C. D. Broad

Entry in Encyclopedia of Religion and Ethics, ed. James Hastings et al, Vol. 10 (Edinburgh and New York, 1919): 587-592.
  1. Existence and reality
  2. Reality of universals
  3. Appearance and reality
  4. Ethical sense of the term

The words 'real' and 'reality' are used in a variety of different senses; it is therefore impossible to give a single satisfactory definition of them. Moreover, in the most fundamental sense in which they are used they are indefinable. Their meaning is best made clear by considering certain correlative expressions in which they are commonly met (e.g., reality and appearance) and by discussing their relations to certain other notions with which they are vary closely connected (e.g., existence).

1.Existence and reality

In the ordinary philosophic use of reality it would seen that a distinction is drawn between it and existence; for some things which would be asserted to exist would be denied by the same philosopher to be real and some things that are said to be real are denied to exist. The two words therefore, cannot be reasonably regarded as having the same intension, and any one who says that their extension is identical is called upon to give some proof of his assertion; e.g., many philosophers deny that such things as colours are real, but it seems hardly possible to deny that they exist. When I see a colour or hear a sound, I am aware of something, and not of nothing. Also I am aware of something different in the two cases, and the difference seems to be between the objects of which I am aware, and not merely between my two awarenesses as mental acts.

Sounds and colours then may be said to exist at any rate so long as any one is aware of them; and those who deny that they are also real are denying something the absence of which is compatible with their existence in the above sense. The two words are not, however, used consistently, and it would perhaps be much in accordance with usage to say that colours are real but do not exist. At any rate, this example shows that reality and existence differ in intension; and we shall see reasons for preferring to say that colours exist even though they be unreal rather than that they are real even though they do not exist.

The fact that reality and existence differ in intension can also be shown from another side. Many philosophers hold that such things as the number 3 are real; but hardly any one would say that 3 exists, though of course certain collections of three things may exist -- e.g., the Estates of the Realm and the Persons of the Trinity.

As a foundation for setting up a consistent terminology, we have the following two facts about the common use of words (a) hardly any one would think it appropriate to say that such things as numbers exist, but many would say that they are real; and (b) there are two kinds of things which almost every one would agree to exist if they be real -- physical objects and minds with their states. With these two facts fixed, we may proceed to deal with the more doubtful cases of such objects as sounds and colours. We note that the two kinds of objects which are said without hesitation to exist if they be real are particular individuals; i.e., they are terms which can be subjects of propositions but not predicates. Minds and physical objects clearly stand in this position. Objects which are said to be real but are seldom naturally said to exist are universals, whether qualities or relations -- i.e., terms which can be subjects of propositions but can also occupy other positions in them. The number 3 is an example; for we can say both that 3 is an odd number and that the Persons of the Trinity are three. We may therefore lay it down as a general rule that objects are most naturally said, not merely to be real but also to exist when they are real and have the logical character of particular individuals.

When a man says that he sees a colour, he means that he is aware of an extended coloured object and not merely of a quality. This coloured object -- e.g., a flash of lightning -- is a particular, and therefore, if real, exists. When we say that red exists, we mean two things: (1) that there are red objects, and (2) that these are particulars. The first part of our meaning corresponds to the wider technical use of existence which is involved when mathematicians talk of existence-theorems. In this sense a universal is said to exist if it can be shown that it has or may have instances. Thus the number 3 exists in this sense because we can point to collections having three terms. But this is not the common use of existence in philosophy. To be able to say that a quality like red exists, we must be able to show both that it has instances and that these are particulars; for it is only particulars that are primarily said to exist, and existence, in the secondary sense in which it is ascribed to red, is derived from the existence, in the primary sense, of its instances. It seems, however, that we do not naturally ascribe existence to a universal in all cases where it has instances which are particulars. The number 3 has instances which are particulars, yet we do not commonly say that it exists. This difference in usage seems to depend on whether or not the judgment in which the quality is asserted of the subject occurs instinctively and without a recognized process of intellectual analysis. When we see a red object, we pass, if we choose, to the judgment 'This is red' without explicit analysis, and so we say that red exists; to judge that a collection which we see has three members, we have to break it up in thought and resynthesize_it, and so we hesitate to say that 3 exists, though we admit that it is real. It is difficult to believe that this difference of usage is of any philosophical importance, but it is necessary to notice it.

2.Reality of universals.

