There Are No Possible Grounds For Induction
Classic Philosophical Questions Part 5 - Knowledge
David Hume, from An Enquiry Concerning Human Understanding
Kem Stone - 3 December 2007
This is one of the most impressive philosophical arguments that I came across during my undergraduate studies in
philosophy.  At the time I was leaning much closer to universal scepticism and to read such a solid argument
questioning the justification for making inferences about future events based on past experiences of cause and
effect was one of those things I had never even considered but upon realising it felt ten times more enlightened
than ever before.  This renders absolutely
all scientific knowledge uncertain, because all scientific knowledge rests
on the presupposition that any cause will always produce the same effect; that the future will always resemble the
past.  But when given careful consideration, this proposition, which we all take for granted without even a second
thought, is actually not based on solid reasoning at all, but mere assumption.

Hume begins his brilliant argument by drawing the essential distinction between the two types of objects of human
reason: Relations of Ideas and Matters of Fact.  This is the old distinction between
a priori knowledge, things that
can be known purely through the operation of reason such as mathematics, and
a posteriori knowledge which is
what we learn through experience and includes all of the natural sciences.  The justification for claims regarding
Relations of Ideas is clear: if a proposition is contradictory or contrary to something already known to be true, it is
false.  But when it comes to Matters of Fact, we rely on past experience for justification, and Hume asks a
question that perhaps nobody before him had ever thought to ask: “What is the nature of that evidence which
assures us of any real existence and matter of fact beyond the present testimony of our senses or the records of
our memory?” (312). In other words, what justifies the appeal to past experience to justify a proposition?

A moment’s thought will make it clear that all such reasoning is founded on the relation of Cause and Effect, by
which we can make claims that go beyond our immediate sensory evidence.  Our reason for holding any factual
belief is an appeal to another reason.  Suppose you are asked why it is snowing.  Your answer will be that it is
cold outside, and this has frozen the water in the air which falls to the ground in the form of snow instead of rain.  
Your answer presupposes a causal connection between the air temperature and the form of precipitation we are
experiencing.  Yet if there were no solid principle to bind the one state of affairs to the other, your inference would
be entirely precarious.  For your answer to be justified, it must be based on a solid principle that can assure us
that precipitation does indeed depend on air temperature.

Hume makes the assertion that the relation of Cause and Effect “is not, in any instance, attained by reasoning
a
priori
; but arises entirely from experience, when we find that any particular objects are constantly conjoined with
each other” (313).  Hume then repeats the conclusion he formed through his argument in the preceding section
defining necessary (causal) connection as a purely mental relation, formed only as a result of witnessing a certain
type of event always followed by the same type of event.  The sensible qualities of an object, such as a billiard
ball, can never produce in the mind an idea of its potential effect, in this case the communication of motion when it
strikes another ball.  We only form an idea of this effect after witnessing the event repeatedly.  “Were any object
presented to us, and were we required to pronounce concerning the effect which will result from it, without
consulting past observation, after what manner, I beseech you, must the mind proceed in this operation?  It must
invent or imagine some event, which it ascribes to the object as its effect; and it is plain that this invention must be
entirely arbitrary” (314).  It is not in any way contradictory to reason to assume that these billiard balls will remain
at rest, or that one will not communicate its motion to the other but be stopped dead in its place or even bounce
back in the other direction.  We only discover the actual effect through repeated observation.

All effects are therefore distinct from their causes, and thus we cannot justify any inductive claim regarding Matters
of Fact by appealing to the relation of Cause and Effect.  The aim of the sciences is to reduce all natural
phenomena to the greatest possible simplicity by pinpointing a few general causes from which all things in
existence have resulted.  We are much closer to the achievement of that goal than the time in which Hume wrote
this argument, and scientists believe they have reduced the universe to four general causes including gravity,
electromagnetism, and the strong and weak nuclear forces.  However, “as to the cause of these general causes,
we should in vain attempt their discovery” (314).  Though the search continues, to date we can only know of the
effects of gravity and only guess as to its cause.  And even if this cause were to be discovered we would then be
left with a new cause with an unknown cause.  There is no foundation in any necessary principle, and therefore
Cause and Effect fail to fully justify claims regarding matters of fact.

