the reverse of what he had been seeking. Gödel's result, informally stated, is that if any logical system of the general type of Principia Mathematica is consistent, then it is incomplete-incomplete in the sense that there is a purely logical formula expressible in the system such that neither that formula nor its negation is provable as a Theorem in the system. This surprising conclusion appeared to have destroyed any hope that logicians might some day realize the dream of Leibnitz. For to serve as a calculus ratiocinator, a logical system must be both consistent and complete. But Gödel proved that if it is consistent then it cannot be complete, which means that no logical system can be both consistent and complete. Hence no logical system can serve as a calculus ratiocinator.Of course, larger and more comprehensive logical systems can be constructed, adequate to the task of appraising the validity of larger classes of arguments. But no logical system of any type hitherto conceived can be adequate to the appraisal of all possible arguments. Some profoundly different conception of "logical system" is necessary if Leibnitz's dream is ever to come true. Many investigators are conducting researches in the field of symbolic logic at the present time. And it may well come to pass that some new and profound insight may bring us to the long awaited calculus ratio cinator. IRVING M. COPISUGGESTED READINGS
ARISTOTLE, The Organon. Oxford University Press, 1928.
CARNAP RUDOLF, The Logical Syntax of Language. Harcourt, Brace, 1937.
Con I. M., Introduction to Logic. Macmillan, 1953.
----- Symbolic Logic. Macmillan, 1954.
DEWEY JOHN, Essays in Experimental Logic. University of Chicago Press, 1916.
----- Logic, the Theory of Inquiry. Holt, 1938.
LEWIS C. I., A Survey of Symbolic Logic. Century, 1918.
RUSSELL BERTRAND, Introduction to Mathematical Philosophy. Macmillan, 1919.
----- The Principles of Mathematics. Cambridge University Press, 1903.
WHITEHEAD A. N., and RUSSELL B. Principia Mathematica. Cambridge University Press, 1910- 1913.

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