KANT’S EXPLANATION OF THE NECESSITY OF GEOMETRICAL TRUTHS
John Watling
Kant was an idealist. His idealism was in some ways, it is true, less extreme than that of Berkeley. He
distinguished his own by calling it ‘transcendental’. It is less extreme than Berkeley’s in two ways. First,
Kant does not assert that everything which exists is essentially mental, as Berkeley does. Second, those
things which he does hold to be essentially mental, he holds to be so in a weaker fashion. Nevertheless
he was an idealist; he held that neither intuition nor thought could concern any object that was not
essentially related to our minds. Since intuition and thought together provide knowledge, and since we
can have no knowledge except through them, it follows that every object of which we have knowledge is
essentially within our minds. Moreover, there is at least one respect in which his idealism is more
extreme than that of Berkeley. He held that the objects of intuition were essentially within our minds,
whereas Berkeley held only that they were essentially within some mind.
Kant was led to his idealism by the desire to establish the possibility of knowledge in a sphere where it
lay in doubt, and so to avoid scepticism. Berkeley, likewise, was led to his idealism by the wish to
establish the possibility of knowledge, although knowledge in another sphere, and so to avoid
scepticism. The scepticisms they sought to allay concerned propositions of different kinds, but their
idealisms meet when they consider the nature of the objects of what Kant calls sensible intuition and
Berkeley calls immediate perception. In sensible intuition and in immediate perception sensible objects
are present to us.
The scepticism which troubled Berkeley arises over our knowledge of those things which we
believe ourselves to perceive. That which troubled Kant arises over propositions which involve, in one
way or another, the idea of necessity. If we are to believe Kant himself, it was Hume’s arguments
concerning causation which first forced this problem upon Kant’s attention. He seems to have
considered
that Hume’s conclusion that we have no idea of necessity is not totally implausible to someone who
takes no other example of necessity but that of causation. However, anyone who considers how
necessity enters also into the propositions of arithmetic and of geometry must see that if we have no
idea of necessity, then we have no understanding of these sciences. Had Hume widened his
considerations in this way — Kant erroneously implies that he did not — his ‘good sense’ would have
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forced him to revise his views. Hume held that if causation implies necessary connection it is
impossible to get an idea of causation or understand a causal proposition. His case against the idea of
necessity, applied to mathematics, would show the impossibility of our understanding the necessary
incompatibility between two lines both being straight lines and enclosing an area, or the necessary
consequence between a closed figure having three straight sides and its included angles adding up to
two right angles. However, Kant makes no attempt to show how we come to be able to grasp these ideas
of incompatibility and consequence. He turns to the question of how it is that these geometrical
theorems can be necessary and how we can know them to be so, leaving aside the question of how we
can understand the necessity they involve. Kant agrees with Hume that no proposition which involves
necessity can be established by experience. Propositions which cannot be established by experience he
calls a priori. However, he held that although no proposition involving necessity could be established by
experience alone, some of them could be established without experience at all, others only with the help
of experience. Propositions of the former sort he calls ‘pure a priori’. The theorems of geometry are of
this sort and so are such principles as that every event has a cause. Propositions concerning particular
causal connections are of the latter sort. As I have just remarked, with geometrical theorems he neglects
a task he should undertake, that of showing how we understand the necessity involved. With
propositions concerning causal connections, such as scientific hypotheses, he concentrates on the
problem of how we come by the idea of causal necessity and almost entirely neglects the problem of
how we can know a particular scientific hypothesis to be a law of nature. The pure a priori principles
which Kant held to stand at the head of natural science, such as that every event has a cause, or that
matter can neither be created nor destroyed, are distinguished. Only with them does he take up both of
the problems which necessity poses:
that of understanding and that of knowledge. However, with neither science nor mathematics does
Kant attempt to analyse the necessary connection involved. Perhaps he neglected the problem of our
under standing of the necessity of geometrical theorems because of the view he took of the origin of
that necessity. The origin lay, he held, not in concepts or our understanding of concepts, but in the
relationship between our faculty of sensible intuition and the nature of the objects with which, by
means of that faculty, we become acquainted. Perhaps, that is, he unconsciously argued that because the
necessity of those propositions had a non-conceptual origin, so our knowledge of them demanded no
understanding of the concept of necessity. If he did, he argued mistakenly. However that may be, he did
neglect the problems of understanding and concentrate on the problem of knowledge.
