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sense, and not the actual bed, which are imitated by the artist, and these pavтáoμaтa or eidwλa are actually like the work of the painter. The appearances to sense are on exactly the same level as the shadows or reflexions or images whether made by God or made by man. Again in Rep. 602 cd we get a clear confirmation of the view that all alo@nois especially sight is included under eixaoía. We are given a simple case of the passage from the appearances to a reality or actuality behind them. Plato points out that so far as sight is concerned, things may appear bent in water and straight outside, a thing may appear concave when it is convex and convex when it is concave, and again if we have two things equal in size they appear different in size to the eye according as they are near or far away. These appearances we suggest are eikóves, and so long as we take them merely at their face value, so long as we are satisfied with making them clear to ourselves and do not seek to go behind them, we are in eixaría. There is so far no question of error. The things do appear so. Every appearance is just different and that is all about it. But if we want to know what the thing actually is, we get at it by counting and weighing and measuring, so that not the apparent size, shape and quantity may rule in our souls but rather the actual size, shape and quantity determined by mathematical measurement or calculation—τὸ μετρεῖν καὶ ἀριθμεῖν καὶ ἱστάναι. By this means we pass to πίστις, to the actual world of solid bodies-in fact to animals, plants, and manufactured articles. This means clearly that as far as secondary qualities are concerned-compare Theaetetus, 154 a— we must always be satisfied with εἰκασία or αἴσθησις. They are what they seem and they may seem different to different men or to the same man at different times. But primary qualities are on a different level; in regard to them we can

* R. 602 d.

distinguish between the merely apparent which is given to εἰκασία and the actual which is determined by πίστις.

And surely in this Plato is right. Like any other image or reflexion these appearances of sense are mere appearances. They are what they seem and they seem what they are. Each dúvaμs gives us its proper objects, we see colours and we hear sounds, but rà κowà, sameness and difference, likeness and unlikeness, and above all ovσía or being cannot be got through sense. Thus alonois apart from thinking has no part in ovola,† and therefore it has no part in truth. Clearly it must be classed not under Trioris but under eixaoía, though there are certain difficulties which we will recur to later.

It is no use saying that the objects of sense perception are distinguished from those of dreams or imagination by following upon what is called an external stimulus. Apart from the difficulty of knowing what this means, we are here describing eikaola not from within but from without. We can indeed come back to cikaoía afterwards with a knowledge of mathematical science and with an explicit metaphysic and we can distinguish its objects in this way, but eixaoía itself knows nothing of external stimuli; for the first stage of cognition all objects are on the same level of reality, and it makes no distinction of less and more real within them. It is for this reason that Hume, that most consistent of all sceptics and that subtlest defender of eixaoía as coextensive with the whole of knowledge, refused to distinguish impressions from ideas by reference to an external reality, and distinguished them only by less or greater degrees of vividness, though in so doing he ignored the fact that the images of our dreams are often more vivid than those of our waking life. It is also for this reason that Hobbes in the first chapter of the Leviathan informs us that "sense is in all cases nothing but original fancy," and again "their appearance to us is fancy the same waking that dreaming."

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We are now in a position to understand better the relation between the objects of εἰκασία and thsse of πίστις. It is only on the level of TiσTis that we pass to the actual which is consciously distinguished from the apparent. The typical case of this is the determination of the actual primary qualities by some sort of mathematical measurement or thinking, ἔργον λογιστικοῦ, R. 602 e.

