quently, adds the writer I have quoted, just as the study of optics
teaches us that the human eye yields a very different picture of the
external world from that given by the eye of a fly, for instance, and
as each of them is equally far from the reality, so the truth which our
intelligence enables us to reach is not less remote from that which is
the absolutely true. He considers that this is proven by the very nature
of the "law of contradiction" itself, which must be inconsistent with
the character of absolute thought. For in the latter, positive truth
only can exist, therefore no negation, and no law about the relation of
affirmative to negative.[102-1]

The latter criticism assumes that negation is of the nature of error, a
mistake drawn from the use of the negative in applied logic. For in
formal logic, whether as quantity or quality, that is, in pure
mathematics or abstract thought, the reasoning is just as correct when
negatives are employed as when positives, as I have remarked before. The
other criticism is more important, for if we can reach the conclusion
that the real laws of the universe are other than as we understand them,
then our intelligence is not of a kind to represent them.

Such an opinion can be refuted directly. The laws which we profess to
know are as operative in the remotest nebulae as in the planet we
inhabit. It is altogether likely that countless forms of intelligent
beings inhabit the starry wastes, receiving through sensory apparatus
widely different from ours very diverse impressions of the external
world. All this we know, but we also know that if those beings have
defined the laws which underlie phenomena, they have found them to be
the same that we have; for were they in the least different, in
principle or application, they could not furnish the means, as those we
know do, of predicting the recurrence of the celestial motions with
unfailing accuracy. Therefore the demonstrations of pure mathematics,
such as the relation of an absciss to an ordinate, or of the diameter to
the circumference, must be universally true; and hence the logical laws
which are the ultimate criteria of these truths must also be true to
every intelligence, real or possible.[103-1]

Another and forcible reply to these objections is that the laws which
our intelligence has reached and recognizes as universally true are not
only not derived from experience, but are in direct opposition to and
are constantly con