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

HYPERSPACES sti
yana lacks; at all events if he have wit, it is not wit in
the sense in which that quality is found in Kant, for example, or Hume or Spinoza or Descartes or Pascal or
Aristotle. As for the quality of precision, it is certain
that neither Santayana nor his reviewer has it or indeed
knows the meaning of it as it is rightly understood by
logicians or mathematicians, for the writers in question
are not logicians. They do indeed produce literaturebeautiful literature-but it does not belong to the literature of knowledge, which is also beautiful; the literature
it belongs to is the literature of opinion, some of which
is not even beautiful, for though it includes such beautiful
writing as that of Benedetto Croce, for example, yet it
embraces work like Professor Bliss Perry's The Present
Confliçt of Ideals, which we must allow is a kind of literature even though it remind one of a traveling salesman displaying his wares or, less dimly, of an indiscriminate "feeder" who loves to talk of the things he has
tasted and who sometimes ascribes to bad food or bad
cuisine distress that is due to enfeebled or feeble digestion.
Indeed Professor Santayana, like his reviewer, is,
primarily and essentially, a poet; but there are three kinds
of poetry: there is the poetry of pure thought,-the
poetry of Logic,-and there are two other kinds-the
hypological and the hyperlogical. Each of the kinds has
a muse of its own; that of the first kind, as Isaid in a
previous lecture, is called Logical Rigor, an austere goddess, guardian of precision, mistress of the silent harmonies of perfect thought. By that muse poets like
Santayana have not been inspired.
Returning from the digression, let us now endeavor
to answer the main question of this lecture: what is the
meaning of the term "hyperspace" or "n-dimensional