This book is based on my doctoral dissertation written at Harvard University in the year of 1963. My interest in Peirce was inspired by Professor D. C. Williams and that in Lewis by Professor Roderick Firth. To both of them lowe a great deal, not only in my study of Peirce and Lewis, but in my general approach toward the problems of knowledge and reality. Specifically, I wish to acknowledge Professor Williams for his patient and careful criticisms of the original manuscripts of this book. I also wish to thank Professor Firth and Professor Israel Scheffler for their many suggestive comments regarding my discussions of induc­ tion. However, any error in this study of Peirce and Lewis is completely due to myself. Chung-ying Cheng Honolulu, Hawaii March,1967 TABLE OF CONTENTS PREFACE V SUMMARY IX CHAPTER I: Introduction I I. Problem of Justifying Induction and Proposal for Its Dissolution I 2. Two Types of Recent Arguments for the Validity of Induction 3 Arguments from Paradigm Cases and Uses of Words 4 3.

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I: Introduction.- 1. Problem of Justifying Induction and Proposal for Its Dissolution.- 2. Two Types of Recent Arguments for the Validity of Induction.- 3. Arguments from Paradigm Cases and Uses of Words.- 4. Practical Arguments.- 5. Induction as a Genuine Problem and Study of Peirce and Lewis.- II: Scope of Peirce's Theory of Induction.- III: The Nature and Validity of Inference.- 1. A General Theory of Inference.- 2. Necessary Inference and Probable Inference.- 3. Validity of Probable Inference.- IV: Probable Inference and Justifying Induction.- 1. Induction and Apagogical Inversion of Statistical Deduction.- 2. Induction As a Valid Probable Inference.- V: Requirements for the Validity of Induction.- 1. General Remakrs.- 2. Peirce on Fair Sampling and Fair Samples.- 3. Principle of Fair Sampling: A New Formulation.- 4. Peirce on Predesignation.- 5. Relevancy of Predesignation for the Validity of Induction.- VI: Probability and the Validity of Induction.- 1. General Remarks.- 2. Peirce's Two Empirical Conceptions of Probability.- 3. Peirce's Objections to the Laplacian Definition of Probability and Criticism.- VII: A Non-Probabilistic Justification of Induction.- 1. General Remarks.- 2. Self-Correcting Nature of Inductive Method.- 3. Criteria for Defining Truth and Justifying Induction.- 4. Other Arguments for the Necessity of General Validity of Induction.- VIII: Concluding Remarks on Peirce's Non-Probabilistic Justification on Induction.- IX: Problems in Lewis's Theory of Induction.- X: Induction and Analysis of Knowledge of Reality.- 1. General Remarks.- 2. Empirical Knowledge and "A priori" Concepts.- 3. A Fundamental Principle in Establishing Criteria of Reality.- XI: An "A Priori Analytical" Justification of Induction.- 1. General Remarks.- 2.Problems of Justifying Induction in the Theories of Reality and Knowledge.- 3. Empirical Generalizations as Interpretations of Experience and Principle A.- 4. Analyticity of Principle A.- XII: Implications of Lewis's "A Priori Analytical Justification of Induction.- 1. From Principle A to Justification of Argument from Past to Future.- 2. Lewis on the Practical Successfulness of Induction.- XIII: Concluding Remarks on Lewis's "A Priori Analytical" Justification of Induction.- XIV: Nature of Probability and Rational Credibility.- 1. General Remarks.- 2. Empirical Interpretation of Probability.- 3. Logical Interpretation of Probability.- 4. Rational Credibility, Fair Sampling and Logical Probability.- XV: Criteria for Determining Rational Credibility.- 1. Questions Regarding Criteria for Determining Rational Credibility.- 2. Degrees of Rational Credibility and Criteria for Determining Them.- 3. Justifying Acceptance of Criteria for Determining Rational Credibility.- XVI: Conclusion.- 1. Similarity Between Peirce's and Lewis's Theories of Induction.- 2. Significances of Peirce's and Lewis's Arguments.- 3. Toward a Comprehensive Theory of Justifying Induction.- 4. Bearings upon Practicist and Linguist Arguments.- Appendix I. A Chronological Listing of Peirce's Papers Directly Bearing upon Induction and Probability.- Appendix II. Proof of the Logical Law of Large Numbers (the Maximum Value Law of Hypergeometric Probability).- Appendix III. Probabilities of Estimates of Values of Population Parameters.- Selected Bibliography.