Books: The Problems of Philosophy
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Bertrand Russell >> The Problems of Philosophy
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In like manner I become aware of the relation of before and after in
time. Suppose I hear a chime of bells: when the last bell of the
chime sounds, I can retain the whole chime before my mind, and I can
perceive that the earlier bells came before the later ones. Also in
memory I perceive that what I am remembering came before the present
time. From either of these sources I can abstract the universal
relation of before and after, just as I abstracted the universal
relation 'being to the left of'. Thus time-relations, like
space-relations, are among those with which we are acquainted.
Another relation with which we become acquainted in much the same way
is resemblance. If I see simultaneously two shades of green, I can
see that they resemble each other; if I also see a shade of red: at
the same time, I can see that the two greens have more resemblance to
each other than either has to the red. In this way I become
acquainted with the universal _resemblance_ or _similarity_.
Between universals, as between particulars, there are relations of
which we may be immediately aware. We have just seen that we can
perceive that the resemblance between two shades of green is greater
than the resemblance between a shade of red and a shade of green.
Here we are dealing with a relation, namely 'greater than', between
two relations. Our knowledge of such relations, though it requires
more power of abstraction than is required for perceiving the
qualities of sense-data, appears to be equally immediate, and (at
least in some cases) equally indubitable. Thus there is immediate
knowledge concerning universals as well as concerning sense-data.
Returning now to the problem of _a priori_ knowledge, which we left
unsolved when we began the consideration of universals, we find
ourselves in a position to deal with it in a much more satisfactory
manner than was possible before. Let us revert to the proposition
'two and two are four'. It is fairly obvious, in view of what has
been said, that this proposition states a relation between the
universal 'two' and the universal 'four'. This suggests a proposition
which we shall now endeavour to establish: namely, _All _a priori_
knowledge deals exclusively with the relations of universals_. This
proposition is of great importance, and goes a long way towards
solving our previous difficulties concerning _a priori_ knowledge.
The only case in which it might seem, at first sight, as if our
proposition were untrue, is the case in which an _a priori_
proposition states that _all_ of one class of particulars belong to
some other class, or (what comes to the same thing) that _all_
particulars having some one property also have some other. In this
case it might seem as though we were dealing with the particulars that
have the property rather than with the property. The proposition 'two
and two are four' is really a case in point, for this may be stated in
the form 'any two and any other two are four', or 'any collection
formed of two twos is a collection of four'. If we can show that such
statements as this really deal only with universals, our proposition
may be regarded as proved.
One way of discovering what a proposition deals with is to ask
ourselves what words we must understand--in other words, what objects
we must be acquainted with--in order to see what the proposition
means. As soon as we see what the proposition means, even if we do
not yet know whether it is true or false, it is evident that we must
have acquaintance with whatever is really dealt with by the
proposition. By applying this test, it appears that many propositions
which might seem to be concerned with particulars are really concerned
only with universals. In the special case of 'two and two are four',
even when we interpret it as meaning 'any collection formed of two
twos is a collection of four', it is plain that we can understand the
proposition, i.e. we can see what it is that it asserts, as soon as
we know what is meant by 'collection' and 'two' and 'four'. It is
quite unnecessary to know all the couples in the world: if it were
necessary, obviously we could never understand the proposition, since
the couples are infinitely numerous and therefore cannot all be known
to us. Thus although our general statement _implies_ statements about
particular couples, _as soon as we know that there are such particular
couples_, yet it does not itself assert or imply that there are such
particular couples, and thus fails to make any statement whatever
about any actual particular couple. The statement made is about
'couple', the universal, and not about this or that couple.
