1.9. PLANES AND DIALECTS OF THOUGHT.

Finally; the Logician, intent upon perfecting the certitudes of his
methods rather than upon expressing the confusing subtleties of truth,
has done little to help thinking men in the perpetual difficulty that
arises from the fact that the universe can be seen in many different
fashions and expressed by many different systems of terms, each
expression within its limits true and yet incommensurable with
expression upon a differing system. There is a sort of stratification in
human ideas. I have it very much in mind that various terms in our
reasoning lie, as it were, at different levels and in different planes,
and that we accomplish a large amount of error and confusion by
reasoning terms together that do not lie or nearly lie in the same
plane.

Let me endeavour to make myself a little less obscure by a flagrant
instance from physical things. Suppose some one began to talk seriously
of a man seeing an atom through a microscope, or better perhaps of
cutting one in half with a knife. There are a number of non-analytical
people who would be quite prepared to believe that an atom could be
visible to the eye or cut in this manner. But any one at all conversant
with physical conceptions would almost as soon think of killing the
square root of 2 with a rook rifle as of cutting an atom in half with a
knife. One's conception of an atom is reached through a process of
hypothesis and analysis, and in the world of atoms there are no knives
and no men to cut. If you have thought with a strong consistent mental
movement, then when you have thought of your atom under the knife blade,
your knife blade has itself become a cloud of swinging grouped atoms,