Notes to Section IV:
Sceptical doubts concerning the operations of the understanding
All the objects of human reason or
enquiry may naturally be divided into two kinds, to wit, Relations
of Ideas, and Matters of Fact. Of the first kind are the
sciences of Geometry, Algebra, and Arithmetic; and in short, every
affirmation which is either intuitively or demonstratively certain.
This is one of Hume's
principles, that incidentally reminds one of a similar distinction by Leibniz between truths
fact and truths of reason. In either case, the
distinction seems to me to be incomplete, and to miss something quite
important, that may be referred to in Humean terms as Relations of
Ideas and Facts, or in modern terms: Semantical Relations.
As the terms chosen indicate,
the best and easiest examples of such relations are those that obtain
between the terms of a natural language and the natural
things they stand for, whatever they may be.
Also, it is clear that these
relations must be learned, and have been learned to a
considerable extent by anyone who knows a natural language, and indeed
have been learned on the basis of associations of the sounds of speech
and the facts of experience.
Furthermore, it is clear that
these semantical relations relate ideas and facts with
the help of the sounds of speech, and that it would be more
confusing than helpful to try to reduce these Semantical Relations
to either Relations of Ideas or Matters of Fact,
precisely because they connect the two, and must be learned,
and involve natural language, and are characteristic for human
beings, since other animals may as well be claimed to have some
Relations of Ideas and to know some Matters of Fact, but evidently lack
the ideas required for language that would allow them to tie the two
together by speech, and use that to communicate the ideas that have
thus been associated to the sounds of speech.
Indeed, it is a curious fact
that Hume missed this third kind of fundamental relation, and also that
I have not read others who made the same point after him, though it
struck me when I first read the Treatise and the Enquiries.
And it is at least fairly
obvious that there are in fact three kinds of reports:
- on reality
- on experience
- on symbolizations
These three kinds of reports
obviously exist, and there are considerable and systematic differences
between them. Reports of real things concern what is there regardless
of experience, and this may and often does differ a lot from
reports of experiences of things. And these in turn tend to be rather
different from symbolizations in the wide sense of stories, drawings,
etc. which involve interpretations of the symbols.
Finally, it should be
mentioned here that arguments that involve what is called 'Hume's
Fork' are such as to presume that human reason only
involves two kinds of fundamental entities 'to
wit, Relations of Ideas, and Matters of Fact',
and may well be mistaken in missing the Semantical Relations,
which are typically human (if indeed not Humean).
Matters of fact, which are the second
objects of human reason, are not ascertained in the same manner; nor is
our evidence of their truth, however great, of a like nature with the
foregoing. The contrary of every matter of fact is still possible;
because it can never imply a contradiction, and is conceived by the
mind with the same facility and distinctness, as if ever so conformable
to reality. That the sun will not rise to-morrow is no less
intelligible a proposition, and implies no more contradiction than the
affirmation, that it will rise. We should in vain, therefore,
attempt to demonstrate its falsehood. Were it demonstratively false, it
would imply a contradiction, and could never be distinctly conceived by
This seems mostly so, and to
be a relevant distinction, but it is unclear in at least three respects.
First, although Hume uses the
term 'Matters of fact' what he often
though not always seems to mean are sensations, that inform us
about facts, but that do not coincide with them.
Second, and related to the
first point, there is the fact that some sensations - such as an oar
dipped in the water that appears bend while it is straight - are known
to be illusive.
Third, and related to both
foregoing points, there are some facts, notably geometrical diagrams,
that may seem necessary in some sense. Thus, a Euclidean triangle has
angles that sum to 180 degrees.
Of these points, the last two
are of relatively minor importance, and possibly in the nature of
nit-picking, but the first confusion, that of Matters of Fact
and Sensations, is of some importance to Hume's arguments.
It may, therefore, be a subject worthy of
curiosity, to enquire 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. This part of
philosophy, it is observable, has been little cultivated, either by the
ancients or moderns; and therefore our doubts and errors, in the
prosecution of so important an enquiry, may be the more excusable;
while we march through such difficult paths without any guide or
Here Hume has started to
prepare the reader for his new ideas concerning Cause and Effect, in
which he knew himself to be an innovator. I will turn to this in
further notes, but want to record here a general answer to his implied
question what it is that 'assures us of any real
existence and matter of fact, beyond the present testimony of our senses'.
The answer is in two words:
Experiment and assumption. That is: We know matters of
fact, apart from teaching and reports, by our senses; we secure such
testimony of our senses by experiments; and if we are convinced that
our senses have not deceived us we may make an assumption to that
effect, and assert a certain kind of - presumptive - fact, such as that
birds lay eggs or that copper conducts electricity.
Now one may well ask what
would justify such an assumption, and in fact there was in Hume's time
a clear answer to that question, namely by Newton, who had added to the
1714-edition of his Principia a set of Rules of Reasoning.
Rules of Reasoning minus his comments (to some of which I will
return) are the following, 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
of degrees" is "which
: 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.
There is a complete version of
Philosophy, including Newton's explanations, on my
Hence, when Hume writes 'This part of philosophy, it is observable, has been
little cultivated, either by the ancients or moderns' he sounds
somewhat disingenuous, especially since he does not even mention Newton
here. (He does refer to these Rules in a footnote in the Enquiry
concerning the Principles of Morals, though.)
However, when Hume writes,
with my added stress 'It may, therefore, be a
subject worthy of curiosity, to enquire 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'
makes sense, and that I shall try to answer below.