We have now to ask in what sense such objects as colours can be said to be unreal though they exist. It certainly seems that in the primitive senses of reality and existence nothing can exist that is not real. And this must be accepted; coloured objects, while we see them, both exist and are real in the primary sense of reality. But both their reality and their existence are denied by many philosophers; those philosophers must therefore be using the term in a new sense. To say that red is unreal though it exists means

  1. that red objects exist while they are perceived;
  2. that nothing is red except when some one perceives it; and
  3. that it is commonly believed that things might be red though no one perceived them.
The third factor is quite essential. Toothache exists only when some one feels it, yet no one calls toothache unreal on this account. We may say, then, that reality is denied of a quality in this special sense when there are particular instances of it which we perceive, and our perception is accompanied by the belief in unperceived instances of it, and this belief is held to be erroneous.

It is clear that every immediate object of our senses both exists and is real in the primary meaning of these terms so long as we remain aware of the object. For it seems to be a synthetic a priori proposition that anything of which we can be directly aware by our senses is both real and particular; and what is real and particular exists in the primary meaning of that word. In a secondary meaning of reality, such objects may be called unreal if they give rise instinctively to judgments asserting the continued existence of the same or similar objects when unperceived, whereas in fact nothing of the kind can exist unperceived. Questions as to the reality of any particular, when reality has its primary sense, can arise only if that particular be not an object of direct awareness. Thus we ask, Does God really exist? or, Are atoms real? The meaning of such questions is as follows: God and atoms are not the direct objects of our minds at any time: if they were, there could be no doubt of their existence and reality in the primary sense at certain times (viz. when we were directly aware of them). But we know what we mean by the words 'God' and 'atom'; e.g., we may mean by 'God' an ens realissimum or a First Cause. But these descriptions which we understand are partly in terms of universals; thus 'first' and 'cause' are universals. When we ask whether God really exists, we mean, Is there an instance of the complex universal involved in the definition or description of what we mean by the word 'God'? We can see that, if there be an instance, it must be a particular; so that, if there be one, God is both real and existent.

We may now turn to those objects that commonly would be said to be real but not to exist. It would seem that every simple universal of which we are immediately aware must be real (a) in the primary sense, and also (b) in a secondary sense which involves the already-mentioned secondary sense of existent as a special case. If we are directly aware of a universal, it is the object of a thought, and is clearly something real in the same sense in which a particular flash of light is real when it is the object of our senses. It does not, however, exist in the primary sense because it is not a particular. Again, to be aware of a single universal, it is necessary to have been aware of some instance of it. Thus any simple universal of which we are directly aware must have instances. It must therefore exist in the mathematical sense. It need not, however, exist in the philosophical sense, because its instances may not be particulars; e.g., we are directly aware of the universal colour, but the instances of colour are red, yellow, etc., which are themselves universals. Thus it seems more natural to say that colours exist than that colour exists. Nevertheless this is largely a matter of mere usage. We cannot become aware of a simple universal of a higher order unless we are aware of one of the next lower grade, and so on till we come to the lowest universals in the hierarchy -- those whose instances are particulars. Thus, to become acquainted with colour, we need to be acquainted with colours; and, to become acquainted with colours, we need to be acquainted through our senses with particular coloured objects. So we may fairly say that every simple universal of which we are directly aware either exists in the secondary sense or is known through universals that are instances of it and themselves exist in the secondary sense.

It follows that the only universals about the reality of which questions can reasonably be asked are either

  1. those which are not directly cognized by us, but are described in terms that we understand, or
  2. complex universals.
The questions that can be asked about the reality of such universals are closely connected; e.g., it may reasonably be doubted whether any one is directly acquainted with the number twelve million and forty-nine. But we all know this number perfectly well under the description of 'the number which is represented in the decimal scale of notation by the symbols 12,000,049,' provided that we are aquainted with all the terms involved in this description and with the significance of their mode of combination in it. It is then open to ask: Is there really such a number? This question involves two others: (a) Is there anything contradictory or incoherent in the description, as there would be if a number were described as that represented in the decimal scale by a bow and arrow? and (b) If the description be self-consistent and intelligible, is there really an object answering to it? If both these questions can be answered in the affirmative, the number will be said to be real in the primary sense. We can then go on to ask the question: Is there any collection of particulars that has this number ? If so, we can add that the number exists in the secondary philosophic sense in which existence can be predicated of universals.