Returning to the main question, Hume again asks what the foundation of all conclusions regarding matters of fact
is.  The answer seems to be the relation of Cause and Effect, but from the arguments above we find that this
answer is inadequate, and must ask what our foundation for conclusions based on that relation is.  In a word, the
answer is experience, but we are now faced with the very difficult matter of determining the foundation of all
conclusions from experience.  Hume admits he can only give a negative answer, that the foundation cannot be
formed by a process of reasoning.  The sensible qualities of bread, for instance, give us no rational clue as to its
secret powers of nourishment, and we only assume that similar substances will also provide similar nourishment
because this has always been the case in the past.

But our past experience only provides us with direct and certain information regarding those precise objects at
that precise time, relegating our belief that they will behave exactly the same in the future to mere assumption.  
“These two propositions are far from being the same; I have found that such an object has always been attended
with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with
similar effects.  I shall allow, if you please, that the one proposition may justly be inferred from the other…But if
you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning” (316).  As
useful as the supposition may be, there is no
a priori foundation for the belief that the future will resemble the past.

Hume states that there are two types of reasoning: demonstrative and moral.  Demonstrative reasoning which
concerns relations of ideas can not provide us with a justification for conclusions regarding experience.  It is not
logically contradictory to assume that because snow is cold today it will not be as hot as fire tomorrow.  It may be
absurd on the level of common sense but there is nothing inherently contradictory about it.  Therefore any
argument that requires us to put our trust in past experience must rest solely on the
probability that objects will
behave in the future just as they have in the past.  Now does it resolve our dilemma to suggest that we can reach
certainty in such matters when they are supported by multiple experiences: “It is only after a long course of
uniform experiments in any kind, that we attain a firm reliance and security with regard to a particular event.  Now
where is that process of reasoning, which, from one instance, draws a conclusion so different from that which it
infers from a hundred instances that are nowise different from that single one?” (317). If we cannot be certain that
water will boil at a particular temperature after witnessing this
once,  we also cannot be certain that water will
always boil at this temperature even after witnessing it hundreds of times.

We have only established that when we witness similar effects followed by similar experiences in multiple
instances, we form a connection between these two events in our mind and come to expect one whenever
presented with the other.  “For all inferences from experience suppose, as their foundation, that the future will
resemble the past, and that similar powers will be conjoined with similar sensible qualities.  If there be any
suspicion that the course of nature may change, and that the past may be no rule for the future, all experience
becomes useless, and can give rise to no inference or conclusion” (318).  No argument from experience can
prove the resemblance of the future to the past, as all such argument rest on the presupposition of that
resemblance.

In the next section, Hume moves beyond the purely negative answer and attempts to pin-point what justification
we actually do rely on when making claims regarding matters of fact.  Regardless of our arguments, Hume admits,
nature will always prevail, and the future will most likely continue to resemble the past even if we have no proof.  
Yet we still make the assumption, and Hume seeks to find what exactly it is, if not a concrete rational principle,
that we base this assumption on.

Hume introduces a thought experiment in which he asks us to imagine a man endowed with strong faculties of
reason to be thrust suddenly into this world.  He will observe a continual succession of events, but will be unable
to discover anything beyond this.  He will observe one event following another but there will be no reason for him
to infer the existence of one from the appearance of the other.  But if we imagine that he remains in this world for a
longer duration and acquires more experience, in all likelihood he
will begin to infer a causal relation between
events.  “Yet he has not, by all his experience, acquired any idea or knowledge of the secret power by which the
one object produces the other; nor is it, by any process of reasoning, he is engaged to draw this inference…There
is some other principle which determines him to form such a conclusion” (319).

