jects
of our thoughts--all feelings and propositions (leaving aside our
sensations as the mere materials and occasions of thinking and feeling),
all our mental furniture--may be classified under one of two heads--as
either within the province of the intellect, something that can be put
into propositions and affirmed or denied; or as within the province
of feeling, or that which, before the name was defiled, was called
the aesthetic side of our nature, and which can neither be proved nor
disproved, but only felt and known.

According to the classification which I have put before you, then, the
subjects of all knowledge are divisible into the two groups, matters
of science and matters of art; for all things with which the reasoning
faculty alone is occupied, come under the province of science; and in
the broadest sense, and not in the narrow and technical sense in which
we are now accustomed to use the word art, all things feelable, all
things which stir our emotions, come under the term of art, in the sense
of the subject-matter of the aesthetic faculty. So that we are shut
up to this--that the business of education is, in the first place, to
provide the young with the means and the habit of observation; and,
secondly, to supply the subject-matter of knowledge either in the shape
of science or of art, or of both combined.

Now, it is a very remarkable fact--but it is true of most things in this
world--that there is hardly anything one-sided, or of one nature; and
it is not immediately obvious what of the things that interest us may be
regarded as pure science, and what may be regarded as pure art. It may
be that there are some peculiarly constituted persons who, before they
have advanced far into the depths of geometry, find artistic beauty
about it; but, taking the generality of mankind, I think it may be
said that, when they begin to learn mathematics, their whole souls
are absorbed in tracing the connection between the premisses and the
conclusion, and that to them geometry is pure science. So I think it
may be said that mechanics and osteology are pure science. On the other
hand, melody in music is pure art. You cannot reason about it; there
is no proposition involved in it. So, again, in the pictorial art, an
arabesque, or a "harmony in grey,"[80] touches none but the aesthetic
faculty. But a great mathematician, and even many persons who are not
great mathematicians, will tell you that they derive immense pleasure