For the moment I observe that
Newton's Rules III and IV do clearly assert that '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' and that 'The qualities of bodies [which are invariant - M] (..) 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' and that it is rather inconceivable to me
that Hume did not know these "Rules of Reasoning in Philosophy".
All reasonings concerning matter of fact
seem to be founded on the relation of Cause and Effect. By
means of that relation alone we can go beyond the evidence of our
memory and senses. If you were to ask a man, why he believes any matter
of fact, which is absent; for instance, that his friend is in the
country, or in France; he would give you a reason; and this reason
would be some other fact; as a letter received from him, or the
knowledge of his former resolutions and promises. A man finding a watch
or any other machine in a desert island, would conclude that there had
once been men in that island. All our reasonings concerning fact are of
the same nature.
Hume is going to be quite
skeptical about this 'relation of Cause and
Effect', and therefore it is well to stress that he wrote
that 'All reasonings concerning matter of fact seem
to be founded' on it.
Also, it makes sense to remark
here that Hume is quite correct in the examples he provides, but that
he does not mention that in natural language the terms 'cause'
and 'effect' are often used as 'reason' or 'premise'
'consequence' or 'conclusion', and are often
used in the sense that what is termed the cause is a sufficient reason
to infer in conclusion what is termed the effect.
If we anatomize all the other reasonings
of this nature, we shall find that they are founded on the relation of
cause and effect, and that this relation is either near or remote,
direct or collateral. Heat and light are collateral effects of fire,
and the one effect may justly be inferred from the other.
This is so only with the
proviso indicated in the previous note, namely that in our reasonings
about nature what we use as reasons or premisses are often called
causes, and what we use as conclusions from these reasons or premisses
are often called effects.
Hume is right that often by
the use of the phrases 'cause and effect' more
is suggested than would be meant had the words 'premise and conclusion'
been used, but it is not the case that this is always so, and indeed
the Ancients already were aware that there are such things as probable
causes, i.e. events that more likely than not have a certain effect,
but not invariably so. An obvious example is "In summer it is warm in
the daytime, usually".
If we would satisfy ourselves, therefore,
concerning the nature of that evidence, which assures us of matters of
fact, we must enquire how we arrive at the knowledge of cause and
This surely is a valid
inquiry, but it should be pointed out, as I did in previous notes, that
'we arrive at the knowledge of cause and effect'
causes, and our deductions from our
I shall venture to affirm, as a general
proposition, which admits of no exception, that the knowledge of this
relation is not, in any instance, attained by reasonings a priori;
but arises entirely from experience, when we find that any particular
objects are constantly conjoined with each other. Let an object be
presented to a man of ever so strong natural reason and abilities; if
that object be entirely new to him, he will not be able, by the most
accurate examination of its sensible qualities, to discover any of its
causes or effects. Adam, though his rational faculties be supposed, at
the very first, entirely perfect, could not have inferred from the
fluidity and transparency of water that it would suffocate him, or from
the light and warmth of fire that it would consume him. No object ever
discovers, by the qualities which appear to the senses, either the
causes which produced it, or the effects which will arise from it; nor
can our reason, unassisted by experience, ever draw any inference
concerning real existence and matter of fact.
Kant, who was 'awoken from his
slumbers' by reading Hume's Enquiries in reaction did 'venture to affirm' that there is an 'a priori' idea of the notion of cause and
I want to avoid considering
Kant, whose reasonings I find generally at least as obscure as his
prose, but should, I think, remind the reader of Kant's reaction, and
the fact that since Hume seems to have denied the existence of innate
ideas, this attempted solution was not open for him. (But see Notes 12
and 14 to Section
In any case, whatever notions
one is born with, Hume's examples in the quotation are adequate, and we
may conclude that whether or not we have an innate tendency to reason
in terms of causes and effects, the actual discovery of such a presumed
relation between a particular cause and its particular effect
must be made in experience.
Incidentally, and without
thinking it necessary to explain Hume's English, by the phrase 'No object ever discovers' he meant 'No object
ever clearly shows'.
This proposition, that causes and
effects are discoverable, not by reason but by experience, will
readily be admitted with regard to such objects, as we remember to have
once been altogether unknown to us; since we must be conscious of the
utter inability, which we then lay under, of foretelling what would
arise from them.
This I accept, given the
provisos I have made in earlier notes, and with a proviso in the next
Such events, as bear little analogy to
the common course of nature, are also readily confessed to be known
only by experience; nor does any man imagine that the explosion of
gunpowder, or the attraction of a loadstone, could ever be discovered
by arguments a priori. In like manner, when an effect is
supposed to depend upon an intricate machinery or secret structure of
parts, we make no difficulty in attributing all our knowledge of it to
I once again refer to my Notes
12 and 14 to
II and ask, in Hume's own
terms used there "what can be meant by asserting,
that (..) the passion between the sexes is not innate?". Indeed,
the modern answer is that this is caused by hormones acting on
capacities one is born with. But I agree with Hume that even so each
young man and young woman will have to discover this for himself and
We are apt to imagine that we could
discover these effects by the mere operation of our reason, without
experience. We fancy, that were we brought on a sudden into this world,
we could at first have inferred that one Billiard-ball would
communicate motion to another upon impulse; and that we needed not to
have waited for the event, in order to pronounce with certainty
concerning it. Such is the influence of custom, that, where it is
strongest, it not only covers our natural ignorance, but even conceals
itself, and seems not to take place, merely because it is found in the
This I select because I agree
with it and because I want to stress Hume's appeal to 'the influence of custom'.
But to convince us that all the laws of
nature, and all the operations of bodies without exception, are known
only by experience, the following reflections may, perhaps, suffice.
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.
