文档介绍：MANY-VA L U E D
LOGICS
J. BARKLEY ROSSER
Professor of Mathematics, Cornell University
Ithaca, N. Y., .
ATWELL R. TURQUETTE
Assoc. Professor of Philosopliy, University of Ninois
Urbana, Ill., ,A.
1952
NORTH-HOLLAND PANY
AMSTERDAM
Copyright 1952 by
. Noord-Hollandsche Uitgevers Maatschapkv
Amsierdam
PRINTED IN HERLANDS
DRUKKERIJ HOLLAND .. AMSTERDAM
ACKNOWLEDGMENTS
The authors of the present work wish to express their appreci-
ation to the North-Holland pany and to Editors
L. E. J. Brouwer, A. Heyting, and E. W. Beth for their kind
invitation to contribute this volume to the series Studies in Logic.
Acknowledgment is due also to Lucille LeRoy Turquette for her
invaluable aid in preparing the manuscript for publication.
J. B. R. and A. R. T.
I
INTRODUCTION
It has e a truism that every statement is either true or
false. It might be supposed that this principle must be disproved
before one can write a serious work on many-valued logic. This is
by no means the case. In fact, the present volume will not con-
stitute a disproof of such a principle. However, in the following
chapters, systems of many-valued logic through the level of the
first order predicate calculus will be constructed in such a manner
that they are both consistent plete. The tools of con-
struction will include the logical procedures of ordinary English
and those of some formalized systems of two-valued logic. Thus,
in effect, we shall use the truism in constructing many-valued
logics. It does not follow from this that ordinary two-valued logic is
necessary for the construction of many-valued logic, but it does
follow that it is sufficient for such constructions. The ability to
establish such a sufficiency is certainly no more mysterious than
the fact that a Harvard graduate can learn Sanskrit using his
native English.
At this point, however, a word of warning is in order, for the
treatment