Spencer's
own illustration of an intuited fact for knowledge--relations
which are equal to the same relation are equal to one another--
would appear to narrow its application to those so-called self-
evident or necessary truths which are unhesitatingly accepted at
first sight. The nature-mystic, however, while unreservedly
recognising this kind of intuition (whatever may be its
origin) demands a wider meaning for the term. A nearer
approach to what he wants is found in the feats of certain
calculating prodigies, who often seem to reach their astounding
results rather by insights than operations. The celebrated
mathematician, Euler, is said to have possessed, in addition to
his extraordinary memory for numbers, "a kind of _divining
power_," by which he perceived almost at a glance, the most
complicated relations of factors and the best modes of
manipulating them. As regards the calculating prodigies, a
thought suggests itself. It has been almost invariably found that
as they learnt more, their special power decreased. Has this any
bearing on the loss of imaginative power and aesthetic insight
which often accompanies the spread of civilisation?--or on the
materialisms and the "brute matter" doctrines which so often
afflict scientists?
But even this expansion of meaning does not satisfy the
nature-mystic. Perhaps the case of musical intuition comes still
nearer to what he is looking for, inasmuch as cognition, in the
sense of definite knowledge, is here reduced to a minimum.
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