Here one can agree mostly with
Hume without doing so fully, because it is quite possible and
conceivable that such 'invention' need not
'be entirely arbitrary'. An example is the
discovery of most young men in their puberty that young women are
But in general terms, as with
the supposedly innate human 'grammar' that enables small children to
rapidly learn the grammar of any natural language: What is innate, if
anything, is in all likelihood quite general and abstract, and needs
combination with specific experiences to be developed.
May not both these balls remain at
absolute rest? May not the first ball return in a straight line, or
leap off from the second in any line or direction? All these
suppositions are consistent and conceivable. Why then should we give
the preference to one, which is no more consistent or conceivable than
the rest? All our reasonings a priori will never be able to
show us any foundation for this preference.
Again a caveat must be
introduced: In so far as what we explain is explained by mathematics,
some hypotheses we might make may seem more sensible than others, not
because of what we know about the natural facts we attempt to explain,
but because the mathematical formulas are clearer, simpler or more
beautiful than they would be for other hypotheses we could conceive.
Precisely what weight should
be given to this consideration is difficult to say, but it is a fact
that quite a few prominent physicists have revealed that part of their
motivations to select a certain hypothesis, that later was confirmed
experimentally, was the mathematical beauty of the formulas necessary
to state the hypothesis.
In a word, then, every effect is a
distinct event from its cause. It could not, therefore, be discovered
in the cause, and the first invention or conception of it, a priori,
must be entirely arbitrary. And even after it is suggested, the
conjunction of it with the cause must appear equally arbitrary; since
there are always many other effects, which, to reason, must seem fully
as consistent and natural. In vain, therefore, should we pretend to
determine any single event, or infer any cause or effect, without the
assistance of observation and experience.
This is again a conclusion I
agree to, apart from a few provisos made in previous notes.
Also, it should be remarked
that Hume's general mode of reasoning is much unlike that of the
Scholastics, who tended to presume that all manner of things concerning
the world, human beings and God, could be derived by a priori reasoning.
good examples of this Scholastic mode of
Hence we may discover the reason why no
philosopher, who is rational and modest, has ever pretended to assign
the ultimate cause of any natural operation, or to show distinctly the
action of that power, which produces any single effect in the universe.
It is confessed, that the utmost effort of human reason is to reduce
the principles, productive of natural phenomena, to a greater
simplicity, and to resolve the many particular effects into a few
general causes, by means of reasonings from analogy, experience, and
observation. But as to the causes of these general causes, we should in
vain attempt their discovery; nor shall we ever be able to satisfy
ourselves, by any particular explication of them.
Obviously, this makes most
philosophers before Hume appear to be not so very 'rational
modest', and evidently Hume's reasoning about 'the causes of these general causes' of which 'we should in vain attempt their discovery'
applies especially to the hypothesis of divinities, angels, devils,
supernatural forces etc.
These ultimate springs and principles are
totally shut up from human curiosity and enquiry. Elasticity, gravity,
cohesion of parts, communication of motion by impulse; these are
probably the ultimate causes and principles which we shall ever
discover in nature; and we may esteem ourselves sufficiently happy, if,
by accurate enquiry and reasoning, we can trace up the particular
phenomena to, or near to, these general principles.
See my previous note: Hume did
not believe in the divine hypothesis, and indeed held that it was both
irrational and immodest to pretend to have knowledge of a God or of
God's wishes, and I entirely agree:
It seems far to much like
explaining what goes on in one's home by assuming that there is an
extra floor in one's house that no one can see or discover, that
supposedly includes a puppeteer or director who generates and controls
all or most of what happens in one's house. Indeed, if your neighbour
adopts such a hypothesis about his house, you will very probably regard
him as mad (if not fraudulent, since so many professions of faith turn
out to be profitable) and possibly dangerous, and I myself see little
reason to believe otherwise about the divine hypothesis, except that I
grant that some very intelligent men have also believed it, though very
probably for emotional and not for rational reasons, and because,
unlike me, they were raised in a religious faith.
The most perfect philosophy of the
natural kind only staves off our ignorance a little longer: as perhaps
the most perfect philosophy of the moral or metaphysical kind serves
only to discover larger portions of it. Thus the observation of human
blindness and weakness is the result of all philosophy, and meets us at
every turn, in spite of our endeavours to elude or avoid it.
Here Hume again states part of
the reason for his academical scepticism, and he is certainly right,
apart from the merits of academical scepticism, that it is always wise
to presume that there is very much that any particular man and all men
together do not know, and that there may be much that is too complex
for human beings to know, or to know more than in outline, and
approximately or schematically at best.
Nor is geometry, when taken into the
assistance of natural philosophy, ever able to remedy this defect, or
lead us into the knowledge of ultimate causes, by all that accuracy of
reasoning for which it is so justly celebrated. Every part of mixed
mathematics proceeds upon the supposition that certain laws are
established by nature in her operations; and abstract reasonings are
employed, either to assist experience in the discovery of these laws,
or to determine their influence in particular instances, where it
depends upon any precise degree of distance and quantity.
This is mostly so, but there
is the point I made in Note 12, that part of
the inspiration that led to natural discoveries was the mathematical
beauty or simplicity of formulas. However, it may be conceded that this
shows far less about nature than about the human mind, and that it is
heuristic rather than factual. (Also, one is less likely to hear about
mathematical theories based on beautiful formulas if these failed to be
But we have not yet attained any
tolerable satisfaction with regard to the question first proposed. Each
solution still gives rise to a new question as difficult as the
foregoing, and leads us on to farther enquiries. When it is asked, What
our reasonings concerning matter of fact? the
proper answer seems to be, that they are founded on the relation of
cause and effect. When again it is asked, What is the foundation of
all our reasonings and conclusions concerning that relation? it may
be replied in one word, Experience. But if we still carry on our
sifting humour, and ask, What is the foundation of all conclusions
from experience? this implies a new question, which may be of more
difficult solution and explication.
