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In defining knowledge, there are two further matters to be taken into consideration, namely the degree of certainty and the degree of precision. All knowledge is more or less uncertain and more or less vague. These are, in a sense, opposing characters: vague knowledge has more likelihood of truth than precise knowledge, but is less useful. One of the aims of science is to increase precision without diminishing certainty.

But we cannot confine the word "knowledge" to what has the highest degree of both these qualities; we must include some propositions that are rather vague and some that are only rather probable. It Is important, however, to indicate vagueness and uncertainty where they are present, and, if possible, to estimate their degree. Where this can be done precisely, it becomes "probable error" and "probability".

David K. Henderson and John Greco

But in most cases precision in this respect is impossible. In advanced scientific knowledge, the distinction between what is a datum and what is inferred is clear in fact, though sometimes difficult in theory. In astronomy, for instance, the data are mainly certain black and white patterns on photographic plates.

These are called photographs of this or that part of the heavens, but of course much inference is involved in using them to give knowledge about stars or planets. Broadly speaking, quite different methods and a quite different type of skill are required for the observations which provide the data in a quantitative science, and for the deductions by which the data are shown to support this or that theory.

There would be no reason to expect Einstein to be particularly good at photographing the stars near the sun during an eclipse. But although the distinction is practically obvious in such cases, It is far less so when we come to less exact knowledge. It may be said that the separation into data and inferences belongs to a well-developed stage of knowledge, and is absent in its beginnings.

But just as we found it necessary to admit that knowledge may be only a characteristic of behaviour, so we shall have to say about inference. What a logician recognises as inference is a refined operation, belonging to a high degree of intellectual development; but there is another kind of inference which is practised even by animals.

We must consider this primitive form of inference before we can become clear as to what we mean by "data". When a dog hears the gong and immediately goes into the dining-room, he is obviously, in a sense, practising inference. That is to say, his response is appropriate, not to the noise of the gong in itself, but to that of which the noise is a sign: his reaction is essentially similar to our reactions to words.

An animal has the characteristic that, when two stimuli have been experienced together, one tends to call out the response which only the other could formerly call out. If the stimuli or one of them are emotionally powerful, one joint experience may be enough-, if not, many joint experiences may be required. This characteristic is totally absent in machines. Suppose, for instance, that you went every day for a year to a certain automatic machine, and lit a match in front of it at the same moment at which you inserted a penny-, it would not, at the end, have any tendency to give up its chocolate on the mere sight of a burning match.

That is to say, machines do not display inference even in the form in which it is a mere characteristic of behaviour. Explicit inference, such as human beings practise, is a rationalising of the behaviour which we share with the animals. Having experienced A and B together frequently, we now react to A as we originally reacted to B. To make this seem rational, we say that A is a "sign" of B , and that B must really be present though out of sight. This is the principle of induction, upon which almost all science is based. And a great deal of philosophy is an attempt to make the principle seem reasonable.

Whenever, owing to past experience, we react to A in the manner in which we originally reacted to B , we may say that A is a "datum" and B is "Inferred". In this sense, animals practise inference. It is clear, also, that much inference of this sort is fallacious: the conjunction of A and B in past experience may have been accidental. What is less clear is that there is any way of refining this type of inference which will make it valid. That, however, is a question which we shall consider later. What I want consider now is the nature of those elements in our experiences which, to a reflective analysis, appear as "data" in the above-defined sense.

Traditionally, there are two sorts of data, one physical, derived from the senses, the other mental, derived from introspection. It seems highly questionable whether this distinction can be validly made among data; it seems rather to belong to what is inferred from them. Suppose, for the sake of definiteness, that you are looking at a white triangle drawn on a black-board. You can make the two judgments: "There is a triangle there", and "I see a triangle.

To illustrate the difference of the propositions: you might say "There is a triangle there", if you had seen it a moment ago but now had your eyes shut, and in this case you would not say "I see a triangle"; on the other hand, you might see a black dot which you knew to be due to indigestion or fatigue, and in this case you would not say "There is a black dot there. In the second case, you refuse to infer a public object, open to the observation of others. This shows that "I see a triangle" comes nearer to being a datum than "There is a triangle there. The word "I" derives its meaning, partly, from memory and expectation, since I do not exist only at one moment.

And the word "see" is a causal word, suggesting dependence upon the eyes; this involves experience, since a new-born baby does not know that what it sees depends upon its eyes.

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However, we can eliminate this dependence upon experience, since obviously all seen objects have a common quality, not belonging to auditory or tactual or any other objects. Let us call this quality that of being "visual". Then we can say: "There is a visual triangle. The difference between the physical and the mental, therefore, would seem to belong to inferences and constructions, not to data. It would thus seem that data, in the sense in which we are using the word, consist of brief events, rousing in us various reactions, some of which may be called "inferences", or may at least be said to show the presence of inference.

The two-fold organisation of these events, on the one hand as constituents of the public world of physics, on the other hand as parts of a personal experience, belongs to what is inferred, not to what is given. For theory of knowledge, the question of the validity of inference is vital.

Unfortunately, nothing very satisfactory can be said about it, and the most careful discussions have been the most sceptical. However, let us examine the matter without prejudice. It is customary to distinguish two kinds of inference, Deduction and Induction. Deduction is obviously of great practical importance, since it embraces the whole of mathematics. But it may be questioned whether it is, in any strict sense, a form of inference at all. A pure deduction consists merely of saying the same thing in another way. Application to a particular case may have importance, because we bring in the experience that there is such a case-for example, when we infer that Socrates is mortal because all men are mortal.

But in this case we have brought in a new piece of experience, not involved in the abstract deductive schema. In pure deduction, we deal with x and y not with empirically given objects such as Socrates and Plato. However this may be, pure deduction does not raise the problems which are of most importance for theory of knowledge, and we may therefore pass it by. The important forms of inference for theory of knowledge are those in which we infer the existence of something having certain characteristics from the existence of something having certain other characteristics.

For example: you read in the newspaper that a certain eminent man is dead, and you infer that he is dead. Sometimes, of course, the inference is mistaken. I have read accounts of my own death in newspapers, but I abstained from inferring that I was a ghost. In general, however, such inferences are essential to the conduct of life. Imagine the life of a sceptic who doubted the accuracy of the telephone book, or, when he received a letter, considered seriously the possibility that the black marks might have been made accidentally by an inky fly crawling over the paper.

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We have to accept merely probable knowledge in daily life, and theory of knowledge must help us to decide when it really is probable, and not mere animal prejudice. Far the most adequate discussion of the type of inference we are considering is obtained in J.

Keynes's Treatise on Probability So superior is his work to that of his predecessors that it renders consideration of them unnecessary. Keynes considers induction and analogy together, and regards the latter as the basis of the former. The bare essence of an inference by analogy is as follows: We have found a number of instances in which two characteristics are combined, and no instances in which they are not combined; we find a new instance in which we know that one of the characteristics is present, but do not know whether the other is present or absent; we argue by analogy that probably the other characteristic is also present.

The degree of probability which we infer will vary according to various circumstances. It is undeniable that we do make such inferences, and that neither science nor daily life would be possible without them. The question for the logician is as to their validity. Are they valid always, never or sometimes? Freud, S. The neuro-psychoses of defence. Strachey Ed. London: Hogarth. The loss of reality in neurosis and psychosis. In On psychopathology: Inhibitions, symptoms, anxiety pp. Richards Ed. Harmondsworth: Penguin. Mourning and melancholia. In On metapsychology: The theory of psychoanalysis pp.

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