Very similar questions arise over complex universals -- e.g., a golden mountain. It would seem that complex universals which involve no internal incoherence must be real in the primary sense if their constituents be real. Thus the universal 'golden mountain' is real even though there are as a matter of fact no golden mountains. If the universal has no instances, it will exist neither in the mathematical nor in the philosophic sense; if it has instances which are not particulars -- as, e.g., the complex universal 'perfect number' -- it will exist in the mathematical but not in the philosophic sense. But very difficult questions arise as to the reality of complex universals which involve a contradiction or some other a priori incoherence -- e.g., a 'round square.' Can we say that such universals are in any sense real?

This question has been discussed very fully and acutely by Meinong and his pupils. The following are arguments for supposing that such universals are in a sense real. These incoherent universals appear as the subjects of propositions -- e.g., in 'A round square is round' and 'A round square is impossible.' Such propositions are not about nothing; they seem to be about round squares; hence even these universals must have primary reality. Again when we understand such a proposition as 'A round square is impossible,' the proposition is the object of an act of judgment, and, as such, is real. But the proposition is i complex, and, to understand it, its elements must also be the objects of acts of presentation. Hence the universal 'round square' must be the object of certain mental acts; it therefore cannot be nothing, and must have primary reality. It will be seen that the question discussed here is similar to that raised by Plato in the Sophist: In what sense, if any, can not-being be?

Meinong and his school have been led to the view that there is a most primitive form of being that applies to all objects about which assertions or denials can be made, whether they be internally coherent or not; that reality is a species of this and existence a species of reality. We may agree that anything that is really the object of a state of mind, or is really the subject of a proposition, has what we have called primary reality; but we are may doubt whether such objects as round squares have any kind of being at all. For Meinong's views lead to very grave difficulties. This form of being will have no opposite, and the law of contradiction will not hold for propositions about impossible objects. Thus the propositions 'A non-human man is human' and 'A non-human man is not human' will both be necessarily true, and yet be contradictory. Again, the expedient leads to an infinite series of orders of being of increasing absurdity. Suppose we agree with Meinong that a round square has being. Then the proposition 'A non-being round square has not being' seems as genuine and necessary as 'A round square is round.' But, if the latter forces us to ascribe a kind of being to round squares, the former must equally force us to ascribe a kind of being to non-being round squares. And this process of postulating fresh and ever more absurd kinds of being will go on indefinitely. Closely connected with these difficulties is the question whether propositions, and in particular false propositions, be in any sense real. Meinong assumes that all mental acts concerned with propositions are founded on an act in which the proposition is before our minds as sense-data and universals are when we are directly aware of them. If so, propositions which we judge, whether they be true or false, have exactly the same claims to primary reality as a red patch that we see or the quality of redness that we cognize. Yet it is very difficult to believe that every false proposition that any one has ever judged is real; whilst, if we reject the reality of false propositions, we can hardly save that of true ones.

The general means of meeting Meinong's difficulty depends on recognizing the fact that, in the verbal forms which stand for propositions, the word or phrase that counts as grammatical subject cannot he regarded always as the proper name of the logical subject of the proposition. In the sentence 'Red is a colour' the grammatical subject 'red' is the proper name of the logical subject of the proposition, and therefore the universal red is real; but it does not follow that in the grammatically similar form of words 'A round square is round,' the phrase 'a round square' is the name of anything. In fact two other possibilities remain open: (1) that the sentence 'A round square is round,' though it has the same verbal form as some sentences which do stand for propositions -- e.g., 'A penny is round' -- does not itself stand for any proposition, and (2) that, whilst the sentence does stand for some proposition, the proposition for which it stands can be analysed into a combination of several in none of which a single object whose name is 'round square' appears as object.

Both these alternatives may be used for dealing with the reality of round squares. In the first place, we may suggest that a sentence like 'A round square is round' seems to stand for a proposition only because of its similarity in grammatical form to certain sentences which do stand for genuine propositions. Actually, when we see these marks or hear the corresponding sounds, we do not think of any proposition whatever. And likewise, when we say that it is necessary that a round square should be round, we mean only that sentences in which the name of a part of the grammatical subject appears as the grammatical predicate stand for necessary propositions if they stand for propositions at all. On the other hand, the statement 'A round square is contradictory does stand for a genuine proposition, but it is not a proposition about as object denoted by the phrase round square.' The proposition really is: 'If an object be round, it cannot be square, and conversely.' This proposition does not contain a complex term denoted by 'round square,' but asserts a relation of incompatibility between roundness and squareness. Hence its reality, truth, and intelligibility do not imply the reality of a complex universal 'round square.'