The answer to that last
question seems to along these lines: Presumption, hypothesis,
assumption - and if one asks once more what are the
foundations of these, the answer seems to be: Imagination, fantasy,
creativity or feelings of beauty - and
the fact that one's hypotheses deductively imply conclusions one should
like to explain by these hypotheses, and deductively imply nothing that
is known to be false, and are consistent with one's further
assumptions, and may have some empirical support that they may be true.
(See below, under abduction.)
And indeed these are the only
means human beings have to generate and support guesses - except, of
course, that it is very wise to check such guesses as one feels one
should make by experiment, and to control them by logic, and in the
light of all other knowledge one supposes oneself to have.
I shall content myself, in this section,
with an easy task, and shall pretend only to give a negative answer to
the question here proposed. I say then, that, even after we have
experience of the operations of cause and effect, our conclusions from
that experience are not founded on reasoning, or any process of
the understanding. This answer we must endeavour both to explain and to
It seems Hume is a little
ironical here, for what follows was quite radical and new, namely a
series of arguments to the effect that 'even
after we have experience of the operations of cause and effect, our
conclusions from that experience are not founded on reasoning,
or any process of the understanding'.
These arguments I shall mostly
excerpt and annotate in the text that follows, but it may be helpful to
the reader to have links to my notes 4 and 5 in this
text, that comment on some of the vagueries of the use and meaning of
the terms "cause" and effect", and to remind the reader that Hume
himself in the previous
III introduced 'Cause or Effect' as
one of 'three principles of connexion among ideas'.
It must certainly be allowed, that nature
has kept us at a great distance from all her secrets, and has afforded
us only the knowledge of a few superficial qualities of objects; while
she conceals from us those powers and principles on which the influence
of those objects entirely depends.
No doubt this is true in most
relevant senses, though there are two relevant qualifications.
First, and in spite of the 'great distance' that 'nature
kept' between human beings and all of nature's 'secrets', it should be noted that there have
been many discoveries of natural things and processes since the time in
which Hume lived that are quite amazing and that are true at least to
the extent - which is an extent that does not at all hold for
religious or political ideas and ideals, that people kill and are
killed for - that enormous amounts of working technology of
many kinds have been based upon these discoveries of science.
Second, while nature may be
presumed to keep other animals at least as far from nature's secrets as
mankind, and while other animals seem rarely or never to make natural
discoveries, even so they live, presumably with little acquired
knowledge, and mostly based on instinct, apparently tuned to nature in
ways men cannot achieve.
But notwithstanding this ignorance of
natural powers[H1] and principles, we always presume,
when we see like sensible qualities, that they have like secret powers,
and expect that effects, similar to those which we have experienced,
will follow from them. If a body of like colour and consistence with
that bread, which we have formerly eat, be presented to us, we make no
scruple of repeating the experiment, and foresee, with certainty, like
nourishment and support. Now this is a process of the mind or thought,
of which I would willingly know the foundation.
A - classical - answer one
might give here is: That like follows from like. As we shall find
below, Hume is not satisfied with it.
And it may be well to outline
schematically the sort of inference Hume had in mind and found
Given in experience : if a is
P, then a is Q, and
b is Q, and
m is Q
every x, if x is P, then x is Q
or one concludes
the next n, if n is P, then n is Q
based on the examples a .. m
one found in experience. The 'like follows from like' in the present
case is based on the presumed facts that a if P is also Q, b if P is
also Q and so on.
It should be obvious that Hume
is right that neither inference is logically implied by the evidence,
in a deductively valid manner, though the evidence does support
it to some extent.
It is allowed on all hands that there is
no known connexion between the sensible qualities and the secret
powers; and consequently, that the mind is not led to form such a
conclusion concerning their constant and regular conjunction, by
anything which it knows of their nature. As to past Experience,
it can be allowed to give direct and certain
information of those precise objects only, and that precise period of
time, which fell under its cognizance: but why this experience should
be extended to future times, and to other objects, which for aught we
know, may be only in appearance similar; this is the main question on
which I would insist.
Here we have a precisification
of the 'process of the mind or thought'
that Hume inquired after in the previously quoted passage. The logical
problem that lies behind Hume's question he himself expresses here as 'why this experience should be extended to future
times, and to other objects'.
That is: What is the
foundation of the judgment that like does follow from like, if we also
know that this connection is not deductively valid (contingent
connections need not remain as they are) nor necessary (the bread we
see and believe to be nutrious in fact may be rotten)?
The bread, which I formerly eat,
nourished me; that is, a body of such sensible qualities was, at that
time, endued with such secret powers: but does it follow, that other
bread must also nourish me at another time, and that like sensible
qualities must always be attended with like secret powers? The
consequence seems nowise necessary. At least, it must be acknowledged
that there is here a consequence drawn by the mind; that there is a
certain step taken; a process of thought, and an inference, which wants
to be explained.
Again I answer that the
psychological explanation seems easy to me: We expect that like
follows like, and therefore expect that what seems to be bread that
looks much like the bread that nourished us before, will do so again,
and indeed expect a connection to happen again the more confidently the
more often we have experienced the connection.
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: I know, in fact, that it always is inferred.
