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PARTISAN REVIEW
calculi would find it difficult to decide where to begin setting right
Mr. Hayakawa's caricature. For one thing, the subject itself is too
complex and specialized for adequate statement in anything but a
technical journal. Mr. Hayakawa's treatment is not merely as
unintelligible to the general public as, for example, a string of
formulae from quantum mechanics. It would be equally mysterious
to the creators of the n-valued calculi themselves. First of all it is
inaccurate to equate semanticists with non-Aristotelians, opponents
of the law of excluded middle. Tarski, in a fundamental mono–
graph on the subject, explicitly postulates that a statement is either
true or false, and not both; a two-valued scheme is definitely pre–
supposed. The n-valued logics are nothing like the descriptions of
them offered by Chase, Hayakawa, or Korzybski. They are in no
sense incompatible with the 2-valued calculus. Actually, it has been
demonstrated that the n-valued calculus is completely translatable
into a 2-valued one; in short, it has been proven that they are
equivalent.
2.
Non-Aristotelianism.
Mr. Hayakawa is professedly a non-Aristotelian. One would
· expect a writer on such an important subject as non-Aristotelian
· logic at least to understand what he is opposing. Mr. Hayakawa's
rejection of the two-valued law of excluded middle does not fulfill
one's expectations in this regard. Here Hayakawa is no worse than
the people he defends. The principle of excluded middle says of
two contradictory sentences that one must be true and one false and
that there is no third alternative. While some of Mr. Hayakawa's
explanations do take it in this sense, his entire account is so foggy
that it is hard to see just what middle he is refusing to exclude.
For he maintains in one place that the opposition involved is the
opposition of 'all' and 'none.' As if anybody ever maintained that
either all men are red-headed or none are red-headed and
that
no
middle ground
is
logically possible.
Any elementary text-book, traditional or modern, is at pains
to point out that 'all'-statements and 'none'-statements are con–
traries, not contradictories: both
may
be false. Mr. Hayakawa is
not only unable to understand the advances in logic of the last
century; it would seem that he is unacquainted with the very first
steps in traditional logic: the square of opposition.