Besides truths which are ordinarily regarded as theorems of geometry Kant set out to explain
the necessity of such properties of space as these. ‘Space has three dimensions, no more and no less.’
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‘There is only one space. Divisions can be introduced into it, but the divisions do not result in parts
which could exist independently.’ ‘It is possible that a pair of things in space should be incongruent
counterparts’. Incongruent counterparts are pairs of things, such as a pair of gloves, which are
incongruent, in that one of them will not always fit where the other will, yet exact counterparts, in that
their parts are similar and similarly related among themselves. He also set out to explain why those
things which are in space could not exist except in space. These examples show that he was not satisfied
to explain only the relationships holding between the spatial properties of things, about which geometry
informs us, but sought the origin of the most fundamental properties of space and even of the spatial
nature of objects. Of course, it would be possible to seek an explanation of the necessity of the spatial
relationships of which geometry informs us without raising the more fundamental questions. John
Stuart Mill’s theory of geometry is an example of such a more restricted inquiry.
Kant held all these propositions to be synthetic, not analytic. Had he held the opposite view, the
problem of the origin of their necessity and of how we can know them would scarcely have been, in his
eyes, any problem at all. An analytic proposition, such as ‘All cubes have six faces’, cannot extend our
knowledge. It merely serves to make more evident what it is to be a cube. In knowing it to be true we
know nothing, and its necessity is not the necessity of anything. Of course, this account given by Kant
of the nature of analytic propositions does raise problems. If, in knowing them to be true, we know
nothing, how can we know them to be true? If their necessity is not the necessity of anything how can
they be necessary propositions? However, since Kant denied the analyticity of most geometrical
theorems, these problems are irrelevant to our purpose. Kant does indeed admit that some geometrical
propositions, such as that the whole is greater than the part, are analytic; he argues for the synthetic
character of the rest.
That the straight line between two points is the shortest, is a synthetic proposition. For my
concept of straight contains nothing of quantity, but only of quality. The concept of the shortest
is wholly an addition, and cannot be derived, through any process of analysis, from the concept
of the straight line. Intuition, therefore, must here be called in; only by its aid is synthesis
possible.
(CPR p. 53, B 17)1
1
CPR = Immanuel Kant’s Critique of Pure Reason, trans. Norman Kemp Smith (London: Macmillan,
1964)
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Kant’s point is that until we look at, or, what is just as good, imagine, a straight line we cannot see the
proposition to be true.
Gottfried Martin claims that there is historical evidence to show that Kant was aware of the
failure of Saccheri’s attempt to prove the inconsistency of a system of geometry which was exactly like
that of Euclid except that the fifth axiom — the parallels axiom — was replaced by one which
contradicted it. Martin argues that this failure convinced Kant that there could be a self-consistent
system of geometry contradicting Euclid’s, and hence that Euclid’s geometry was not analytic. This
explanation of Kant’s rejection of the analytical character of geometric truths is plausible, but not
entirely convincing. No systems of arithmetic were known which were self-consistent but inconsistent
with ordinary arithmetic. Why did Kant accept the non-analytic character of both the theorems of
geometry and those of arithmetic? Again, it is not clear that the mutual consistency of the axioms of
Saccheri’s non-Euclidean system proves that the axiom which denied Euclid’s parallels axiom was selfconsistent. It proves only that there is no inconsistency between that non-Euclidean axiom and the rest
of Euclid’s assumptions. To put the same point another way round, it may be that Euclid’s parallels
axiom is analytic even though it does not follow from the rest of Euclid. The failure of the attempts to
show Saccheri’s system inconsistent was only the failure to prove Euclid’s parallels axiom from the rest
of Euclid’s assumptions. Of course, even though this argument failed to show that the parallels axiom
could be denied without contradiction, Kant may have believed that it did. What is more, if geometers
were beginning to speak as if they found no contradiction in denying the axiom, that was quite good
evidence that there was none.