Before leaving this subject, a word must be said about the reality of objects that involve an a priori incompatibility, but in which the incompatibility is not obvious without proof as in the case of 'round' and 'square.' Does the phrase, 'an algebraic equation of the second degree one of whose roots is p,' stand for any real object? It does not, for it involves a priori incompatibilities. But we must not say that sentences with this phrase as their grammatical subject as used by most people are in the same position as 'A round square is round.' For persons who do not see the a priori incompatibility these sentences may stand for propositions, though they cannot be about any object of which the phrase in question is the name.

3. Appearance and reality.

The question of the reality of propositions would lead us into problems connected with Bertrand Russell's theory of judgment ad G. F Stout's doctrine of real possibilities which would carry us too far afield. We will therefore pass at once to the opposition between reality and appearance, with which is connected the doctrine that there are degrees of reality.

The simplest and most obvious case of this opposition is what is known as the contrast between sensible appearances and physical realities. A cup is believed to be round, yet from all points of view but those which lie in a line through the centre of the circle and at right angles to its plane it appears elliptical. The elliptical shapes seen from the various point of view are called the 'sensible appearances' of the cup, and are contrasted with its real shape. It must be noticed that the opposition between sensible appearance and physical reality is not simply that between true and false judgment. The elliptical appearance may never lead us to the false judgment that the cup is elliptical; moreover, if it should do this and the error should afterwards be corrected, the cup does not cease to appear elliptical. It is important to be clear on this point because efforts are sometimes made to hold that appearances are not objects connected in a certain way with a physical reality, but are certain ways of viewing a physical reality. The latter theory makes appearances mind-dependent in a way in which the former does not. When we talk of different ways of viewing one reality, the differences must be supposed to qualify our acts of viewing, and not the object viewed; they are thus differences in mental acts and can subsist only while the acts themselves exist. But, if we suppose different appearances to be different objects, then, though it is possible and may be probable that these objects exist only when the acts which cognize them exist, it remains a fact that they are not in any obvious sense states of mind or qualities of such states.

Now it seems certain that different sensible appearances are different objects, and not merely different mental relations to the same object. Inspection shows clearly that the elliptical shape wish is seen from the side is as good an object as the circular shape seen from above. Moreover, if we call the appearances mental acts, to what precisely does the quality 'elliptical' which we ascribe to the appearances belong? Surely not (a) to any mental act, for these have no shape; nor (b) to the physical object, for this is supposed to be round; and, if it be said (c) that it applies to 'the physical object as seen from such and such a place,' the supporter of this alternative may be asked to state what he supposes this partly mental and partly physical complex to be, and how he supposes it to have the spatial predicate of ellipticity. The view against which we are arguing is somewhat supported by the common phrase, 'The cup is round but looks elliptical.' But the only meaning which it seems possible to give to this is the following: viewing the cup from a position from which the real shape cannot be seen, we are aware of an appearance that has the same shape as we should see if we looked straight down on a cup that was really elliptical.

We may say, then, that a sensible appearance is a reality, but it is not a physical reality, because it does not obey the laws of physics; and it is not a mental reality in the sense of a state of mind, nor is it any quality of a mental act, though it is commonly believed that it exists only as the object of an act of sensation or perception. We may agree, then, so far with two celebrated dicta about appearance and reality: 'Reality must in some way include all its appearances,'1 and 'Wieviel Schein soviel Hindeutung auf Sein.'2 Since an appearance, taken by itself, is as real as anything else (in the primary sense of reality), it can be called an appearance only in virtue of some essential reference in it to something with which it is contrasted. Thus sensible appearance is contrasted with physical reality; both are real in the primary sense, but the former is called an appearance because it always tends to make us think of the existence and qualities of the latter, and we have a tendency to ascribe qualities to the one that belong only to the other.

The last point is of considerable importance with reference to the statement that Reality is a harmonious whole and that appearances are condemned because of their internal incoherence or contradiction. Reality is here used as a concrete substantive, and means the whole system of what really exists. But presumably it is also true that anything that is real, and therefore any part of Reality, must be internally coherent. Now, sensible appearances are real, as we have tried to show; hence they must be internally consistent. There is no internal inconsistency in a real elliptical patch seen by say one, and the person who calls this an appearance does not do so because of any internal incoherence, if he know what he is about. The coherence arises when the elliptical red patch is taken to be identical with some other part of Reality (e.g., a colourless circle) whose qualities are incompatible with its own. The elliptical red patch is certainly real, and the colourless circle may very well be real; the former is called an appearance, and the latter a reality, because objects of the latter kind are of much greater practical interest and importance as obeying the laws of physics, and because the intimate relations between the two are liable to cause us to make the mistake of identifying the qualities of the two where they really differ. Reality -- the whole system of all that exists -- must include both the elliptical red patch and the colourless circle, if both be real; and their precise nature and relations are a matter for further philosophical investigation.