But if you insist that the inference is made by a chain of reasoning, I
desire you to produce that reasoning. The connexion between these
propositions is not intuitive. There is required a medium, which may
enable the mind to draw such an inference, if indeed it be drawn by
reasoning and argument. What that medium is, I must confess, passes my
comprehension; and it is incumbent on those to produce it, who assert
that it really exists, and is the origin of all our conclusions
concerning matter of fact.
I grant that Hume is quite
right in the opening sentence of this quotation, and that indeed the
inference from a series of similar connections of things - A1
with B1, A2 with B2, A3
with B3 and so on up to An and Bn
- in the past to the statement that it will happen again, and that
"therefore" An+1 will and must be joined with Bn+1 is
However... an answer to Hume's
'if you insist that the inference is made by a
chain of reasoning, I desire you to produce that reasoning'
seems fairly simple, and is as follows, in principle, and without
It would seem that the
connection is not necessary but probabilistic, and that
one can suppose that the mind keeps track of stable associations in a
probabilistic manner, in such a way that the more often an association
has been experienced without fail, the stronger the mind expects that
it will happen again.
This may turn out to be a
mistake, but it is not difficult - in this day and age - to write a
computer program that does this, at least for specific kinds of
connections. And indeed, since Hume lived, there has been an enormous
development of probability-theory and statistics, including topics like
There is more on this in a later note in this section, for Hume does also
briefly consider probability, and we shall then see that his objection
to it is in fact the same: From the fact that something has
happened 19 times out of 20 in our experience, it does not
follow with logical necessity that it will continue to happen
in the future in the same proportion (or indeed in any other
This is a cogent objection I
shall below return to. Even so, I think I
have answered part of his demand, for I have indicated what sort of
reasoning might be used by the mind (or indeed a computer that has been
thus programmed) to arrive at the expectation that something will
happen from the facts of experience, however mistaken that expectation
might turn out to be.
here I shall now also provide an answer to Hume's other problem 'There is required a medium, which may enable the mind
to draw such an inference, if indeed it be drawn by reasoning and
argument. What that medium is, I must confess, passes my comprehension;
and it is incumbent on those to produce it, who assert that it really
exists, and is the origin of all our conclusions concerning matter of
In brief, the answer is:
Abduction - the mode of inference that consists in the proposing of
hypotheses to account for (supposed) facts.
First, what is an inference?
the assertion of a conclusion, in general
because one has already asserted (and thus accepted) certain premisses one
considers sufficient to assert the conclusion.
There are three basic kinds of
inference, that cover very many specific sorts of inferences:
To infer conclusions that follow from given assumptions.
2. Abductions: To infer
assumptions from which given given conclusions follows.
3. Inductions: To
confirm or infirm (support or undermine)
assumptions by showing their conclusions do (not)
conform to the observable facts.
Normally in reasoning all
three kinds are involved: We explain
supposed facts by
abductions; we check the abduced assumptions by deductions of
the facts they were to explain; and we test the assumptions
arrived by deducing consequences and then revise by inductions
the probabilities of the
assumptions by probabilistic
reasoning when these
consequences are verified or falsified.
Next, here is a simple
characterization of abduction by Charles S. Peirce, who first clearly
identified this mode of inference and saw its importance:
"Hypothesis [or abduction] may be defined as an argument which proceeds
upon the assumption that a character which is known necessarily to
involve a certain number of others, may be probably predicated of any
object which has all the characteristics which this character is known
to involve." (5.276) "An abduction is [thus] a method of forming a
general prediction." (2.269) But this prediction is always in reference
to an observed fact; indeed, an abductive conclusion "is only justified
by its explaining an observed fact." (1.89) If we enter a room
containing a number of bags of beans and a table upon which there is a
handful of white beans, and if, after some searching, we open a bag
which contains white beans only, we may infer as a probability, or fair
guess, that the handful was taken from this bag. This sort of inference
is called making an hypothesis or abduction. (J. Feibleman, "An
Introduction to the Philosophy of Charles S. Peirce", p. 121-2. The
numbers referred to are to paragraphs in Peirce's "Collected Papers".)
Accepting the conclusion
that an explanation is needed when facts contrary to what we should
expect emerge, it follows that the explanation must be such a
proposition as would lead to the prediction of the observed facts,
either as necessary consequences or at least as very probable under the
circumstances. A hypothesis then, has to be adopted, which is likely in
itself, and renders the facts likely. This step of adopting a
hypothesis as being suggested by the facts, is what I call abduction.
(Idem, p. 121-2)
Abduction (..) is the
first step of scientific reasoning, as induction is the concluding
step. Nothing has so much contributed to present chaotic or erroneous
ideas of the logic of science as failure to distinguish the essentially
different characters of different elements of scientific reasoning; and
one of the worst of these confusions, as well as one of the commonest,
consists in regarding abduction and induction together (often also
mixed with deduction) as a simple argument.
Accordingly, it seems as if
what is true of theories conforms to the following diagram, that
involves 6 named arrows and three kinds of inference I will briefly
is a set of statements that accounts for some Observations.
is a statement of particular fact (usually known fact, sometimes
is inferred by abduction from some Observations.
is an inference towards the best explanation for (presumed) facts. As a
rule, abductions are creative hypotheses that may involve guesses and
assumed postulated entities of many kinds.
between an Observation and a theory is an explanation if the
Observation can be deduced from the Theory.
is a statement about some particular (usually a presumptive fact) that
is deduced from a Theory.
is a re-calculation of the probability of a theory, given that a
Prediction of the theory is found to be true or false in fact. It is a
deductive consequence based on probability theory.
is the deduction that a certain Observation is in fact implied or
contradicted by a Prediction from a Theory, and thus may serve
for an inductive argument about the probability of the Theory.
is the deduction that an Observation is implied by a Prediction
from a Theory.