Thus the statement 'two and two are four' deals exclusively with
universals, and therefore may be known by anybody who is acquainted
with the universals concerned and can perceive the relation between
them which the statement asserts. It must be taken as a fact,
discovered by reflecting upon our knowledge, that we have the power of
sometimes perceiving such relations between universals, and therefore
of sometimes knowing general _a priori_ propositions such as those of
arithmetic and logic. The thing that seemed mysterious, when we
formerly considered such knowledge, was that it seemed to anticipate
and control experience. This, however, we can now see to have been an
error. _No_ fact concerning anything capable of being experienced can
be known independently of experience. We know _a priori_ that two
things and two other things together make four things, but we do _not_
know _a priori_ that if Brown and Jones are two, and Robinson and
Smith are two, then Brown and Jones and Robinson and Smith are four.
The reason is that this proposition cannot be understood at all unless
we know that there are such people as Brown and Jones and Robinson and
Smith, and this we can only know by experience. Hence, although our
general proposition is _a priori_, all its applications to actual
particulars involve experience and therefore contain an empirical
element. In this way what seemed mysterious in our _a priori_
knowledge is seen to have been based upon an error.
It will serve to make the point clearer if we contrast our genuine _a
priori_ judgement with an empirical generalization, such as 'all men
are mortals'. Here as before, we can _understand_ what the
proposition means as soon as we understand the universals involved,
namely _man_ and _mortal_. It is obviously unnecessary to have an
individual acquaintance with the whole human race in order to
understand what our proposition means. Thus the difference between an
_a priori_ general proposition and an empirical generalization does
not come in the _meaning_ of the proposition; it comes in the nature
of the _evidence_ for it. In the empirical case, the evidence
consists in the particular instances. We believe that all men are
mortal because we know that there are innumerable instances of men
dying, and no instances of their living beyond a certain age. We do
not believe it because we see a connexion between the universal _man_
and the universal _mortal_. It is true that if physiology can prove,
assuming the general laws that govern living bodies, that no living
organism can last for ever, that gives a connexion between _man_ and
_mortality_ which would enable us to assert our proposition without
appealing to the special evidence of _men_ dying. But that only means
that our generalization has been subsumed under a wider
generalization, for which the evidence is still of the same kind,
though more extensive. The progress of science is constantly
producing such subsumptions, and therefore giving a constantly wider
inductive basis for scientific generalizations. But although this
gives a greater _degree_ of certainty, it does not give a different
_kind_: the ultimate ground remains inductive, i.e. derived from
instances, and not an _a priori_ connexion of universals such as we
have in logic and arithmetic.
Two opposite points are to be observed concerning _a priori_ general
propositions. The first is that, if many particular instances are
known, our general proposition may be arrived at in the first instance
by induction, and the connexion of universals may be only subsequently
perceived. For example, it is known that if we draw perpendiculars to
the sides of a triangle from the opposite angles, all three
perpendiculars meet in a point. It would be quite possible to be
first led to this proposition by actually drawing perpendiculars in
many cases, and finding that they always met in a point; this
experience might lead us to look for the general proof and find it.
Such cases are common in the experience of every mathematician.
The other point is more interesting, and of more philosophical
importance. It is, that we may sometimes know a general proposition
in cases where we do not know a single instance of it. Take such a
case as the following: We know that any two numbers can be multiplied
together, and will give a third called their _product_. We know that
all pairs of integers the product of which is less than 100 have been
actually multiplied together, and the value of the product recorded in
the multiplication table. But we also know that the number of
integers is infinite, and that only a finite number of pairs of
integers ever have been or ever will be thought of by human beings.
Hence it follows that there are pairs of integers which never have
been and never will be thought of by human beings, and that all of
them deal with integers the product of which is over 100. Hence we
arrive at the proposition: 'All products of two integers, which never
have been and never will be thought of by any human being, are over
100.' Here is a general proposition of which the truth is undeniable,
and yet, from the very nature of the case, we can never give an
instance; because any two numbers we may think of are excluded by the
terms of the proposition.
