace, or that a man will live beyond a certain
age. Such an approximation to knowledge as is thus acquired
is as much as we can ever afterwards hope to get,
unless we resort to other methods of enquiry. We do not, as
in Induction, feel ourselves on the brink of some experimental
or other proof which at any moment may raise it
into certainty. It is nothing but a conjecture of a certain
degree of strength, and such it will ever remain, so long as
Probability is left to deal with it. If anything more is ever
to be made out of it we must appeal to direct experience, or
to some kind of inductive proof. As we have so often said,
individual facts can never be determined here, but merely
ultimate tendencies and averages of many events. I may,
indeed, by a second appeal to Probability improve the
character of my conjecture, through being able to refer it to
a narrower and better class of statistics; but its essential
nature remains throughout what it was.
It appears to me therefore that the account of the Materialist
view of logic indicated at the commencement of this
chapter, though substantially sound, needs some slight reconsideration
and re-statement. It answers admirably so far as
ordinary Induction is concerned, but needs some revision
if it is to be equally applicable to that wider view of
the nature and processes of acquiring knowledge wherein
the science of logic is considered to involve Probability
also as well as Induction.
9. Briefly then it is this. We regard the scientific
thinker, whether he be the original investigator who discovers,
or the logician who analyses and describes the proofs
that may be offered, as surrounded by a world of objective
phenomena extending indefinitely both ways in time, and in
every direction in space. Most of them are, and always will
remain, unknown. If we speak of them as facts we mean
that they are potential objects of human knowledge, that
under appropriate circumstances men could come to determinate
and final agreement about them. The scientific or
material logician has to superintend the process of converting
as much as possible of these unknown phenomena into what
are known, of aggregating them, as we have said above, about
the nucleus of certain data which experience and observation
had to start with. In so doing his principal resources are
the Methods of Induction, of which something has been
said in a former chapter; another resource is found in the
Theory of Probability, and another in Deduction.
Now, however such language may be objected to as
savouring of Conceptualism, I can see no better compendious
way of describing these processes than by saying that we are
engaged in getting at conceptions of these external phenomena,
and as far as possible converting these conceptions
into facts. What is the natural history of 'facts' if we trace
them back to their origin? They first come into being as
mere guesses or conjectures, as contemplated possibilities
whose correspondence with reality is either altogether disbelieved
or regarded as entirely doubtful. In this stage, of
course, their contrast with facts is sharp enough. _How_ they
arise it does not belong to Logic but to Psychology to say.
Logic indeed has little or nothing to do with them whilst
they are in this form. Everyone is busy all his life in entertaining
such guesses upon various subjects, the superiority of
the philosopher over the common man being mainly found in
the quality of his guesses, and in the skill and persistence
with which he sifts and examines them. In the next stage
they mostly go by the name of theories or hypotheses, when
they are comprehensive in their scope, or are in any way on
a scale of grandeur and importance: when however they are
of a trivial kind, or refer to details, we really have no distinctive
or appropriate name for them, and must be content
therefore to call them 'conceptions.' Through this stage
they flit with great rapidity in Inductive Logic; often the
logician keeps them back until their evidence is so strong
that they come before the world at once in the full dignity
of facts. Hence, as already remarked, this stage of their
career is not much dwelt upon in Logic. But the whole
business of Probability is to discuss and estimate them at
this point. Consequently, so far as this science is concerned,
the explanation of the Material logician as to the reference
of names and propositions has to be modified.
10. The best way therefore of describing our position
in Probability is as follows:--We are _entertaining a conception_
of some event, past, present, or future. From the nature
of the case this conception is all that can be actually entertained
by the mind. In its present condition it would be
incorrect to call it a fact, though we would willingly, if we
could, convert it into such by making certain of it one way
or the other. But so long as our conclusions are to be
effected by considerations of Probability only, we cannot do
this. The utmost we can do is to _estimate_ or _evaluate_ it.
The whole function of Probability is to give rules for so
doing. By means of reference to statistics or by direct
deduction, as the case may be, we are enabled to say how
much this conception is to be believed, that is in what proportion
out of the total number of cases we shall be right
in so doing. Our position, therefore, in these cases seems
distinctly that of entertaining a conception, and the process
of inference is that of ascertaining to what extent we are
justified in adding this conception to the already received
body of truth and fact.
So long, then, as we are confined to Probability these
conceptions remain such. But if we turn to Induction we
see that they are meant to go a step further. Their final
stage is not reached until they have ripened into facts, and
so taken their place amongst uncontested truths. This is
their final destination in Logic, and our task is not accomplished
until they have reached it.
11. Such language as this in which we speak of our
position in Probability as being that of entertaining a conception,
and being occupied in determining what degree of
belief is to be assigned to it, may savour of Conceptualism,
but is in spirit perfectly different from it. Our ultimate
reference is always to facts. We start from them as our data,
and reach them again eventually in our results whenever it
is possible. In Probability, of course, we cannot do this in
the individual result, but even then (as shown in Ch. VI.) we
always _justify_ our conclusions by appeal to facts, viz. to what
happens in the long run.
The discussion which has been thus given to this part of
the subject may seem somewhat tedious, but it was so obviously
forced upon us when considering the distinction
between the two main views of Logic, that it was impossible
to pass it over without fear of misapprehension and confusion.
Moreover, as will be seen in the course of the next
chapter, several important conclusions could not have been
properly explained and justified without first taking pains
to make this part of our ground perfectly plain and satisfactory.