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.

-97-

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American Philosophy
Table of contents

Table of contents

  • Title Page iii
  • Table of Contents vii
  • List of Contributors ix
  • Introduction - Orientation of Thought xi
  • Suggested Readings xviii
  • Part I - Fields and Problems of American Philosophy 1
  • The Philosophy of Science: The Problem of Factual Truth 3
  • Suggested Readings 19
  • Axiology: the Problem Of Human Values 21
  • Suggested Readings 33
  • Aesthetics: the Problem of Art And Beauty 34
  • Suggested Readings 47
  • Ethics: the Problem of Morality 49
  • Suggested Readings 63
  • Semantics: the Problem Of Meaning 64
  • Suggested Readings 82
  • Logic: the Problem of Reasoning 84
  • Suggested Readings 97
  • Metaphysics: the Problems Of Knowledge and Existence 98
  • Suggested Readings 113
  • Philosophy of Religion: The Problem of Faith 114
  • Suggested Readings 127
  • Part II - Sources and Choices of Philosophy 129
  • Transcendentalism 131
  • Suggested Readings 137
  • Idealism 138
  • Suggested Readings 146
  • Thomism 147
  • Suggested Readings 154
  • Personalism 155
  • Suggested Readings 161
  • Pragmatism 162
  • Suggested Readings 171
  • Humanism 172
  • Suggested Readings 182
  • Logical Positivism 183
  • Suggested Readings 191
  • Realism 193
  • Suggested Readings 202
  • Naturalism 203
  • Suggested Readings 210
  • Oriental Philosophy in America 211
  • Part III - American Thinkers 221
  • American Thought: A Chart 223
  • William Penn 227
  • Samuel Johnson 230
  • Jonathan Edwards 233
  • Benjamin Franklin 235
  • Thomas Paine 238
  • Thomas Jefferson 241
  • Benjamin Rush 244
  • William Ellery Channing 247
  • John Caldwell Calhoun 250
  • Ralph Waldo Emerson 253
  • Abraham Lincoln 256
  • Henry David Thoreau 259
  • Walt Whitman 262
  • Robert Green Ingersoll 265
  • Charles Sanders Peirce 268
  • Oliver Wendell Holmes, Jr. 271
  • John Fiske 274
  • William James 277
  • Ambrose Bierce 280
  • Borden Parker Bowne 283
  • Josiah Royce 285
  • John Dewey 288
  • George Santayana 291
  • Morris Raphael Cohen 294
  • Franklin Delano Roosevelt 297
  • Suggested Readings 300
  • Conclusion 303
  • Index 311
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