THE LIMITS OF INFERENCE
"The question in what cases we may believe that
which goes beyond our experience, is a very large and delicate one,
extending to the whole range of scientific method, and requiring a
considerable increase in the application of it before it can be
answered with anything approaching to completeness. But one rule, lying
on the threshold of the subject, of extreme simplicity and vast
practical importance, may here be touched upon and shortly laid down."
The rule Clifford has in mind
will be discussed below, but here it should be remarked that his
opening question - "in what cases we may believe
that which goes beyond our experience" - is a basic one, and
covers many problems of the philosophy of science, such as relates to
scientific methodologies; the problem of induction; the questions what
characterizes good statistics and what is probability, and more.
Also, he is right that these are
difficult questions to answer rationally, and he would have been right
had he added that each science has its own methodological problems,
while what makes a science into science is a core of tested
rational methods to learn from experience and to objectively test,
control and where possible and necessary improve and revise any results
of these rational methods.
An excellent modern text that
contains much relevant knowledge and ideas of these kinds is: Wolfgang Stegmüller:
Probleme und Resultate der Wissenschaftstheorie und Analytische
Philosophie. (Four thick or some 25
thin volumes. I have been told it has been translated, but never saw
the translation, that contains the words "philosophy of science" in the
title. Much recommended to anyone interested in rational belief of any
"A little reflection will show us that every
belief, even the simplest and most fundamental, goes beyond experience
when regarded as a guide to our actions. A burnt child dreads the fire,
because it believes that the fire will burn it to-day just as it did
yesterday; but this belief goes beyond experience, and assumes that the
unknown fire of to-day is like the known fire of yesterday. Even the
belief that the child was burnt yesterday goes beyond present
experience, which contains only the memory of a burning, and not the
burning itself; it assumes, therefore, that this memory is trustworthy,
although we know that a memory may often be mistaken."
Precisely - the experience we
really have is limited to "the specious present", which has an extent
of a few seconds at most. And as I pointed put before: There simply is
no possibility of testing a theory without predictions which go beyond
known experience, nor is a theory any use to guide one's actions if it
doesn't go beyond such experiences as one has or remembers.
"The question is not, therefore, "May we believe
what goes beyond experience?" for this is involved in the very nature
of belief; but "How far and in what manner may we add to our experience
in forming our beliefs?" "
Indeed. I shall below discuss
Clifford's - consciously partial and superficial - recommendation, and
here refer the interested reader to my On
Principles Of Scientific Explanation. Text.
"And an answer, of utter simplicity and
universality, is suggested by the example we have taken: a burnt child
dreads the fire. We may go beyond experience by assuming that what we
do not know is like what we do know; or, in other words, we may add to
our experience on the assumption of a uniformity in nature. What this
uniformity precisely is, how we grow in the knowledge of it from
generation to generation, these are questions which for the present we
lay aside, being content to examine two instances which may serve to
make plainer the nature of the rule."
The principle Clifford proposes
is: "We may go beyond experience by assuming that
what we do not know is like what we do know; or, in other words, we may
add to our experience on the assumption of a uniformity in nature."
Actually, there are somewhat
better formulations and motivations. Clifford himself provides a better
formulation than "assumption of a uniformity in
nature", which is too general and unspecific in many cases,
namely "what we do not know is like what we do
know", which merely counsels us to rely (rather than not) on
whatever we have established by careful reasoning and experimentation.
Next, the kind of principle
Clifford has in mind has been formulated several times explicitly,
possibly first by the Chinese. Here is a beautiful quotation from
Robert Temple's "The
genius of China" (that popularizes Joseph Needham's work):
formulated his First Law of Motion in the eighteenth century. It stated
that 'every body continues in its state of rest, or uniform motion in a
right line, unless it is compelled to change that state by forces
impressed upon it.
have now established that this law was stated in China in the third or
fourth centuty BC. We read in the Mo Ching: 'The cessation of
motion is due to the opposing force... If there is no opposing force
... the motion will never stop. This is as true as that an ox is not a
horse." (p. 161)
Furthermore, Newton's First Law
of Motion was closely related to a methodological principle Newton
formulated himself as follows below, namely as his Third Rule of
Reasoning, as Clifford undoubtedly knew.
of Reasoning minus his comments are as follows, where it should
be realised that in the following quotation Newton meant by "experimental
philosophy" what we call "natural science" and that a
shorter version of "which admit neither intensifcation nor remission
of degrees" is "which are invariant". Newton added these
rules to the second edition of his Principia, in 1714:
Rule I :
We are to admit no more causes of natural things than such as are both
true and sufficient to explain their appearances.