It should be noted that all
relations represented by arrows in the diagram other than abduction
are deductions, but that what is here called induction
also involves probability theory, next to standard logic, which is what
is used for the other deductions indicated in the diagram.
What is here called induction
is otherwise known as Bayesian reasoning, and consists in
essence in recalculating the probability of a theory using probability theory and
facts from experience.
Next, what is here called
abduction is normally a creative leap to account for some puzzling
fact, and is based on imagination, fantasy, analogy or anything else
that may be useful to account for something one has no ready-made
convincing explanation for.
Abductions, in the form of the
theories they produce, are tested and checked in two ways: First, by
deducing the facts they are meant to explain from the theory that is
supposed to explain them, and this is a necessary condition for the
abduction to make sense. Second, by induction in the above sense, to
infer what the probability of the theory should be given that one has
made an observation that is implied or contradicted by a prediction
that follows from the theory.
This negative argument must certainly, in
process of time, become altogether convincing, if many penetrating and
able philosophers shall turn their enquiries this way and no one be
ever able to discover any connecting proposit-ion or intermediate step,
which supports the understanding in this conclusion. But as the
question is yet new, every reader may not trust so far to his own
penetration, as to conclude, because an argument escapes his enquiry,
that therefore it does not really exist. For this reason it may be
requisite to venture upon a more difficult task; and enumerating all
the branches of human knowledge, endeavour to show that none of them
can afford such an argument.
Here Hume pretends some
modesty, with an ironical twist to it that he may have missed: When he
claims that 'This negative argument must
certainly, in process of time, become altogether convincing, if many
penetrating and able philosophers shall turn their enquiries this way
and no one be ever able to discover any connecting proposition or
intermediate step' what he in fact says is that sufficiently
many combinations of failures to explain the reasoning he wants
explained will make it certain that the reasoning cannot be explained.
But since Hume knew that his
argument was new and radical, he restates it once more, and I will
chart it in the selections that follow.
All reasonings may be divided into two
kinds, namely, demonstrative reasoning, or that concerning relations of
ideas, and moral reasoning, or that concerning matter of fact and
existence. That there are no demonstrative arguments in the case seems
evident; since it implies no contradiction that the course of nature
may change, and that an object, seemingly like those which we have
experienced, may be attended with different or contrary effects. May I
not clearly and distinctly conceive that a body, falling from the
clouds, and which, in all other respects, resembles snow, has yet the
taste of salt or feeling of fire? Is there any more intelligible
proposition than to affirm, that all the trees will flourish in
December and January, and decay in May and June? Now whatever is
intelligible, and can be distinctly conceived, implies no
contradiction, and can never be proved false by any demonstrative
argument or abstract reasoning ŕ priori.
In the opening statement of
this quotation Hume harks back to an assumption he made in the
beginning of the section, that I found fault with under Note 1, and he also restates the distinction, and
adds an assumption, namely that the 'relations of
ideas' all belong to 'demonstrative
reasoning', by which he means the same as we do by deductive
reasoning, which is always such that the premisses of a valid deductive
argument cannot be true while the conclusion of the argument are not
Now if it is this sort of
reasoning, that is deductively valid, that Hume desires in
explanation of an non-deductive inference from contingent facts
to contingent conclusions, then he surely is right that such deductive
reasoning cannot be produced, precisely because the relation is
supposed to be not known to be deductively valid to start with.
And the examples he gives
indeed are all good examples of logical possibilities that do not
square with ordinary expectations based on experience, but yet are
logically possible for all that.
If we be, therefore, engaged by arguments
to put trust in past experience, and make it the standard of our future
judgement, these arguments must be probable only, or such as regard
matter of fact and real existence, according to the division above
mentioned. But that there is no argument of this kind, must appear, if
our explication of that species of reasoning be admitted as solid and
satisfactory. We have said that all arguments concerning existence are
founded on the relation of cause and effect; that our knowledge of that
relation is derived entirely from experience; and that all our
experimental conclusions proceed upon the supposition that the future
will be conformable to the past. To endeavour, therefore, the proof of
this last supposition by probable arguments, or arguments regarding
existence, must be evidently going in a circle, and taking that for
granted, which is the very point in question.
Here Hume attempts to answer
the sort of probabilistic approach and attempted solution I mentioned
above. His own argument presupposes his own definitions and
assumptions, but may be recast without these and to the same effect:
That so-and-so has happened with such-and-such a probability in
the past, does not imply that so-and-so will happen with
such-and-such a probability now or in the future.
This is true, but it is only a
cogent argument if one disregards abduction, and tacitly insists that
all cogent argumentation must be deductive, as Hume does. If one does
not make these Humean assumptions, one can, with Newton, suppose that
such theoretical assumptions as one has found to account deductively
for the facts one desires to explain, and that are not refuted by such
knowledge as one has, do hold irrespective of time, until refuted (or
qualified) by further knowledge.
This makes such assumptions
clearly guesses, that are only supported and not
deductively proved by experiments, and that may be refuted by
further experiments, but that is no valid objection to a scientific hypothesis.
