applicable to this terrestial life, but only to an imagined celestial existence. Where, however, this celestial existence would differ from ours, so far as logic is concerned, would be not in the nature of what is known, but only in the accuracy of our knowledge. Therefore, if the hypothesis of a precise symbolism enables us to draw any inferences as to what is symbolised, there is no reason to distrust such inferences merely on the ground that our actual symbolism is not precise. We are able to conceive precision; indeed, if we could not do so, we could not conceive vagueness, which is merely the contrary of precision. This is one reason why logic takes us nearer to heaven than most other studies. On this point I agree with Plato. But those who dislike logic will, I fear, find my heaven disappointing.

It is now time to tackle the definition of vagueness. Vagueness, though it applies primarily to what is cognitive, is a conception, applicable to every kind of representation— for example, a photograph, or a barograph. But before defining vagueness it is necessary to define accuracy. One of the most easily intelligible definitions of accuracy is as follows: One structure is an accurate representation of another when the words describing the one will also describe the other by being given new meanings. For example, "Brutus killed Caesar" has the same structure as "Plato loved Socrates," because both can be represented by the symbol "x R y," by giving suitable meanings to x and R and y, But this definition, though easy to understand, does not give the essence of the matter, since the introduction of words describing the two systems is irrelevant. The exact definition is as follows: One system of terms related in various ways is an accurate representation of another system of terms related in various other ways if there is a one-one relation of the terms of the one to the terms of the other, and likewise a one-one relation of the relations of the one to the relations of the other, such that, when two or more terms in the one system have a relation belonging to that system, the corresponding terms of the other system have the corresponding relation belonging to the other system. Maps, charts, photographs, catalogues, etc., all come within this definition in so far as they are accurate.

Per contra, a representation is vague when the relation of the representing system to the represented system is not one-one, but one-many. For example, a photograph which is SO smudged that it might equally represent Brown or Jones or Robinson is vrgu. A small-scale map is usually vaguer than a large-scale map, because it does not show all the turns and twists of the roads, rivers, etc., so that various slightly differ

ent courses are compatible with the representation that it gives. Vagueness, clearly, is a matter of degree, depending upon the extent of the possible differences between different systems represented by the same representation. Accuracy, on the contrary, is an ideal limit.

Passing from representation in general to the kinds of representation that are specially interesting to the logician, the representing system will consist of words, perceptions, thoughts, or something of the kind, and the would-be one-one relation between the representing system and the represented system will be meaning. In an accurate language, meaning would be a one-one relation; no word would have two meanings, and no two words would have the same meaning. In actual languages, as we have seen, meaning is one-many. (It happens often that two words have the same meaning, but this is easily avoided, and can be assumed not to happen without injuring the argument.) That is to say, there is not only one object that a word means, and not only one possible fact that will verify a proposition. The fact that meaning is a one-many relation is the precise statement of the fact that all language is more or less vague. There is, however, a complication about language as a method of representing a system, namely, that words which mean relations are not themselves relations, but just as substantial or unsubstantial as other words. In this respect a map, for instance, is superior to language, since the fact that one place is to the west of another is represented by the fact that the corresponding place on the map is to the left of the other; that is to say, a relation is represented by a relation. But in language this is not the case. Certain relations of higher order are represented by relations, in accordance with the rules of syntax. For example, "A precedes B" and "B precedes A" have different meanings, because the order of the words is an essential part of the meaning of the sentence. But this does not hold of elementary relations; the word "precedes," though it means a relation, is not a relation. I believe that this single fact is at the bottom of the hopeless muddle which has prevailed in all schools of philosophy as to the nature of relation. It would, however, take me too far from my present theme to pursue this line of thought.

It may be said: How do you know that all knowledge is vague, and what does it matter if it is? The case which I took before, of two glasses of water, one of which is wholesome while the other gives you typhoid, will illustrate both points. Without

(A word is a class of series, and both classes and series are logical fictions. See "Analysis of Mind," chapter x; "Introduction to Mathematical Philosophy," chapter xvii.)

calling in the microscope, it is obvious that what you see of a man who is 200 yards away is vague compared to what you see of a man who is 2 feet away; that is to say, many men who look quite different when seen close at hand look indistinguishable at a distance, while men who look different at a distance never look indistinguishable when seen close at hand. Therefore, according to the definition there is less vagueness in the near appearance than in the distant one. There is still less vagueness about the appearance under the microScope. It is perfectly ordinary facts of this kind that prove the vagueness of most of our knowledge, and lead us to infer the vagueness of all of it.