Into the exact character of this mathematical thinking we need not enter in detail—that would belong to a discussion of πίστις and we are primarily concerned only with εἰκασία. But it is not simply a matter of measurement. The actual size of any object we never can see at all. It can never appear to us in εἰκασία. The size of any object as far as εἰκασία is concerned is never twice the same. If it is far enough away it will appear a mere point, if it is near enough it will blot out the heavens. This applies as much to a measure, e.g., a foot rule as to anything else. When we say that an object is a foot long we are not merely stating an equation between two infinite series, we are not merely saying that if we have the apparent object and the apparent foot rule in juxta-position whether near the eye or far from it they always have the same apparent size. We do not think that either the foot rule or the object actually becomes smaller as it recedes from the eye. On the contrary, we think their actual size is unvarying and is always relatively in the same proportion to other actually unvarying sizes. This is believed to be the only reasonable theory capable of explaining our experiences in sense. When one reflects on the extraordinary amount of subtle scientific thinking involved in reaching this conclusionthinking in comparison with which the discovery of the law of gravitation is mere child's play—and when one remembers that it is done by all of us in the first few years of childhood, one is impressed with a profound respect for the intellectual attainments of even the meanest of the human race.

This brings us to another point, that the objects of Tíoτis

as opposed to those of eixaría are wholly unperceivable, i.e., they can never be given to us in sense. We have seen that the actual size of any object is unperceivable and that we can identify the actual size with no one of the infinite apparent sizes. The same obviously applies to all solid shapes whatsoever. If we take even such an elementary figure as a solid regular sphere we can certainly never see it. All we can see is an infinite number of apparent hemispherical shapes varying infinitely both in colour and in size. By thinking about these sensations we conclude they can only be explained by the hypothesis that behind them is a solid sphere unvarying in size and incapable of being seen, i.e., that they are the many varying appearances of one solid sphere. When one comes to the theories of the scientists-who of course are only carrying on the same process more systematically-this becomes still more clear. The atoms and electrons of the scientist are believed in, but they can certainly never be seen.

Our view then is meant to be a defence of so-called realism against the idealists of the Berkeleyan school, a defence of the ordinary man's belief in the existence of a solid and relatively permanent world of actual things in space. It is also an attempt at least partially to justify the claims of science to be true against those who hold-like Benedetto Croce-that science is a mere invention or fiction made by us for purposes of convenience. The actual solid bodies of ordinary consciousness and science are no doubt an invention, a construction-they are not and cannot be given in sense-but if their existence is the only reasonable explanation of our experience in sense and is the condition of our having such an experience, we are justified in believing in their actual existence and in rejecting the unworkable theory of idealism which involves itself in hopeless difficulties as soon as it tries to understand our experience in detail. On the other hand Plato is surely right in calling our cognition of such objects mere faith or ioris and not knowledge. We cannot know certainly anything but an intelligible necessity,

which excludes of itself any possible alternative. This we are never in a position to assert positively either about the general theory that actual solid bodies exist or about any particular attempt to work out that theory in detail. And of course we must admit that the relation between our sensations and actual solid bodies-at first so simple-involves perhaps insurmountable difficulties, especially if we attempt to reverse the process of transition and to understand how ether waves or chemical changes in the brain can become for instance a sensation of red. But here we may be asking ourselves wrong questions or creating difficulties for ourselves, and in any case these difficulties are not greater than those which meet the idealist when he denies the existence of solid bodies altogether. Plato would perhaps put down these difficulties to the positively unreal and unintelligible character of all γιγνόμενα.

We would add here that these difficulties arise for the idealist as for the realist-as soon as he tries to explain the possibility of communication between different spirits. A noteworthy instance of this is Croce's intolerably confused account of the extrinsecation of art. Nor is this an accident. Although in most cases the idealists appear to assume the existence of other spirits besides themselves, they have no real reason for doing so which would not equally justify them in assuming the existence of actual solid bodies. Both assumptions are a matter of reasonable faith and not of knowledge, and indeed they appear to be bound up with one another. We pass to other spirits by a kind of syllogism in the sphere of πioris. These variously coloured appearances are, we say, explained by the movements of an actual solid human body. These movements in turn can be explained only by the volition of an eternal spirit. This appearance is the sign of a body. This body is the sign of a spirit. Thus we pass from heard sounds or seen colours to a spirit which is their source. The second stage of the argument involves some sort of philosophic thinking as opposed to the mathematical thinking of the first stage, but

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