y 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.

* Strictly speaking, the limit of this, i.e. the derivative
of the response with respect to the stimulus.

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.

The whole of the above discussion of vagueness and accuracy was
occasioned by the attempt to interpret the word "this" when we judge in
verbal memory that "this occurred." The word "this," in such a judgment,
is a vague word, equally applicable to the present memory-image and to
the past occurrence which is its prototype. A vague word is not to be
identified with a general word, though in practice the distinction
may often be blurred. A word is general when it is understood to be
applicable to a number of different objects in virtue of some common
property. A word is vague when it is in fact applicable to a number of
different objects because, in virtue of some common property, they
have not appeared, to the person using the word, to be distinct. I
emphatically do not mean that he has judged them to be identical, but
merely that he has made the same response to them all and has not judged
them to be different. We may compare a vague word to a jelly and
a general word to a heap of shot. Vague words precede judgments
of identity and difference; both general and particular words are
subsequent to such judgments. The word "this" in the primitive
memory-belief is a vague word, not a general word; it covers both the
image and its prototype because the tw