icular shade
of blue, for instance, which it never has been his fortune to meet
with. Let all the different shades of that colour, except that single
one, be plac'd before him, descending gradually from the deepest to
the lightest; 'tis plain that he will perceive a blank, where that
shade is wanting, and will be sensible, that there is a greater
distance in that place betwixt the contiguous colours, than in any
other. Now I ask, whether 'tis possible for him, from his own
imagination, to supply this deficiency, and raise up to himself the
idea of that particular shade, tho' it had never been conveyed to him
by his senses? I believe there are few but will be of opinion that he
can; and this may serve as a proof, that the simple ideas are not
always derived from the correspondent impressions; tho' the instance
is so particular and singular, that 'tis scarce worth our observing,
and does not merit that for it alone we should alter our general
maxim."[14]

[14] Hume, _Treatise_, Bk. I, Part 1, Sec. 1.

CHAPTER XII

THE ANALOGIES OF EXPERIENCE

Each of the three categories of relation, i. e. those of substance and
accident, of cause and effect, and of interaction between agent and
patient involves, according to Kant, a special principle, and these
special principles he calls 'analogies of experience'. They are stated
thus:[1] (1) In all changes of phenomena the substance is permanent,
and its quantity in nature is neither increased nor diminished. (2)
All changes take place according to the law of the connexion of cause
and effect. (3) All substances, so far as they can be perceived in
space as coexistent, are in complete interaction. The justification of
the term _analogy_ of experience is as follows. In mathematics an
analogy is a formula which asserts the equality of two _quantitative_
relations, and is such that, if three of the terms are given, we can
discover the fourth, e. g. if we know that _a_ : _b_ = _c_ : _d_, and
that _a_ = 2, _b_ = 4, _c_ = 6 we can discover that _d_ = 12. But in
philosophy an analogy is the assertion of the equality of two
_qualitative_ relations and is such that, if three of the terms are
given, we can discover, not the fourth, but only the relation of the
third to the fourth, though at the same time we are furnished with a
clue whereby to search for the fourth in experience. In this
philosophical sense, the principles involved in the categories of
relation are analogies. Fo