Kant held, then, that geometry was a body of propositions providing genuine knowledge about objects
in space, which held for all of them, from atoms to stars, the smallest to the largest, the nearest to the
furthest, but which stood in no danger of contradiction by experience and had no need of support from
it. The explanation of these facts, and of our having knowledge of them, lay, for Kant, in the nature of
our faculty of intuition: i.e. that faculty without which objects could not be present to us. Kant believed
that perception, or experience, could he separated into two parts: sensible acquaintance with objects, on
the one hand, and propositional thought about them, on the other. The former he called intuition, the
latter, thought, and to each of them there corresponded a faculty, in the former case called the
sensibility, in the latter, the understanding. There corresponds also, in the first part of The Critique of
Pure Reason, a division to each: the aesthetic, where he discusses intuition and the sensibility, and the
analytic, where he discusses thought and the understanding. Although it would be impossible for us to
perceive, or have experience of, any object in space without the faculty of understanding, the necessity
of the propositions of geometry, and the possibility of our knowledge of them, arise from our faculty of
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intuition. It is from the character of that faculty, which might, Kant often stresses, have been different,
and which may be different in other sentient beings, that geometrical facts and other facts about space
arise.
If we depart from the subjective condition under which alone we can have outer intuition,
namely, liability to be affected by objects, the representation of space stands for nothing
whatsoever. This predicate can be ascribed to things only in so far as they appear to us, that is,
only to objects of sensibility. (CPR, p.71, B43)
He speaks of ‘outer intuition’ here to distinguish the faculty which presents objects in space to us from
another faculty also a faculty of intuition — which he believes we possess: that which presents to us
inner states. Inner states were, for him, non-spatial states of ourselves, e.g. pains or other sensations.
[Space] is the subjective condition of sensibility, under which alone outer intuition is possible for us.
Since, then, the receptivity of the subject, its capacity to be affected by objects, must necessarily precede
all intuitions of these objects, it can readily be understood how the form of all appearances can be given
prior to all actual perceptions. (CPR, p. 71, B 42)
But quite how did Kant suppose that the conditions imposed by our own nature, by the constitution of
our own faculty, could explain the necessary facts of geometry, facts that concern the things we
perceive?
Obviously it might be that the character of our own faculty made us unable to intuit, and hence unable
to perceive, any objects which were not spatial and which did not obey the laws of geometry. That is,
the character of our own faculty might imply the truth of the proposition: If we can intuit a thing, it is
in space and obeys the laws of geometry. This would mean that the character of our own faculty of
intuition, which enables objects in space to be present to us, also imposes on us a disability: objects
which are not in space, or which do not obey the laws of geometry, cannot be present to us. This would
explain why we can intuit nothing which is not in space and does not obey the laws of geometry. The
idealism it implies is a limited one. Such truth as it yielded to the laws of geometry would arise from the
character of our minds, but the objects which we could intuit would be perfectly independent of our
minds. They would exist whether or not we could intuit them and, although they would not lack spatial
properties when we intuited them, they could lack spatial properties. In just the same way, the fact that
if a fish can meet a thing, that thing is in water, explains the restricted nature of a fish’s experience but
does not imply the dependence of the things it can meet on the presence of water. However, such an
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explanation could not have satisfied Kant. The facts he took geometry to express were stronger than
such an explanation can explain.