Rule II : Therefore to the same natural effects
we must, as far as possible, assign the same reasons.
Rule III : The qualities of bodies, which admit
neither intensification nor remission of degrees, and which are found
to belong to all bodies within the reach of our experiments, are to be
esteemed the universal qualities of all bodies whatsoever.
Rule IV : In experimental philosophy we are to
look upon propositions inferred by general induction from phenomena as
accurately or very nearly true, notwithstanding any contrary hypotheses
that may be imagined, till such time as other phenomena occur, by which
they may be either made more accurate, or liable to exception.
So what Clifford proposes is much
like Newton's Rules II to IV, simplified to their common essence.
Finally, I have shown elsewhere
these rules can be mostly argued rationally with the help of
probability theory, and note here that there is a principle at the
bottom of them that can be stated simply thus:
- Human beings can learn from
For if they can, they
must use such knowledge as they believe they have to find more and to
correct what was mistaken - and that they can do so is shown
by scientific technology: The very many thousands of human artifacts
made with the help of scientific theories, that show these theories are
far bettter tools to explain and improve the world than the far less
rational or tolerant religious or political creeds. Text.
"But this is the kind of assumption which we are
justified in using when we add to our experience. It is an assumption
of uniformity in nature, and can only be checked by comparison with
many similar assumptions which we have to make in other such cases."
Yes, but as I pointed out in Note 84, it is usually more sensible to make the
assumption more specific: What will probably happen is like what mostly
happened so far.
Furthermore, the Chinese version
I quoted above has the nice feature that it suggests the following form
- Things will continue to happen
as they did before, unless there is a reason they don't.
Hence, if we know of no reason
that what has been happening so often before will happen again, then
our best guess about what will happen is that it will happen
Perhaps it is well to also
briefly indicate the reasons why this is rational to believe:
First, see Note
84. Next, supposing that theories are attempts to explain features
of things in each and any circumstances, to the extent that our
theories have been reliable in the past and to the extent that they
have good evidence, they may be relied upon to keep working if there
are no intervening reasons. Text.
"But is this a true belief (..)? Can it help in
the right guidance of human action?
Certainly not, if it is accepted on unworthy grounds, and without some
understanding of the process by which it is got at. But when this
process is taken in as the ground of the belief, it becomes a very
serious and practical matter."
Well, it certainly is a belief
that in very many distinct known cases has been true in the past, to
the best of our knowledge.
Furthermore, as I pointed out in Note 59, the whole
notion of human scientific knowledge of reality, that has produced so
much technology, discoveries and inventions that would not exist
without it, and that surely shows that mankind has some real
knowledge about the real world they are all part of, is based on the
possibility of guessing that certain general statements
are true, that represent some real feature(s) of some real thing(s) in
general, in all circumstances and at all times, and until we have found
evidence this is not so in some circumstances, for some
And in the end the best argument
for the scientific method, for science, and for rational thinking are
the very many discoveries and inventions that would not exist without
science, and that were wholly beyond the grasp or dreams of all systems
of religious faith and all Holy Books supposedly informed by divine
infinite knowledge. Text.
"Whereas the acceptance of the spectroscopic
method as trustworthy has enriched us not only with new metals, which
is a great thing, but with new processes of investigation, which is
This is a point Clifford made
before, but which stands repeating: Far more important than actual
results, which are always particular, are general rational methods and
tools by which new results can be found. Text.
"We find also that men do not, as a rule, forge
books and histories without a special motive; we assume that in this
respect men in the past were like men in the present; and we observe
that in this case no special motive was present. That is, we add to our
experience on the assumption of a uniformity in the characters of men.
Because our knowledge of this uniformity is far less complete and exact
than our knowledge of that which obtains in physics, inferences of the
historical kind are more precarious and less exact than inferences in
many other sciences."