This possibility, of knowledge of general propositions of which no
instance can be given, is often denied, because it is not perceived
that the knowledge of such propositions only requires a knowledge of
the relations of universals, and does not require any knowledge of
instances of the universals in question. Yet the knowledge of such
general propositions is quite vital to a great deal of what is
generally admitted to be known. For example, we saw, in our early
chapters, that knowledge of physical objects, as opposed to
sense-data, is only obtained by an inference, and that they are not
things with which we are acquainted. Hence we can never know any
proposition of the form 'this is a physical object', where 'this' is
something immediately known. It follows that all our knowledge
concerning physical objects is such that no actual instance can be
given. We can give instances of the associated sense-data, but we
cannot give instances of the actual physical objects. Hence our
knowledge as to physical objects depends throughout upon this
possibility of general knowledge where no instance can be given. And
the same applies to our knowledge of other people's minds, or of any
other class of things of which no instance is known to us by
acquaintance.
We may now take a survey of the sources of our knowledge, as they have
appeared in the course of our analysis. We have first to distinguish
knowledge of things and knowledge of truths. In each there are two
kinds, one immediate and one derivative. Our immediate knowledge of
things, which we called _acquaintance_, consists of two sorts,
according as the things known are particulars or universals. Among
particulars, we have acquaintance with sense-data and (probably) with
ourselves. Among universals, there seems to be no principle by which
we can decide which can be known by acquaintance, but it is clear that
among those that can be so known are sensible qualities, relations of
space and time, similarity, and certain abstract logical universals.
Our derivative knowledge of things, which we call knowledge by
_description_, always involves both acquaintance with something and
knowledge of truths. Our immediate knowledge of _truths_ may be
called _intuitive_ knowledge, and the truths so known may be called
_self-evident_ truths. Among such truths are included those which
merely state what is given in sense, and also certain abstract logical
and arithmetical principles, and (though with less certainty) some
ethical propositions. Our _derivative_ knowledge of truths consists
of everything that we can deduce from self-evident truths by the use
of self-evident principles of deduction.
If the above account is correct, all our knowledge of truths depends
upon our intuitive knowledge. It therefore becomes important to
consider the nature and scope of intuitive knowledge, in much the same
way as, at an earlier stage, we considered the nature and scope of
knowledge by acquaintance. But knowledge of truths raises a further
problem, which does not arise in regard to knowledge of things, namely
the problem of _error_. Some of our beliefs turn out to be erroneous,
and therefore it becomes necessary to consider how, if at all, we can
distinguish knowledge from error. This problem does not arise with
regard to knowledge by acquaintance, for, whatever may be the object
of acquaintance, even in dreams and hallucinations, there is no error
involved so long as we do not go beyond the immediate object: error
can only arise when we regard the immediate object, i.e. the
sense-datum, as the mark of some physical object. Thus the problems
connected with knowledge of truths are more difficult than those
connected with knowledge of things. As the first of the problems
connected with knowledge of truths, let us examine the nature and
scope of our intuitive judgements.
CHAPTER XI
ON INTUITIVE KNOWLEDGE
There is a common impression that everything that we believe ought to
be capable of proof, or at least of being shown to be highly probable.
It is felt by many that a belief for which no reason can be given is
an unreasonable belief. In the main, this view is just. Almost all
our common beliefs are either inferred, or capable of being inferred,
from other beliefs which may be regarded as giving the reason for
them. As a rule, the reason has been forgotten, or has even never
been consciously present to our minds. Few of us ever ask ourselves,
for example, what reason there is to suppose the food we are just
going to eat will not turn out to be poison. Yet we feel, when
challenged, that a perfectly good reason could be found, even if we
are not ready with it at the moment. And in this belief we are
usually justified.