Kant did hold that geometry has a restricted subject-matter — it deals only with things we can
intuit — but he did not hold that it has restricted implications concerning that subject-matter. He did
not hold that it informs us only of the properties the things we can intuit have if we can intuit them, he
held that it informs us of the properties the things we can intuit must have. Now the fact that if a fish
can meet a thing, that thing is in water does not imply that if a fish can meet a thing, that thing is a
thing which is necessarily in water, and so does not imply that the things a fish can meet are things
which are necessarily in water. In just the same way, the explanation we have been considering does not
imply that if we can intuit a thing, that thing is a thing which is necessarily in space and necessarily
obeys the laws of geometry, and so does not imply that the things we can intuit are things which are
necessarily in space and necessarily obey the laws of geometry.
An obvious suggestion is to reinforce our explanation by declaring the connection between
being a thing we can intuit and being in space to be one which holds necessarily. The objection to this
reinforcement is that Kant stresses that our intuition might have been of a different type. However, by
itself, the reinforcement fails to achieve what we require of it. It is a fact that necessarily, if a fish meets a
thing, that thing is met by a fish, but it is not a fact, and so cannot follow, that necessarily, if a fish meets
a thing, that thing is a thing which is necessarily met by a fish. I have been met by a fish, yet I am not a
thing which was necessarily met by a fish. Similarly, our reinforced explanation does not have the
consequence that, necessarily, if we can intuit a thing, that thing is a thing which is necessarily in space
and necessarily obeys the laws of geometry.
It is true that there is a passage in The Critique of Pure Reason which suggests that Kant did
accept the validity of such inferences.
Since we cannot treat the special conditions of sensibility as conditions of the possibility of
things, but only of their appearances, we can indeed say that space comprehends all things that
appear to us as external, but not all things in themselves, by whatever subject they are intuited,
or whether they be intuited or not. For we cannot judge in regard to the intuitions of other
thinking beings, whether they are bound by the same conditions as those which limit our
intuition and which for us are universally valid. If we add to the concept of the subject of a
judgment the limitation under which the judgment is made, the judgment is then
unconditionally valid. The proposition, that all things are side by side in space, is valid under the
limitation that these things are viewed as objects of our sensible intuition. If, now, I add the
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condition to the concept, and say that all things, as outer appearances, are side by side in space,
the rule is valid universally and without limitation. (CPR, p. 72, A 27)
When, in this passage, Kant asserts the principle ‘If we add to the concept of the subject of a
judgment the limitation under which the judgment is made, the judgment is then unconditionally valid’
he seems to countenance the inference from ‘If we can intuit a thing, it is in space’ to ‘The things we
intuit are in space’. This is just the inference which leads to trouble when necessity enters the picture, as
Kant requires. It is worth observing that the inference leads to trouble over universality as well as over
necessity. Our explanation expressing the limitation of our faculty of intuition should take the form
that if we can intuit a thing, then at that time it is in space. This does not imply that if we can intuit a
thing, then it is a thing which is always in space. However, although this passage suggests that Kant
accepted the inference, there is another, which I will quote presently, which strongly suggests that he
did not. Whether or not he did accept the inference, it is in fact invalid, so that our reinforced
explanation needs further reinforcement. It needs an addition which there is every reason to think Kant
accepted. It is this, that if we can intuit a thing, then it is a thing which necessarily can be intuited by us.
With this addition our explanation entails, what it did not entail before, that if we can intuit a thing,
then it is a thing which is necessarily in space and necessarily obeys the laws of geometry. It entails that
the things we can intuit are necessarily in space and necessarily obey the laws of geometry.
Two things stand in the way of regarding this explanation of the necessity of geometry as the
one Kant intended. First, what I have already pointed out, that Kant explicitly rejects the necessity of
our having the faculty of intuition which, as a matter of fact, we have. Second, the fear that the
explanation proves that the conclusion that the things we intuit obey the laws of geometry is an analytic
proposition, and so perhaps proves what Kant denied. To take the second difficulty first: what Kant
denied was the analyticity of the theorems themselves. He denied, for example, that being a straight line
analytically involved being the shortest distance between any two points on that line. Perhaps he would
not have denied that being a straight line on a thing we can intuit analytically involved this. After all,
although he insists that intuition is necessary to establish geometrical truths, he does not rely on
intuition in the explanation of the necessity of geometrical truths which he argues for in the Critique.