This seems obvious enough when we consider only the contrast between sensible appearance and physical reality. But we must notice that eminent philosophers use the contrast in many cases where what they call the appearance is not an object of sense-perception. F. H. Bradley, e.g., argues that the self and goodness and relations are all appearances, though appearances of different degrees of reality. What precisely does this mean? Primarily, that certain notions which we all use in thinking about the world are internally inconsistent. We treat the world, e.g., as consisting of various term in various relations to each other. Bradley tries to show that such a view involves vicious infinite regresses. When appearance is used in this sense, it seems to be connected with a special kind of false judgment, viz. The assertion that the world or some part of it has incompatible characteristics. This is very different from the kind of false judgment connected with sensible appearances. (1) As we saw, no kind of false judgment need be made there, and, if it be made and corrected, the sensible appearance continues to exist and be perceived. (2) There is nothing self-contradictory in the predicate that is wrongly ascribed to physical reality through confusing it with sensible appearance. The judgment 'This cup is elliptical' is false, not because there is anything self-contradictory in the predicate 'elliptical,' but because it is incompatible with the circularity that the physical cup is supposed to possess. On the other hand, if the self be an appearance in Bradley's sense, the assertion 'Socrates is a self' is false, because the predicate is self-contradictory: it is like saying 'Socrates is both tall and short.' The quality of being a self can be truly asserted of nothing, whilst that of being elliptical can be truly asserted at least of the sensible appearance. There is thus a great difference between what is meant by calling the seen ellipse an appearance and calling the self an appearance.

When this difference is recognized, we see that, whilst it is obvious that sensible appearances are contained in Reality, it is not at all obvious in what sense such appearances as the self can be contained in it; for these would seem to be in the position of round squares. This brings us to the doctrine that there are degrees of reality. It is held that all appearances are internally incoherent, but that some are more coherent than others. As a corollary to this, it is maintained that no appearance is as such contained in Reality; on the other hand, as Bradley puts it, 'appearances are transmuted' in order to be contained in Reality, and the one-sidedness of one appearance cancels out with and is corrected by that of others. This doctrine seems to be closely connected with three others:

  1. Reality as a whole being a harmonious system, it is assumed that, the more an appearance needs to be modified and supplemented in order to take its place in Reality, the less coherent and therefore the less real it is; and
  2. this is largely dependent on the view that all appearances is connected with the peculiar position of finite minds, which can know Reality only fragmentarily and from an individual angle; lastly
  3. it is held that no part of Reality can be internally coherent in abstraction from its relation to the rest of Reality. We may trace the development of this view in Spinoza's doctrine of the three kinds of knowledge and in The Hegelian dialectic to its completest form in Bradley's philosophy.

It is clear that both (a) and (b) are needed if it is to be assumed that Reality is the only harmonious system. And this is assumed; for very often something is condemned as appearance, not so much because of any internal incoherence that can be directly detected in it as because it obviously cannot be predicated of Reality as a whole. It is impossible to give a fair and adequate criticism of so subtle and elaborate a doctrine here. But the following remarks may be made:

(1)Either Reality can be correctly regarded as possessing parts or not. If so, it would seem that there must be some propositions that are true about the parts and not about the whole (e.g., that they are parts). And again, if the parts be real, they must be as internally harmonious as the whole. It may be perfectly true that what we take as one self-subsistent differentiation of Reality is often neither one nor self-subsistent, but a mere fragment whose limits do not correspond with those of any single differentiation (cf. here Spinoza's distinction between the hierarchy of infinite and eternal modes and the finite modes, and his closely connected theory of error). But even a fragment is something and has a nature of its own, and perfectly true judgment should be possible about it. We may of course make erroneous judgments if we ignore the fact that it is a fragment, and if we make assertions about that in it which depends on its relations to what is outside it. But we do not always ignore the fact that what we are talking about is not the whole; e.g., when we say that Socrates is a self, we are perfectly aware that Socrates is only a part of Reality, and that our statement may be false of the whole. And it is not obvious that all assertions about a fragment must depend for their truth on what is outside the fragment (cf. here Spinoza's doctrine of the function of the notiones communes in passing from imaginative to rational knowledge). If, on the other hand, we suppose that Reality cannot be correctly regarded as having parts, the question arises: What precisely is it that is called an appearance, and what precisely is supposed to be 'transmuted and supplemented' in Reality? Something must be transmuted and supplemented; it cannot be Reality as a whole; what can it be unless Reality has real parts? Bradley has seen these difficulties perhaps more clearly than any other philosopher of his general way of thinking; but it is hard to believe that his doctrine that Reality is a supra-relational unity, and that all predication involves falsification is a satisfactory solution. Indeed, it perhaps comes to little more than a restatement of the theological position that the nature of God can be described only in negative terms which at least ward off error.

