Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

THE MATHEMATICS OF PSYCHOLOGY 385
Q2 Q3 or that both of these inequalities subsist despite
the verdict of sensation to the contrary. But what does
that mean? It means that we are driven to assume that
there are quantities of magnitude so small as to be insensible, too small to be sensed or felt or perceived. And
what does that mean? It means-and the answer is
fundamentally important-that we are driven to posit or
postulate the existence of purely conceptual quantities or
amounts of magnitude. And we do it.
Properties of the Conceptual Magnitudes.-We must
not fail to note some of the properties with which our
human minds have been constrained to endow such conceptual magnitudes. If we were to suppose our discriminative sensibility to be by some means so increased or
refined as to bring. the assumed insensible quantity
Q1i Q2 (the difference between the sensible quantities
Qi and Q2) well within the domain of the increased sensibility, we have no reason to doubt that the old phenomenon would recur therein; we should, that is, expect to
find quantities qi, q2, q3 within the interval QIaQ2 such
that
ql =q2, q2=q3, qi qa3;
that is to say, fatal violence to the mentioned law of
logic would remain. And so it would did we suppose
our sensibility to be again increased so as to render
sensible the newly postulated quantity, qicq2; and so
on and on. Observe attentively that the indicated process
of intercollating ever smaller and smaller insensible
quantities is precisely like that by which symbols called
rational fractions are interlarded between the integers
and then other rational fractions are inserted between the
former ones, apd so on and on. Observe also that, in