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

~08 MATHEMATICAL PHILOSOPHY
finely pulverized chalk,-a box of, say, red powder and
a box of blue; one of the powders gives us the sensation
red, the other the sensation blue; let us thoroughly mix
the powders; the mixture gives us a color sensation;
we agree to say that we have mixed the sensations and
that the new sensation is the result of mixing the old
ones. As the combination of any two color sensations is
a color sensation, Sul has, you see, the group property.
Is it a group? Evidently condition (b) is satisfied. Are
conditions (c) and (d) also satisfied?
Let us pass from colors to figures or shapes,-to figures
or shapes, I mean, of physical or material objects,-rocks,
chairs, trees, animals and the like,-as known to senseperception. No doubt what we ordinarily call perception
of an object's figure or shape is genetically complex, a
result of experience contributed to by two or more senses,
as sight, touch, motion; let us not, however, try to
analyze it thus; let us take it at its face value-let us
regard it as being, what it appears to be before analytic
reflection upon it, a sense-given datum; and let us confine
ourselves to the sense of sight. Here is a dog; its ears
have shape; so, too, its eyes, its nose and the other
features of its head; these shapes combine to make the
shape or figure of the head; each other one of its visible
organs has a shape of its own; these shapes all of them
combine to make that thing which we call the shape or
figure of the dog. Yonder is a table; it has a shape, and
this is due to some sort of combination of the shapes of its
parts-legs, top, and so on; upon it are several objectsa picture frame, a candlestick, some vases; each has a
shape; the table and the other things together constitute
one object-disclosed as such to a single glance of the eye;
this object has a figure or shape due to the combined pres