(2) Sensible appearances, which, as we have seen, differ in important respects from others, are also held to exhibit what may be called degrees of reality in a special sense. As we know these realities are called appearances and unreal only with respect to their relation to a supposed physical reality about which they are held to be an indispensable source of information. Now, those who deny the physical reality of secondary qualities would be inclined to say that the colours seen in waking life are less real than the shapes that are seen at the same time, and more real than the colours and shapes seen in dreams, delirium, or illusions. We may usefully compare here Kant's distinction between Schein, Erscheinung, and Ding-an-Sich in his example about the rainbow to that between the colours and shapes of dreams, the colours of waking life, and the qualities of physical objects (it is not of course suggested that Kant had in mind precisely the distinctions which we are now considering).

As far as can be seen, the ascription of degrees of reality to sensible appearances simply depends on how intimately their qualities are supposed to be connected with those of a corresponding physical Reality. To a man who takes the position of Locke and of most natural scientists the elliptical shapes seen in waking life (to revert to our old example) are the most real of appearances, because the corresponding physical reality actually has a shape, and that shape is a closed conic section connected by simple laws with that of the appearance. The colours seen in waking life are less real appearance because it is not believed that any physical object has colour, though it is held that the colour seen is correlated with the internal structure of the corresponding object. And the shapes and colours of dreams or hallucinations are held to have the lowest degree of reality, because, while it is admitted that they are correlated with distinctions that exist somewhere in the physical world, it is held that these distinctions exist in the brain or in the medium rather than in any object that can be regarded as specially corresponding to the appearance in the way in which the round physical cup corresponds to the elliptical visual appearance seen in waking life.

4 Ethical sense of the term

It remains to notice one more use of the words 'real' and 'reality.' They are sometimes used in an ethical sense to stand for what ought to be as distinct from what is. This is rather a paradoxical use of terms. Often we contrast real and ideal, and say that what actually exists is real, whilst what ought to exist but does not is ideal. Yet some ethical writers use the word 'real' for 'ideal,' when they speak of the real or true self, meaning the self that ought to be as contrasted with that which now is. This use of terms is generally connected with metaphysical theories of ethics such as Kant's or Green's, which hold that the self that ought to be really exists and has a higher degree of reality than that would commonly be called the self as it really is.


The following works are of importance in connexion with the subject of this article.

  1. On the relation of reality to existence and on the reality of contradictory objects.
    • Plato, Sophist and Theaetetus;
    • St. Anselm, Prosologium and c. Insipientem;
    • A. Meinong, Über Annahmen, Leipzig, 1910, Über die Stellung der Gegenstandstheorie, do. 1906-09, Untersuchungen zur Gegenstandstheorie und Psychologie, do. 1904;
    • B. A. Russell, The Problems of Philosophy, London, 1012, The Principles of Mathmatics, Cambridge, 1903;
    • A. N. Whitehead and B. A. W. Russell, Principia Mathematica, do. 1910;
    • G. F. Stout, 'The Object of Thought and Real Being,' Proc. of the Aristotelian Society, 1911.
  2. On the relation of appearance to reality.
    • Spinoza, Ethics, tr. W. H. White, London, 1894;
    • F. H. Bradley, Appearance and Reality, London, 1902, Essays on Truth and Reality, Oxford, 1914.
  3. On sensible appearance and physical reality.
    • Descartes, Meditations;
    • G. Berkeley, Principles of Human Knowledge, London, 1776;
    • Kant, Critique of Pure Reason, tr. J. H. Sterling, Edinburgh, 1881;
    • H. A. Prichard, Kant's Theory of Knowledge, 0xford, 1909;
    • Russell, Our Knowledge of the External World, Chicago, 1914;
    • Stout, Manual of Psychology, London, 1913;
    • S. Alexander, artt. in Mind, new ser., xxi (1912), Proc. Arist. Soc., new ser., xi. [1910-11], and Proc. British Academy, vi. [1914].

Transcribed into hypertext by Andrew Chrucky, May 27, 2000.