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

LECTURE VI
Non-Geometric Interpretation
NOT ALL THAT GLITTERS IS GOLD-A DIAMOND TEST OF
HARMONY-TWO-DIMENSIONAL DOCTRINE OF NUMBER
DYADS AND SYSTEMS THEREOF-THE THREE-DIMENSIONAL ANALOGUE.
THE interpretations, or doctrines, vThich have hitherto
concerned us-Di, D2, D3 of HaF and Dl', D2', D3' of
IiAF'-ought to be called, and I have called them,
geometric doctrines because their content or subjectmatter,-that which the doctrines are doctrines of or
about,-consists of things, whether sensible or purely
conceptual, that are essentially and ultimately spatial in
kind. The distinction is psychological; mathematicians,
not being able to tell precisely what space is, and disdaining or affecting to disdain psychology, may ignore
the distinction, if they like-such asininity not being
penalized by municipal law in any land. Let us not be
so uncandid or so dull as to ignore the essential distinction
between spatial and non-spatial doctrines merely because
they happen to have the sameform. Not all that glitters
is gold. Let us not so easily lose our common sense-a
box of table sugar is not a box of table salt even if the
two boxes are identical in size and form.
In the present lecture I invite your attention to a nongeometric interpretation of our doctrinal functions-to an
interpretation, or doctrine, to be properly called nongeometric because, though the same in form as the fore86