The first difficulty is more troublesome, but there is one way of overcoming it. Before explaining what
that way is, I must say a little more about the addition which completed our explanation.
It could be expressed as: The things we can intuit are things which, necessarily, can be intuited
by us. Again, it could be put as: It is true of the things we can intuit that to be is to be intuitable by us. I
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believe it is this which Kant expresses when he asserts that the things we intuit are appearances, not
things in themselves.
Space does not represent any property of things in themselves, nor does it represent them
[things in themselves] in their relation to one another… Space is nothing but the form of all
appearances of outer sense. (CPR, p. 71, A 26)
He is speaking of the things we intuit when he says. ‘As appearances, they cannot exist in themselves,
but only in us’ (CPR, p. 82, A 42). There are passages, it is true, which suggest, at least in Kemp Smith’s
translation, that the things we intuit have some properties ‘in themselves’. A few sentences before the
sentence I last quoted, he says: ‘The things which we intuit are not in themselves what we intuit them as
being…’ (CPR, p. 82, A 42). This does seem to suggest that they are something in themselves and so
exist in themselves and not merely in us. That suggestion is, however. immediately contradicted in the
earlier quotation: ‘As appearances, they cannot exist in themselves, but only in us’. Moreover, a little
further on in the Critique, a passage occurs which indicates fairly conclusively that Kant saw that
without the premise that the things we can intuit are necessarily intuitable by us, he could never prove
that geometry holds necessarily of those things. He is discussing how this might be proved in a
particular example, ‘Given three straight lines, a figure is possible’. He mentions various ways in which
it cannot be done and goes on:
If there did not exist in you a power of a priori intuition; and if that subjective condition were
not also at the same time, as regards its form, the universal a priori condition under which alone
the object of this outer intuition is itself possible; if the object (the triangle) were something in
itself, apart from any relation to you, the subject, how could you say that what necessarily exist
in you as subjective conditions for the construction of a triangle, must of necessity belong to the
triangle itself? (CPR, p. 86, A 48)
I think that this passage clinches my interpretation of Kant’s explanation of the necessity
belonging to geometrical laws. It also suggests a short way with the first of the two difficulties which
that interpretation faces, for in it Kant speaks of ‘what exist necessarily in you as subjective conditions
for the construction of a triangle’ in contradiction to what he says elsewhere. My other suggestion for
resolving the first difficulty is that we might weaken the first part of our explanation, so that it implies
only a contingent connection between our being able to intuit a thing and that thing being in space, and
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strengthen the second part, so that it implies that if a thing can be intuited by us, then it is a thing which
is not only necessarily intuitable by us, but necessarily intuitable by us with the faculty of intuition we
now have. That strengthening would mean that appearances were things that, necessarily, can be
perceived with the faculty of intuition we have. It would mean that appearances were not only in us, but
in our faculty of intuition. Perhaps Kant did not distinguish these alternatives clearly. He speaks most
often of appearances being necessarily in us, but one passage, which I will quote later, suggests that they
are in our faculty of intuition.
The passage I quoted last mentions something upon which depends Kant’s explanation of how,
independently of experience, we can know the laws of geometry to be true. This is what he calls ‘the
power of a priori intuition’. The properties of a thing in space divide, according to Kant, into two: those
which it has essentially, and could not lack, which he calls its form, and those which it might have
lacked, which he calls its matter. That the path of the planets is an ellipse is not, paradoxically, part of its
form. That, if the path of the planets is an ellipse traversed at constant speed, then the radii sweep out
equal areas in equal times, is part of its form. Since this latter fact is necessarily true, no experience of
the planetary orbits can refute it. The question remains why we can get to know this geometrical fact
without experience of the planetary orbits? Kant might have replied, but did not, ‘Because experience of
any other elliptical thing would do as well. In investigating these questions concerning any object of
intuition you are in fact investigating your own faculty of intuition, your own sensibility; you can do
this as well with one object of intuition as another.’ However, Kant must have felt that this allowed
experience a larger place than it deserved. He considers that this investigation of your own faculty,
which you do when you investigate an object of intuition, can be done without investigating any object.
