has been developed from an animal form by
natural selection, it does not necessarily follow that his mental
nature, even though developed _pari passu_ with it, has been developed
by the same causes only. To illustrate by a physical analogy. Upheaval
and depression of land, combined with sub-aerial denudation by wind and
frost, rain and rivers, and marine denudation on coastlines, were long
thought to account for all the modelling of the earth's surface not
directly due to volcanic action; and in the early editions of Lyell's
_Principles of Geology_ these are the sole causes appealed to. But when
the action of glaciers was studied and the recent occurrence of a
glacial epoch demonstrated as a fact, many phenomena--such as moraines
and other gravel deposits, boulder clay, erratic boulders, grooved and
rounded rocks, and Alpine lake basins--were seen to be due to this
altogether distinct cause. There was no breach of continuity, no sudden
catastrophe; the cold period came on and passed away in the most gradual
manner, and its effects often passed insensibly into those produced by
denudation or upheaval; yet none the less a new agency appeared at a
definite time, and new effects were produced which, though continuous
with preceding effects, were not due to the same causes. It is not,
therefore, to be assumed, without proof or against independent evidence,
that the later stages of an apparently continuous development are
necessarily due to the same causes only as the earlier stages. Applying
this argument to the case of man's intellectual and moral nature, I
propose to show that certain definite portions of it could not have been
developed by variation and natural selection alone, and that, therefore,
some other influence, law, or agency is required to account for them.
If this can be clearly shown for any one or more of the special
faculties of intellectual man, we shall be justified in assuming that
the same unknown cause or power may have had a much wider influence, and
may have profoundly influenced the whole course of his development.

_The Origin of the Mathematical Faculty._

We have ample evidence that, in all the lower races of man, what may be
termed the mathematical faculty is, either absent, or, if present, quite
unexercised. The Bushmen and the Brazilian Wood-Indians are said not to
count beyond two. Many Australian tribes only have words for one and
two, which are combined to make three, four, five, or six,