and finally
{~GREEK SMALL LETTER ALPHA~}infinity for the absolute truth valid in infinity.

To make it easier to explain, I will illustrate the suggestions by an
example. Let us suppose that the human time-binding capacities or energies
in the _organic_ chemistry correspond to radium in the _inorganic_
chemistry; being of course of different dimensions and of absolutely
different character. It may happen, for it probably is so, that the
complex time-binding energy has many different stages of development and
different kinds of "rays" _A_, _B_, _C_, ... _M_....

Let us suppose that the so-called mental capacities are the _M_ rays of
the time-binding energy; the "spiritual" capacities, the _A_ rays; the
"will" powers, the _B_ rays; and so on. Psychological truths will then be
a function of all rays together, namely _A_ _B_ _C_ ... _M_ ... or _f_
(_A_ _B_ _C_ ... _M_ ...), the character of any "truth" in question will
largely depend upon which of these elements prevail.

If it were possible to isolate completely from the other rays the "mental"
process--the "logos"--the _M_ rays--and have a complete abstraction (which in
the present could only be in mathematics), then the work of _M_ could be
compared to the work of an impersonal machine which always gives the same
_correctly_ shaped product _no matter what is_ the material put into it.

It is a fact that mathematics is correct--impersonal--passionless. Again, as
a matter of fact, all the basic axioms which underlie mathematics are
"psychological axioms"; therefore it may happen that these "axioms" are
not of the {~GREEK SMALL LETTER ALPHA~}infinity type but are of the _f_ (_A_ _B_ _C_ ...) personal
type and this may be why mathematics cannot account for psychological
facts. If psychology is to be an _exact science_ it must be mathematical
in principle. And, therefore, mathematics must find a way to embrace
psychology. Here I will endeavor to outline a way in which this can be
done. To express it correctly is more than difficult: I beg the
mathematical reader to tolerate the form and look for the sense or even
the feelings in what I attempt to express. To make it less shocking to the
ear of the pure mathematician, I will use for the "infinitesimals" the
words "very small numbers," for the "finite" the words "normal numbers"
and for the "transfinite" the words "very great numbers." Instead of using
the word "number" I will sometimes use the word "magnitude" and under the