tiplication of experiences gives materials for definite
conceptions--only as observation year by year discloses the less
conspicuous attributes which distinguish things and processes previously
confounded together--only as each class of co-existences and sequences
becomes familiar through the recurrence of cases coming under it--only
as the various classes of relations get accurately marked off from each
other by mutual limitation, can the exact definitions of advanced
knowledge become truly comprehensible. Thus in education we must be
content to set out with crude notions. These we must aim to make
gradually clearer by facilitating the acquisition of experiences such as
will correct, first their greatest errors, and afterwards their
successively less marked errors. And the scientific formulae must be
given only as fast as the conceptions are perfected.

3. To say that our lessons ought to start from the concrete and end in
the abstract, may be considered as in part a repetition of the first of
the foregoing principles. Nevertheless it is a maxim that must be
stated: if with no other view, then with the view of showing in certain
cases what are truly the simple and the complex. For unfortunately there
has been much misunderstanding on this point. General formulas which men
have devised to express groups of details, and which have severally
simplified their conceptions by uniting many facts into one fact, they
have supposed must simplify the conceptions of a child also. They have
forgotten that a generalisation is simple only in comparison with the
whole mass of particular truths it comprehends--that it is more complex
than any one of these truths taken singly--that only after many of these
single truths have been acquired does the generalisation ease the memory
and help the reason--and that to a mind not possessing these single
truths it is necessarily a mystery. Thus confounding two kinds of
simplification, teachers have constantly erred by setting out with
"first principles": a proceeding essentially, though not apparently, at
variance with the primary rule; which implies that the mind should be
introduced to principles through the medium of examples, and so should
be led from the particular to the general--from the concrete to the
abstract.

4. The education of the child must accord both in mode and arrangement
with the education of mankind, considered historically. In other words,
the genesis of knowledge in the in