There is a further difficulty
Hume might raise here, that is in fact covered by the next quotation
In reality, all arguments from experience
are founded on the similarity which we discover among natural objects,
and by which we are induced to expect effects similar to those which we
have found to follow from such objects. And though none but a fool or
madman will ever pretend to dispute the authority of experience, or to
reject that great guide of human life, it may surely be allowed a
philosopher to have so much curiosity at least as to examine the
principle of human nature, which gives this mighty authority to
experience, and makes us draw advantage from that similarity which
nature has placed among different objects. From causes which appear similar
we expect similar effects. This is the sum of all our experimental
Hume's position is, in short,
that, as a practical or as a scientific man he is quite willing to
reason inductively and to expect that the future will be like the past,
but that as philosopher he should like a reason for the assumption that
'From causes which appear similar we
expect similar effects.'
Now here are two possible
One proceeds from the
assumption that all such reasons as are acceptable must be deductively
valid, and follow deductively from known evidence. This is, in effect,
Hume's position, and involves a tacit assumption that abductions do not
exist or should be rejected because abductive inferences are not
The other proceeds from the
assumption that one may give abductive reasons, and that the only
standards abductions must satisfy is that they do deductively
entail what they are supposed to explain and that there is no known
evidence that refutes them.
And then one can simply assume
that one lives in a reality in which there are both varying and
constant properties and relations i.e. such properties and relations
that do not remain the same in time and such as do, and that one can
learn from experience at least some of these, and can learn this by
guessing, experimentation, and probabilistic confirmation.
Now it seems evident that, if this
conclusion were formed by reason, it would be as perfect at first, and
upon one instance, as after ever so long a course of experience. But
the case is far otherwise. Nothing so like as eggs; yet no one, on
account of this appearing similarity, expects the same taste and relish
in all of them. 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.
Here Hume considers the sort
of reasoning I proposed in Note 24, and
insists in conclusion that '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.'
Actually, this is not quite
true: A burned child fears the fire, and not after having been burned
many times, but after only one time.
Clearly, the reason is that a
single painful experience is sufficient for the human mind to adopt
fargoing hypotheses, such that all fire burns.
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? This question I propose as much for the sake of
information, as with an intention of raising difficulties. I cannot
find, I cannot imagine any such reasoning. But I keep my mind still
open to instruction, if any one will vouchsafe to bestow it on me.
I think I have given this
reasoning, namely abduction,
Newton's Rules of Reasoning in
Philosophy, and was first clearly identified by Peirce.
Should it be said that, from a number of
uniform experiments, we infer a connexion between the sensible
qualities and the secret powers; this, I must confess, seems the same
difficulty, couched in different terms. The question still recurs, on
what process of argument this inference is founded? Where is
the medium, the interposing ideas, which join propositions so very wide
of each other?
The answer is, in general
terms: Probability theory.
Here, then, is our natural state of
ignorance with regard to the powers and influence of all objects. How
is this remedied by experience? It only shows us a number of uniform
effects, resulting from certain objects, and teaches us that those
particular objects, at that particular time, were endowed with such
powers and forces. When a new object, endowed with similar sensible
qualities, is produced, we expect similar powers and forces, and look
for a like effect. From a body of like colour and consistence with
bread we expect like nourishment and support. But this surely is a step
or progress of the mind, which wants to be explained. When a man says, I
instances, such sensible qualities conjoined
with such secret powers: And when he says, Similar sensible
qualities will always be conjoined with similar secret powers, he
is not guilty of a tautology, nor are these propositions in any respect
the same. You say that the one proposition is an inference from the
other. But you must confess that the inference is not intuitive;
neither is it demonstrative: Of what nature is it, then? To say it is
experimental, is begging the question. 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. It is impossible, therefore, that any arguments from
experience can prove this resemblance of the past to the future; since
all these arguments are founded on the supposition of that resemblance.
In this selection we have, I
think, Hume's clearest general statement of his position concerning
induction. Clearly, the basic problem is the inference that the future
will be like the past in some respect. He says and asks:
When a man
says, I have found, in all past instances, such sensible qualities
conjoined with such secret powers: And when he says, Similar
sensible qualities will always be conjoined with similar secret powers,
he is not guilty of a tautology, nor are these propositions in any
respect the same. You say that the one proposition is an inference from
the other. But you must confess that the inference is not intuitive;
neither is it demonstrative: Of what nature is it, then?
My answer is: Its nature is
abductive. And indeed the
inference from (1) 'I have found, in all past instances, such sensible qualities
conjoined with such secret powers' to (2) 'Similar sensible qualities will always be conjoined with
similar secret powers' is not
deductively valid - but the inference of (1) from (2) is
deductively valid, at least if 'always'
to the past, which shows that (2) can explain
And the point that Hume did
not clearly see - and that indeed Peirce may have been the first to see
clearly - is that one need not invalidly infer (2) from (1) but
that, since one must make assumptions anyway, one may assume
(2) by abduction and infer (1) from it by deduction, and then seek to
support (2) by deriving further consequences from it and comparing
these with experience.
Here three remarks must be
added concerning truth and probability.
First, when Hume speaks of the
inference of (2) from (1) and rejects it, he speaks of deductive
inference, and rightly rejects the proposed inference, because (2) may
be false while (1) is true.
Second, when I speak of the
abductive inference of (2) based on (1), I do not suggest that it is
deductively valid, but I do suggest that the inference of (1) from (2)
is deductively valid, and that this fact offers a ground to make (2) an
assumption and is what makes the inference of (2) from (1) an abductive
Third, the abductive inference
of (2) does not make (2) true, but it does make it into a possibly true
explanation of (1) that may be supported, undermined or refuted by
further experimental evidence.
When Hume in the above
To say it is
experimental, is begging the question. 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
he is confused for several
First, the inference of (2) is
by an abductive step, that was not obvious to Hume, and that he might
have rejected as not deductively valid had he seen it, but this does
not mean it is without experimental evidence. Indeed, the experimental
evidence for it is summarized by (1).
