Among the philosophies of modern times there is no other which emphasises
so much the importance of form and formal thought as the monism of _The
Monist_. An expression thereof is found in the following passages:
“The order that prevails among the facts of reality is due
to the laws of form. Upon the order of the world depends its
cognisability.
“... The laws of form are no less eternal than are matter and
energy and ‘Verily I say unto you, till heaven and earth pass,
one jot or one tittle shall in no wise pass from the law!’
“The laws of form and their origin have been a puzzle to all
philosophers. ‘Ay, there’s the rub!’ The difficulties of Hume’s
problem of causation, of Kant’s _a priori_, of Plato’s ideas,
of Mill’s method of deduction, etc., etc., all arise from a
one-sided view of form and the laws of form and formal thought.”
Considering the great results which engineering and other applied
sciences accomplish through the assistance of mathematics, we must
confess that the forms of thought are wonderful indeed, and it is not
at all astonishing that the primitive thinkers of mankind when the
importance of the laws of formal thought in some way or another first
dawned on their minds, attributed magic powers to numbers and geometrical
figures.
We shall devote the following pages to a brief review of magic squares,
the consideration of which has made many a man believe in mysticism.
And yet there is no mysticism about them unless we either consider
everything mystical, even that twice two is four, or join the sceptic in
his exclamation that we can truly not know whether twice two might not be
five in other spheres of the universe.
[Illustration: ALBERT DÜRER’S ENGRAVING