e,
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.

* This is a necessary but not a sufficient condition. The
subject of accuracy and vagueness will be considered again
in Lecture XIII.

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