It can be done in an a priori intuition. I take it that you have an a priori intuition when you imagine an
object. Kant speaks not only of the power of a priori intuition, but also of things which are intuited
when we exercise that power. These he calls ‘a priori intuitions’; his view that here are such things
comes close to being a contradiction in terms. As I explained at the beginning of the lecture, the term
‘pure a priori’ means ‘without experience’ so that pure a priori knowledge is knowledge that can be got
without experience and a pure a priori intuition is an intuition which one can have without having any
experience. In Kant’s usage the view that there are pure a priori intuitions was not a contradiction in
terms because he took the term ‘experience’ to mean ‘perception of objects which exist in space and
time’, rather than ‘perception of anything whatever’. There can be pure a priori intuitions because there
are things we can intuit which do not exist in space and time. These things we intuit when we imagine
objects in space and time. They are space and time themselves.
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Kant’s idealism is well summed up in his contention that the things in space which we intuit
‘cannot exist in themselves, but only in us’ (CPR, p. 82, A 42). Berkeley and Kant share the view that
any drop of rain we perceive is in our minds. However, whereas Berkeley holds, of such a rain drop,
that to be is to be perceived, Kant holds of it, that to be is to be perceivable by us. Since being perceived
entails being perceivable, while being perceivable does not entail being perceived, it may seem that
Berkeley’s idealism comprises Kant’s, but that Kant’s does not comprise Berkeley’s. The latter, indeed,
is obviously true. Kant allowed that things in space could exist unperceived. However, I think it equally
true that Berkeley would have agreed, had the question occurred to him, that things which could not
exist unperceived could exist although they were unperceivable by us. His idealism does not comprise
Kant’s. I do not know whether it occurred to Berkeley that something which was perceivable to a being
of one kind, for example, a creator, might not be perceivable to a being of another kind, for example, a
created being. If it did, he must, I think, have held that ‘to be is to be perceived’ entails ‘to be is to be
perceivable to a being of some kind’ and denied that it entails ‘to be is to be perceivable by us’.
Berkeley himself produces arguments for his idealism which are not easily set aside but, it seems
to me, they go for nothing in the face of the arguments against it. The arguments I mean consist in
showing what implausible consequences it has for the nature of perception. Does Kant’s idealism
escape such implausibilities?
G. E. Moore’s article ‘The Refutation of Idealism’ contains an argument which, it seems to me,
does refute Berkeley’s idealism. Perhaps it is not quite that which Moore himself employs. The
argument is this. The principle that to be is to be perceived entails the identity of whatever is perceived
and the perception of it. Things which are perceived are, therefore, perceptions or, perhaps more
explicitly, perceivings. But some perceivings are perceivings of one thing and others are perceivings of
other things. If the things perceived are the perceivings of them, then the difference between
perceivings which differ must lie in the perceivings having different properties. For the perceivings are
their own objects and so can only differ in their objects if they themselves differ. Therefore two
perceivings which we might regard as differing in respect of their objects differ only, according to this p
in that one is of one kind and one of another. But this consequence is absurd. How could it be that the
difference be tween perceiving the colour green and perceiving the colour red was a difference between
two kinds of perceiving? This absurd conclusion must arise from an absurdity in our premisses, These
were, first, that to be is to be perceived, second, that some perceivings are of one thing, others of
another. The second premise is not absurd, therefore the first is.
