Memory : Part 7

The Analysis of Mind
by Bertrand Russell

(Page 15 of 22)

Vague identity, which is really close similarity, has been a source of many of the confusions by which philosophy has lived. Of a vague subject, such as a "this," which is both an image and its prototype, contradictory predicates are true simultaneously: this existed and does not exist, since it is a thing remembered, but also this exists and did not exist, since it is a present image. Hence Bergson's interpenetration of the present by the past, Hegelian continuity and identity-in-diversity, and a host of other notions which are thought to be profound because they are obscure and confused. The contradictions resulting from confounding image and prototype in memory force us to precision. But when we become precise, our remembering becomes different from that of ordinary life, and if we forget this we shall go wrong in the analysis of ordinary memory.

Vagueness and accuracy are important notions, which it is very necessary to understand. Both are a matter of degree. All thinking is vague to some extent, and complete accuracy is a theoretical ideal not practically attainable. To understand what is meant by accuracy, it will be well to consider first instruments of measurement, such as a balance or a thermometer. These are said to be accurate when they give different results for very slightly different stimuli. A clinical thermometer is accurate when it enables us to detect very slight differences in the temperature of the blood. We may say generally that an instrument is accurate in proportion as it reacts differently to very slightly different stimuli. When a small difference of stimulus produces a great difference of reaction, the instrument is accurate; in the contrary case it is not.

Exactly the same thing applies in defining accuracy of thought or perception. A musician will respond differently to very minute differences in playing which would be quite imperceptible to the ordinary mortal. A negro can see the difference between one negro and another one is his friend, another his enemy. But to us such different responses are impossible: we can merely apply the word "negro" indiscriminately. Accuracy of response in regard to any particular kind of stimulus is improved by practice. Understanding a language is a case in point. Few Frenchmen can hear any difference between the sounds "hall" and "hole," which produce quite different impressions upon us. The two statements "the hall is full of water" and "the hole is full of water" call for different responses, and a hearing which cannot distinguish between them is inaccurate or vague in this respect.

Precision and vagueness in thought, as in perception, depend upon the degree of difference between responses to more or less similar stimuli. In the case of thought, the response does not follow immediately upon the sensational stimulus, but that makes no difference as regards our present question. Thus to revert to memory: A memory is "vague" when it is appropriate to many different occurrences: for instance, "I met a man" is vague, since any man would verify it. A memory is "precise" when the occurrences that would verify it are narrowly circumscribed: for instance, "I met Jones" is precise as compared to "I met a man." A memory is "accurate" when it is both precise and true, i.e. in the above instance, if it was Jones I met. It is precise even if it is false, provided some very definite occurrence would have been required to make it true.

It follows from what has been said that a vague thought has more likelihood of being true than a precise one. To try and hit an object with a vague thought is like trying to hit the bull's eye with a lump of putty: when the putty reaches the target, it flattens out all over it, and probably covers the bull's eye along with the rest. To try and hit an object with a precise thought is like trying to hit the bull's eye with a bullet. The advantage of the precise thought is that it distinguishes between the bull's eye and the rest of the target. For example, if the whole target is represented by the fungus family and the bull's eye by mushrooms, a vague thought which can only hit the target as a whole is not much use from a culinary point of view. And when I merely remember that I met a man, my memory may be very inadequate to my practical requirements, since it may make a great difference whether I met Brown or Jones. The memory "I met Jones" is relatively precise. It is accurate if I met Jones, inaccurate if I met Brown, but precise in either case as against the mere recollection that I met a man.

The distinction between accuracy and precision is however, not fundamental. We may omit precision from out thoughts and confine ourselves to the distinction between accuracy and vagueness. We may then set up the following definitions:

An instrument is "reliable" with respect to a given set of stimuli when to stimuli which are not relevantly different it gives always responses which are not relevantly different.

An instrument is a "measure" of a set of stimuli which are serially ordered when its responses, in all cases where they are relevantly different, are arranged in a series in the same order.

The "degree of accuracy" of an instrument which is a reliable measurer is the ratio of the difference of response to the difference of stimulus in cases where the difference of stimulus is small. That is to say, if a small difference of stimulus produces a great difference of response, the instrument is very accurate; in the contrary case, very inaccurate.

A mental response is called "vague" in proportion to its lack of accuracy, or rather precision.

These definitions will be found useful, not only in the case of memory, but in almost all questions concerned with knowledge.

It should be observed that vague beliefs, so far from being necessarily false, have a better chance of truth than precise ones, though their truth is less valuable than that of precise beliefs, since they do not distinguish between occurrences which may differ in important ways.

About the Author

Bertrand Arthur William Russell, 3rd Earl Russell OM FRS (18 May 1872 - 2 February 1970), was a British philosopher, logician, mathematician and advocate for social reform. A prolific writer, he was also a populariser of philosophy and a commentator on a large variety of topics, ranging from very serious issues to those much less so.