Here we have an application of
Clifford's rule - say: "what we do not know is
like what we do know" - to the science of history. Actually, we
need not make "the assumption of a uniformity in
the characters of men", but only need to count or get a good
approximate idea of the number of forged histories and of the number of
non-forged histories. As a matter of fact, the latter - especially if
restricted to such books as have been seriously considered and
discussed by historians and other intelligent knowledgeable men - is
far greater than the former, and all that remains is to apply
Clifford's rule to this to get his conclusion. Text.
"We may, then, add to our experience on the
assumption of a uniformity in nature; we may fill in our picture of
what is and has been, as experience gives it us, in such a way as to
make the whole consistent with this uniformity. And practically
demonstrative inference—that which gives us a right to believe in the
result of it—is a clear showing that in no other way than by the truth
of this result can the uniformity of nature be saved. No evidence,
therefore, can justify us in believing the truth of a statement which
is contrary to, or outside of, the uniformity of nature."
This is not quite true, and the
main reason is that, since Clifford lived, the rise of quantum
mechanics has made it necessary to assume that there are real chance
processes in nature. Put otherwise: The "assumption
of a uniformity in nature" can only be retained in the sense
that what remains uniform is a statistical distribution of otherwise
principially unpredictable events. Text.
"If our experience is such that it cannot be
filled up consistently with uniformity, all we have a right to conclude
is that there is something wrong somewhere; but the possibility of
inference is taken away; we must rest in our experience, and not go
beyond it at all. If an event really happened which was not a part of
the uniformity of nature, it would have two properties: no evidence
could give the right to believe it to any except those whose actual
experience it was; and no inference worthy of belief could be founded
upon it at all."
Again, this is not quite so. What
does seem true to me is sketched in Notes 84
- 86, to which I can add the following:
What we seek are adequate
explanations of natural things, events and processes, and to do so we
need sufficient experience of what we try to explain to know that we
can be more certain than not that quite a few things remain invariable,
and can can be predicted and foreseen from a proper interpretation of
their past, if this is known and well understood.
Furthermore, to explain anything
at all we must have some idea what it may be like, and the only way we
can find such an idea is by using our imagination about what we believe
we know has happened in nature so far.
Finally, it is a tested and often
verified truth that things will continue to happen as they did before
unless and until there is a reason they don't, and this truth we may
use both to derive and to test predictions, and indeed we normally do
and did so even if we are not conscious of this. Text.
"Are we then bound to believe that nature is
absolutely and universally uniform? Certainly not; we have no right to
believe anything of this kind. The rule only tells us that in forming
beliefs which go beyond our experience, we may make the assumption that
nature is practically uniform so far as we are concerned. Within the
range of human action and verification, we may form, by help of this
assumption, actual beliefs; beyond it, only those hypotheses which
serve for the more accurate asking of questions."
Yes, here Clifford is again quite
right, and argues along the lines of my comments in this section.
Also, his idea that there are "hypotheses which serve for the more accurate asking of
questions" is sensible - and indeed one often must make
suppositions, see whether these are confirmed, and then take it from
there to try to account imaginatively to explain such results as one
found. (For more see my On
Principles Of Scientific Explanation.) Text.
"We may believe what goes beyond our experience,
only when it is inferred from that experience by the assumption that
what we do not know is like what we know."
No, not quite, for there is a
slight complication: We also know from experience that many things
can't continue to do what they did for a long time. Men die eventually;
a piece of iron that is bend and bend again eventually breaks; elastic
bands remains elastic a long time but then grow brittle, and so on.
But Clifford is right that these
facts are also known from experience, and that to suggest that
something will end that has gone for some time we need some evidence to
the effect that something like it has ended. Text.
"We may believe the statement of another person,
when there is reasonable ground for supposing that he knows the matter
of which he speaks, and that he is speaking the truth so far as he
Precisely - and usually, as men
are on average, more to the point: We need not believe a
statement of another person, however honest and sincere that person may
be, if we have no reason to believe he knows of what he speaks and no
reason to believe that he is honest. Text.
"It is wrong in all cases to believe on
insufficient evidence; and where it is presumption to doubt and to
investigate, there it is worse than presumption to believe."
And this is Clifford's dictum
plus another very memorable claim that may be restated thus: You have
no right to claim any rational belief in cases where you have no right
to doubt and investigate, and about cases where you never doubted nor