Moore put forward a view of the nature of sensation according to which it is not true even of
sensations that to be is to be perceived. He suggested that a sensation of blue is an awareness of blue, so
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that a sensation of green differs from a sensation of blue, not in the element of awareness, for exactly
the same kind of awareness is present in both instances, but in the colour which is the object of the
sensations.
‘Blue’ is as much an object, and as little a mere content, of my experience, when I experience it,
as the most exalted and independent real thing of which I am ever aware. There is, therefore, no
question of how we are to ‘get outside the circle of our own ideas and sensations’. Merely to have
a sensation is already to be outside that circle. It is to know something which is as truly and
really not a part of my experience, as anything I can ever know. (Philosophical Studies, p.27)
Moore came later to reject this account of the nature of sensation. He did so because he came to
reject the possibility of a person being aware of a colour except by being aware of something which is
that colour. It was for that reason that he introduced the notion of sense-data, the things which we are
aware of in sensation; some are things which are blue, others things which are green. I do not myself see
why he came to this view. No doubt when we perceive things in space we perceive things which are
blue, but often when we have a sensation of blue, or imagine the colour, the truth seems to me to be
that we sense, or imagine, the colour without perceiving or imagining anything which has the colour. I
have mentioned this change of mind on Moore’s part because it raises another possibility for the
interpretation of what Berkeley intended by the principle that to be is to be perceived. It is an
interpretation which contradicts the view Moore came to hold. It is certainly one thing Berkeley
intended by his principle. The only question is whether he also held the view against which Moore’s
argument in ‘The Refutation of Idealism’ is directed. Berkeley often argues for the view that colours
cannot be exemplified in things as their qualities, except by exemplification in minds by being
perceived. That is, Berkeley might have meant no more by the principle that to be is to be perceived
than that colours cannot be qualities of non-mental things but can only be things perceived by minds.
This principle would be better expressed as the principle that to be exemplified is to be perceived; or
that being perceived is the only way in which a quality can be exemplified — the only way in which a
quality can be directly related to a particular. If Berkeley held no more than this, then Moore’s
refutation is misdirected and the relation between his philosophy and that of Kant is very different from
the one I have depicted. Kant’s principle that to be is to be intuitable by us cannot be given a
corresponding interpretation, since he held that we intuit particular objects, not qualities.
Moore’s refutation of idealism does not depend on the verbal point that whenever a term seems
to indicate a relation of a person to an object, as the term ‘perception’ does, then there must be such a
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relation. That point is shown to be false by an example given by Ducasse in a discussion of Moore’s
refutation. Ducasse points out that the difference between dancing a waltz and dancing a foxtrot does
consist in a difference between two ways of dancing. However, the example does no damage to Moore’s
argument for there is no plausibility in the interpretation of ‘He perceived the colour blue’ as ‘He
perceived bluely’. What sort of activity could this objectless perception be, and how could it be
performed ‘bluely’?
This example of Ducasse’s points to a general conclusion concern ing the conditions under
which what is spoken of as the object of an activity can be identical with that activity: it can be so only if
it either is the activity itself or is a mode in which the activity can be carried on. How else could what a
man x-ed be his x-ing of it? Now, just as Berkeley’s idealism committed him to the identity of what is
perceived and the perceiving of it, so Kant’s commits him to the identity of what we can intuit and our
ability to intuit it. If my general conclusion is right, then this identity could only hold if an object we
can intuit were a mode of the ability to intuit. There is a passage in which Kant speaks of objects of
intuition in this way.
We then realise that not only are the drops of rain mere appearances, but that even their round
shape, nay even the space in which they fall, are nothing in themselves, but merely modifications
or fundamental forms of our sensible intuition. . . . (CPR, p. 85, A 46)
This consequence of Kant’s idealism is, if anything, more absurd than the corresponding consequence
of Berkeley’s, for blue, an object of sensation, is at least a mode of something, although it is difficult to
see how it can be a mode of whatever non-relational activity or state sensation might be. A raindrop, an
object of the ability to intuit, being a particular thing, cannot be a mode at all.
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