There is not the
least evidence for the existence of organisms with a single
differentiated sense organ, nor the least evidence that there ever was
such an organism. Indeed, according to modern accounts of the evolution
of the nervous system (cf. G. H. Parker, _Pop. Sci. Month._, Feb., 1914)
different senses have arisen through a gradual differentiation of a more
general form of stimulus receptor, and consequently, the possibility of
the detachment of special senses is the latter end of the series and not
the first. But, however this may be, the mathematical concepts that we
are studying have only been grasped by a highly developed organism, man,
but they had already begun to be grasped by him in an early stage of his
career before he had analyzed his experience and connected it with
specific sense organs. It may of course be a pleasant exercise, if one
likes that sort of thing, to assume with most psychologists certain
elementary sensations, and then examine the amount of information each
can give in the light of possible mathematical interpretations, but to
do so is not to show that a being so scantily endowed would ever have
acquired a geometry of the type in question, or any geometry at all.
Inferences of the sort are in the same category with those from
hypothetical children, that used to justify all theories of the
pedagogue and psychologist, or from the economic man, that still, I
fear, play too great a part in the world of social science.

VI

MATHEMATICAL INTELLIGENCE

The real nature of intelligence as it appears in the development of
mathematics is something quite other than that of sensory analysis.
Intelligence is fundamentally skill, and although skill may be acquired
in connection with some sort of sensory contact of an organism and
environment, it is only determined by that contact in the sense that if
the sensory conditions were different the needs of the organism might be
different, and the kind and degree of skill it could attain would be
other than under the conditions at first assumed. Whenever the
beginnings of mathematics appear with primitive people, we find a stage
of development that calls for the exercise of skill in dealing with
certain practical situations. Hence we found early in our investigations
that it was impossible to affirm a weak intelligence from limited
achievements in counting, just as it would be absurd to assume the
feeble intelligence of a philosopher from his inability