Second, it is not true that 'all inferences from experience
suppose, as their foundation, that the future will resemble the past', for experience also shows that some
properties do not last forever, or occur only for a brief time.
You may bend a steel wire many times, but eventually your continueing
to bend it will break it; and many persons have for thousands of days
expected that they would survive the next day, and yet died the next
Third, if Hume were to say
here, as he probably would, that the eventual breaking of a steel wire
by bending and the eventual dying of a man are both also learned from
experience, I of course agree. My difference with Hume is that I hold
that one can and does and may make abductive inferences based
on experimental evidence, which result in hypothetical assumptions that
deductively imply the evidence, and which one can then proceed to test
by further experimental evidence, and which one may adopt as the best
explanation until refuted or made improbable by experimental evidence.
Indeed, here is the place to
remark that Newton's fourth Rule of
Reasoning, where he says 'In experimental philosophy we are to look
upon propositions inferred by general induction from phenomena as
accurately or very nearly true,
may be imagined, till such
time as other phenomena occur, by which they may be either made more
accurate, or liable to exception'
be better restated along these lines: 'In
experimental philosophy we are to look upon propositions
inferred by abduction from phenomena as possible explanations, that may
be true, and that can be tested when other relevant phenomena occur, by
which they may be either made more accurate, or liable to exception.'
In this context it is quite
interesting that Hume also says
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.
Thus, Hume insists that we can
learn from experience. His problem is that he presumes all steps of
inference must be deductive, for which reason he cannot believe
in the above inference of (2) from (1), and for which reason he
impossible, therefore, that any arguments from experience can prove
this resemblance of the past to the future; since all these arguments
are founded on the supposition of that resemblance.
This is true if one reads 'prove' as 'deductively prove', but not if one
replaces it by 'suggest the abductive guess that, in specific cases
Hence it seems, in summary,
that Hume's difficulties with induction are mainly due to the following
A. He insists that all argumentation to be credible must be deductively
B. He was not aware that assumptions may be supported by their verified
And the solution I offer (in
line with Newton and Peirce) is accordingly based on
A'. Since we must make assumptions
anyway, we may do so by abductions: To infer that a certain hypothesis
makes sense, because it explains certain facts one cannot otherwise
explain, while the hypothesis itself is not contradicted by such
evidence as one has.
One can support hypotheses and assumptions by their consequences with
the help of probability theory: If T implies P and neither T nor P are
certainly true or certainly false, then the probability of T given that
P is verified is higher than it was before knowing P is verified, and
is higher in proportion with P's improbability.
Here is the mathematics
involved in the last point. Given that:
pr(P|T)=1 - T implies P so
the probability of P given T is 1
pr(T)=t - Let t be the probability of T and
p(P)=p - Let p be the probability of P
and assume 0<p<1
it follows that
by probability theory
In fairness to Hume it should
be remarked that this mode of reasoning was hardly known in his day and
age, though the Reverend Bayes did first articulate it in the 18th C as
a way to learn from experience by probability theory.
Let the course of things be allowed
hitherto ever so regular; that alone, without some new argument or
inference, proves not that, for the future, it will continue so. In
vain do you pretend to have learned the nature of bodies from your past
experience. Their secret nature, and consequently all their effects and
influence, may change, without any change in their sensible qualities.
This happens sometimes, and with regard to some objects: Why may it not
happen always, and with regard to all objects? What logic, what process
of argument secures you against this supposition? My practice, you say,
refutes my doubts. But you mistake the purport of my question. As an
agent, I am quite satisfied in the point; but as a philosopher, who has
some share of curiosity, I will not say scepticism, I want to learn the
foundation of this inference. No reading, no enquiry has yet been able
to remove my difficulty, or give me satisfaction in a matter of such
importance. Can I do better than propose the difficulty to the public,
even though, perhaps, I have small hopes of obtaining a solution? We
shall at least, by this means, be sensible of our ignorance, if we do
not augment our knowledge.
Here it should be remarked
that this whole Humean argument against reasoning in terms of Cause and
Effect seemed to have been part of Hume's argument in favour of
scepticism: "Look, there is not even a cogent deductive argument from
Cause to Effect, though this mode of reasoning is the foundation of all
My answer to this is: You are
right, but there is a cogent abductive argument of possible causes from
effects, and such possible causes may then be tested further
experimentally, and supported or infirmed probabilistically.
It is certain that the most ignorant and
stupid peasants—nay infants, nay even brute beasts—improve by
experience, and learn the qualities of natural objects, by observing
the effects which result from them. When a child has felt the sensation
of pain from touching the flame of a candle, he will be careful not to
put his hand near any candle; but will expect a similar effect from a
cause which is similar in its sensible qualities and appearance. If you
assert, therefore, that the understanding of the child is led into this
conclusion by any process of argument or ratiocination, I may justly
require you to produce that argument; nor have you any pretence to
refuse so equitable a demand. You cannot say that the argument is
abstruse, and may possibly escape your enquiry; since you confess that
it is obvious to the capacity of a mere infant. If you hesitate,
therefore, a moment, or if, after reflection, you produce any intricate
or profound argument, you, in a manner, give up the question, and
confess that it is not reasoning which engages us to suppose the past
resembling the future, and to expect similar effects from causes which
are, to appearance, similar. This is the proposition which I intended
to enforce in the present section. If I be right, I pretend not to have
made any mighty discovery. And if I be wrong, I must acknowledge myself
to be indeed a very backward scholar; since I cannot now discover an
argument which, it seems, was perfectly familiar to me long before I
was out of my cradle.