But let us imagine some insistent Socrates, who, whatever reason we
give him, continues to demand a reason for the reason. We must sooner
or later, and probably before very long, be driven to a point where we
cannot find any further reason, and where it becomes almost certain
that no further reason is even theoretically discoverable. Starting
with the common beliefs of daily life, we can be driven back from
point to point, until we come to some general principle, or some
instance of a general principle, which seems luminously evident, and
is not itself capable of being deduced from anything more evident. In
most questions of daily life, such as whether our food is likely to be
nourishing and not poisonous, we shall be driven back to the inductive
principle, which we discussed in Chapter VI. But beyond that, there
seems to be no further regress. The principle itself is constantly
used in our reasoning, sometimes consciously, sometimes unconsciously;
but there is no reasoning which, starting from some simpler
self-evident principle, leads us to the principle of induction as its
conclusion. And the same holds for other logical principles. Their
truth is evident to us, and we employ them in constructing
demonstrations; but they themselves, or at least some of them, are
incapable of demonstration.
Self-evidence, however, is not confined to those among general
principles which are incapable of proof. When a certain number of
logical principles have been admitted, the rest can be deduced from
them; but the propositions deduced are often just as self-evident as
those that were assumed without proof. All arithmetic, moreover, can
be deduced from the general principles of logic, yet the simple
propositions of arithmetic, such as 'two and two are four', are just
as self-evident as the principles of logic.
It would seem, also, though this is more disputable, that there are
some self-evident ethical principles, such as 'we ought to pursue what
is good'.
It should be observed that, in all cases of general principles,
particular instances, dealing with familiar things, are more evident
than the general principle. For example, the law of contradiction
states that nothing can both have a certain property and not have it.
This is evident as soon as it is understood, but it is not so evident
as that a particular rose which we see cannot be both red and not red.
(It is of course possible that parts of the rose may be red and parts
not red, or that the rose may be of a shade of pink which we hardly
know whether to call red or not; but in the former case it is plain
that the rose as a whole is not red, while in the latter case the
answer is theoretically definite as soon as we have decided on a
precise definition of 'red'.) It is usually through particular
instances that we come to be able to see the general principle. Only
those who are practised in dealing with abstractions can readily grasp
a general principle without the help of instances.
In addition to general principles, the other kind of self-evident
truths are those immediately derived from sensation. We will call
such truths 'truths of perception', and the judgements expressing them
we will call 'judgements of perception'. But here a certain amount of
care is required in getting at the precise nature of the truths that
are self-evident. The actual sense-data are neither true nor false.
A particular patch of colour which I see, for example, simply exists:
it is not the sort of thing that is true or false. It is true that
there is such a patch, true that it has a certain shape and degree of
brightness, true that it is surrounded by certain other colours. But
the patch itself, like everything else in the world of sense, is of a
radically different kind from the things that are true or false, and
therefore cannot properly be said to be _true_. Thus whatever
self-evident truths may be obtained from our senses must be different
from the sense-data from which they are obtained.
It would seem that there are two kinds of self-evident truths of
perception, though perhaps in the last analysis the two kinds may
coalesce. First, there is the kind which simply asserts the
_existence_ of the sense-datum, without in any way analysing it. We
see a patch of red, and we judge 'there is such-and-such a patch of
red', or more strictly 'there is that'; this is one kind of intuitive
judgement of perception. The other kind arises when the object of
sense is complex, and we subject it to some degree of analysis. If,
for instance, we see a _round_ patch of red, we may judge 'that patch
of red is round'. This is again a judgement of perception, but it
differs from our previous kind. In our present kind we have a single
sense-datum which has both colour and shape: the colour is red and the
shape is round. Our judgement analyses the datum into colour and
shape, and then recombines them by stating that the red colour is
round in shape. Another example of this kind of judgement is 'this is
to the right of that', where 'this' and 'that' are seen
simultaneously. In this kind of judgement the sense-datum contains
constituents which have some relation to each other, and the judgement
asserts that these constituents have this relation.