That principle, Hume asserts, is nothing more than Custom or Habit.  Whenever the repetition of a particular act
or operation brings about a propensity to renew the same operation, we call this the effect of Custom.  It is
Custom that is really at the heart of our assumptions concerning cause and effect, as the repetition of one
particular event following another produces a propensity within us to infer that the one event will always follow the
other.  “This hypothesis seems even the only one which explains the difficulty, why we draw, from a thousand
instances, an inference which we are not able to draw from one instance that is, in no respect, different from them”
(319).  We can draw the same inferences from one circle as we can from a thousand circles, but no man can infer
after witnessing the behaviour of one body that all like bodies will behave in the same manner.  Thus all of our
inferences from experience are effects of custom rather than reasoning.

But Hume concludes by noting that no conclusions can be drawn from experience by custom alone without at
least one fact present to the senses or memory from which our inferences can first proceed.  A man wandering in
the desert, stumbling upon the remains of large buildings would infer that a civilisation had once dwelt there.  Yet if
he had no knowledge of civilisation or had never seen a building before, he would be unable to draw this
inference.  “If I ask why you believe any particular matter of fact which you relate, you must tell me some reason;
and this reason will be some other fact connected with it.  But as you cannot proceed after this manner,
in
infinitum
, you must at last terminate in some fact which is present to your memory or senses; or must allow that
your belief is entirely without foundation” (320).  Thus Hume’s conclusion is that all beliefs regarding matters of
fact are derived from a customary conjunction between two objects or events, and a fact which is already present
to the memory or senses.

Unless everyone who has ever studied this argument has missed something, it would appear irrefutable.  Indeed it
is one of the most solid chains of reasoning that I have ever encountered in all of the works of philosophy I have
ever read, and I do not cease to be impressed by it.  However, in spite of its genius this argument is completely
without real consequence.  It may be absolutely true that we cannot base our assumption that the future will
resemble the past on any solid rational principle, but we have no choice but to make this assumption.  If we give
up any and all conclusions which have been reached by drawing this kind of inference, we will find ourselves with
a very short supply of knowledge indeed.  This argument only serves to point out the startling lack of certainty we
have regarding all of our beliefs derived through experience, in that its foundation is nothing more than the effect of
custom.

This conclusion points to a fundamental division between the two kinds of beliefs we can form—relations of ideas
and matters of fact.  Hume has shown that there can be no
a priori justification for an a posteriori claim.  One
cannot offer a fact regarding a relation of ideas as proof of a claim regarding a matter of fact.  No logical formula
or mathematical theorem can ever serve to justify a claim regarding gravity or any other natural phenomenon.  Nor
can a purely rational claim ever have a justification derived through experience.  That the square of the hypotenuse
of a right triangle is equal to the square of the remaining sides is not justified by our drawing the triangle and
measuring the sides, but is justified purely because its falsehood is a logical impossibility.  There is only one
instance in which an
a posteriori claim may be justified by an a priori principle, and this is existential necessity.  
Yet because there are no necessary beings within existence, this only works in the case of existence itself.  It
would be contradictory for
nothing to exist, as non-existence by its very nature can not exist.  The existence of
non-existence is contradictory, and here you have the only empirical claim that can be justified by a rational
principle.

Hume has successfully shown that there is no foundation in certainty for any of our knowledge based on
experience, but nor is there any certain foundation for knowledge derived through pure reason.  All a priori
knowledge rests on the principle of contradiction, but this principle itself is not immune to doubt.  If it could be the
case that the sum of two and two could at the same time equal and
not equal four, all of our rational beliefs would
be called into question; just as all of our empirical beliefs would be called into question if we had but proof of a
single miracle, such as the defiance of gravity or the complete disappearance of a quantity of matter from the
universe.  The more thought we give to epistemology, the more we seek to uncover the fundamental principles
upon which all of our knowledge is founded, the more we find that these principles are indeed fallible, and thus
that absolute certainty regarding anything other than the existence of existence is beyond reach.