It would be a great mistake to suppose that vague knowledge must be false. On the contrary, a vague belief has a much better chance of being true than a precise one, because there are more possible facts that would verify it. If I believe that so-and-so is tall, I am more likely to be right than if I believe that his height is between 6ft. 2in. and 6ft 3in. In regard to beliefs and propositions, though not in regard to single words, we can distinguish between accuracy and precision. A belief is precise when only one fact would verify it; « it is accurate when it is both precise and true. Precision diminishes the likelihood of truth, but often increases the pragmatic value of a belief if it is true-for example, in the case of the water that contained the typhoid bacilli. Science is perpetually trying to substitute more precise beliefs for vague ones; this makes it harder for a scientific proposition to be true than for the vague beliefs of uneducated persons to be true, but makes scientific truth better worth having if it can be obtained.

Vagueness in our knowledge is, I believe, merely a par- ticular case of a general law of physics, namely, the law that what may be called the appearances of a thing at different places are less and less differentiated as we get further away from the thing. When I speak of "appearances" I am speaking of something purely physical-the sort of thing, in fact, that, if it is visual, can be photographed. From a close-up photograph it is possible to infer a photograph of the same object at a distance, while the contrary inference is much more precarious. That is to say, there is a one-many relation between distant and close-up appearances. Therefore the distant appearance, regarded as a representation of the closeup appearance, is vague according to our definition. I think all vagueness in language and thought is essentially analogous to this vagueness which may exist in a photograph. My own belief is that most of the problems of epistemology, in so far

as they are genuine, are really problems of physics and physiology; moreover, I believe that physiology is only a complicated branch of physics. The habit of treating knowledge as something mysterious and wonderful seems to me unfortunate. People do not say that a barometer "knows" when it is going to rain; but I doubt if there is any essential difference in this respect between the barometer and the meteorologist who observes it. There is only one philosophical theory which seems to me in a position to ignore physics, and that is solipsism. If you are willing to believe that nothing exists except what you directly experience, no other person can prove that you are wrong, and probably no valid arguments exist against your view. But if you are going to allow any inferences from what you directly experience to other entities, then physics supplies the safest form of such inferences. And I believe that (apart from illegitimate problems derived from misunderstood symbolism) physics, in its modern forms, supplies materials for answers to all philosophical problems that are capable of being answered, except the one problem raised by solipsism, namely: Is there any valid inference ever from an entity experienced to one inferred? On this problem, I see no refutation of the sceptical position. But the sceptical philosophy is so short as to be uninteresting; therefore it is natural for a person who has learnt to philosophise to work out other alternatives, even if there is no very good ground for regarding them as preferable.

PSYCHO-ANALYSIS IN ITS RELATION TO TRADITIONAL PSYCHOLOGY.*

I

By

H. TASMAN LOVELL, M.A., Ph.D., Associate Professor of Psychology, University of Sydney.

SHALL assume a general acquaintance with the principles of psycho-analysis. You all know that its fundamental conception is that of the "repressed wish," that a wish, as psychoanalysts regard it, is a movement of our very being, saturated with our feeling, and involving life itself. You also know of Freud's contention that wishes which conflict with our better and more social self tend, in spite of their urgent nature, to be repressed by us into what he is pleased to call the "unconscious.' You will remember, too, that this is not the last one hears of such dismissed wishes, that they are for ever trying to express or realise themselves, that this persistent striving of the unconscious wish requires that some sort of "resistance" to its re-entry into consciousness should be established; that Freud finds this resistance in the social, ethical, and religious principles which had already repressed the wish because of its incompatibility with themselves. You are aware that he calls this resistance the "censor of consciousness," imagining it as an active sentinel stationed, not at the entrance to explicit consciousness, but at the junction of the "fore-conscious" and the "unconscious," so that the mental conflicts with which he is concerned go on in the unconscious, that is, below the level of explicit consciousness. This is important to remember if one is adequately to comprehend Freud's view of mental conflict and his reason for saying that a patient who is being subjected to analysis, is unable to tell the physician the cause of his illness or the nature of his mental distress; there has supervened upon the repression an amnesia, or loss of memory, for the repressed wish, since its incompatibility with the personality makes it unwelcome and disturbing. You are aware that during sleep, and perhaps at other times, the censor or resistance is off guard to some extent, or manifests a lessened vigilance; that while this lessening of vigilance is usually insufficient to allow of an unabashed re-entry of the repressed wish, yet it does permit of return, provided the wish distort itself enough to be unrecognised by the censor as the old enemy. It is this process of distortion which is said to produce the dream and the neurotic symptom, the pursuit of

*This and the following paper were read before the Australasian Association of Psychology and Philosophy at its General Meeting held on May 19th, 1923.