Another class of intuitive judgements, analogous to those of sense and
yet quite distinct from them, are judgements of _memory_. There is
some danger of confusion as to the nature of memory, owing to the fact
that memory of an object is apt to be accompanied by an image of the
object, and yet the image cannot be what constitutes memory. This is
easily seen by merely noticing that the image is in the present,
whereas what is remembered is known to be in the past. Moreover, we
are certainly able to some extent to compare our image with the object
remembered, so that we often know, within somewhat wide limits, how
far our image is accurate; but this would be impossible, unless the
object, as opposed to the image, were in some way before the mind.
Thus the essence of memory is not constituted by the image, but by
having immediately before the mind an object which is recognized as
past. But for the fact of memory in this sense, we should not know
that there ever was a past at all, nor should we be able to understand
the word 'past', any more than a man born blind can understand the
word 'light'. Thus there must be intuitive judgements of memory, and
it is upon them, ultimately, that all our knowledge of the past
depends.
The case of memory, however, raises a difficulty, for it is
notoriously fallacious, and thus throws doubt on the trustworthiness
of intuitive judgements in general. This difficulty is no light one.
But let us first narrow its scope as far as possible. Broadly
speaking, memory is trustworthy in proportion to the vividness of the
experience and to its nearness in time. If the house next door was
struck by lightning half a minute ago, my memory of what I saw and
heard will be so reliable that it would be preposterous to doubt
whether there had been a flash at all. And the same applies to less
vivid experiences, so long as they are recent. I am absolutely
certain that half a minute ago I was sitting in the same chair in
which I am sitting now. Going backward over the day, I find things of
which I am quite certain, other things of which I am almost certain,
other things of which I can become certain by thought and by calling
up attendant circumstances, and some things of which I am by no means
certain. I am quite certain that I ate my breakfast this morning, but
if I were as indifferent to my breakfast as a philosopher should be, I
should be doubtful. As to the conversation at breakfast, I can recall
some of it easily, some with an effort, some only with a large element
of doubt, and some not at all. Thus there is a continual gradation in
the degree of self-evidence of what I remember, and a corresponding
gradation in the trustworthiness of my memory.
Thus the first answer to the difficulty of fallacious memory is to say
that memory has degrees of self-evidence, and that these correspond to
the degrees of its trustworthiness, reaching a limit of perfect
self-evidence and perfect trustworthiness in our memory of events
which are recent and vivid.
It would seem, however, that there are cases of very firm belief in a
memory which is wholly false. It is probable that, in these cases,
what is really remembered, in the sense of being immediately before
the mind, is something other than what is falsely believed in, though
something generally associated with it. George IV is said to have at
last believed that he was at the battle of Waterloo, because he had so
often said that he was. In this case, what was immediately remembered
was his repeated assertion; the belief in what he was asserting (if it
existed) would be produced by association with the remembered
assertion, and would therefore not be a genuine case of memory. It
would seem that cases of fallacious memory can probably all be dealt
with in this way, i.e. they can be shown to be not cases of memory in
the strict sense at all.
One important point about self-evidence is made clear by the case of
memory, and that is, that self-evidence has degrees: it is not a
quality which is simply present or absent, but a quality which may be
more or less present, in gradations ranging from absolute certainty
down to an almost imperceptible faintness. Truths of perception and
some of the principles of logic have the very highest degree of
self-evidence; truths of immediate memory have an almost equally high
degree. The inductive principle has less self-evidence than some of
the other principles of logic, such as 'what follows from a true
premiss must be true'. Memories have a diminishing self-evidence as
they become remoter and fainter; the truths of logic and mathematics
have (broadly speaking) less self-evidence as they become more
complicated. Judgements of intrinsic ethical or aesthetic value are
apt to have some self-evidence, but not much.
Degrees of self-evidence are important in the theory of knowledge,
since, if propositions may (as seems likely) have some degree of
self-evidence without being true, it will not be necessary to abandon
all connexion between self-evidence and truth, but merely to say that,
where there is a conflict, the more self-evident proposition is to be
retained and the less self-evident rejected.
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