Foundations of the Logical Theory of Scientific Knowledge (Complex Logic)

Boston Studies in the Philosophy of Science are devoted to symposia, con­ gresses, colloquia, monographs and collected papers on the philosophical foundations of the sciences. It is now our pleasure to include A. A. Zi­ nov'ev's treatise on complex logic among these volumes. Zinov'ev is one of the most creative of modern Soviet logicians, and at the same time an innovative worker on the methodological foundations of science. More­ over, Zinov'ev, although still a developing scholar, has exerted a sub­ stantial and stimulating influence upon his colleagues and students in Moscow and within other philosophical and logical circles of the Soviet Union. Hence it may be helpful, in bringing this present work to an English-reading audience, to review briefly some contemporary Soviet investigations into scientific methodology. During the 1950's, a vigorous new research program in logic was under­ taken, and the initial published work -characteristic of most Soviet pub­ lications in the logic and methodology of the sciences - was a collection of essays, Logical Investigations (Moscow, 1959). Among the authors, in addition to Zinov'ev himself, were the philosophers A. Kol'man and P. V. Tavanec, and the mathematicians and linguists, S. A. Janovskaja, A. S. Esenin-Vol'pin, S. K. Saumjan, G. N. Povarov.

One/the Logical Theory of Scientific Knowledge.- 1. Scientific Knowledge1.- 2. Basic Abstractions1.- 3. Three Aspects of the Investigation of Knowledge2.- 4. Intuition4.- 5. Logical Calculi4.- 6. Ordinary Language and Scientific Language5.- 7. Objectivity of Approach6.- Two/Signs.- 1. Object8.- 2. Selection8.- 3. Comparison9.- 4. Correspondence9.- 5. Sign12.- 6. Value of the Sign13.- 7. Relations Between Signs14.- 8. Simple and Complex Signs15.- 9. Meaning of the Sign17.- 10. Construction of Signs18.- 11. Categories of Signs19.- 12. Existence of Objects19.- Three/Terms.- 1. Terms21.- 2. Definitions23.- 3. Traditional Rules of Definition25.- 4. Definitions and Assertions26.- 5. Definition and Selection27.- 6. Concept28.- 7. Meaning and Context29.- 8. The Reduction Problem30.- 9. Terms of Terms31.- Four/Sentences.- 1. The Problem of Defining Sentences32.- 2. Basic Principles of the Construction of Sentences33.- 3. Sentential Operators34.- 4. Complex Terms and Sentences35.- 5. Simple and Complex Sentences36.- 6. Cognitive Activities37.- 7. The Construction of Sentences38.- 8. The Meaning of Sentences40.- 9. Definitions with Sentences41.- 10. Terms from Sentences41.- 11. Truth-Values42.- 12. Sentential Structure and Truth-Values45.- 13. The Number of Truth-Values46.- 14. Truths48.- 15. Verification49.- 16. Local and Universal Sentences50.- 17. Metasentences50.- Five/Sentential Logic.- 1. Sentential Logic52.- 2. The Meaning of Sentences52.- 3. Truth-Values55.- 4. Local and Universal Sentences57.- 5. Types of Sentences59.- 6. Truth Functions60.- 7. Truth Conditions61.- 8. The Construction of Sentences62.- 9. Terms63.- Six/the General Theory of Logical Entailment.- 1. The Problem of Logical Entailment64.- 2. Classical Theory of Entailment65.- 3. Non-Classical Theory of Entailment65.- 4. The General Theory of Logical Entailment.- 5. The Intuitive Theory of Logical Entailment69.- 6. Degenerate Entailment72.- 7. Quasi-Entailment72.- 8. Reasoning and Entailment72.- 9. Sentences about Entailment73.- Seven/Formalization of the General Theory of Logical Entailment.- 1. Strong Logical Entailment75.- 2. Another Variant of the System of Strong Entailment78.- 3. Weakened Logical Entailment81.- 4. Maximal Logical Entailment82.- 5. Converse Logical Entailment82.- 6. Degenerate Logical Entailment83.- 7. Quasi-Entailment83.- 8. Logical Entailment and Classical Sentential Calculus84.- 9. Paradoxes of Entailment84.- 10. Classical and Non-Classical Sentential Relations86.- 11. Non-Classical Cases in the General Theory of Deduction88.- 12. Expansion of the General Theory of Logical Entailment89.- Eight/Subject-Predicate Structures.- 1. Objects and Attributes90.- 2. The Most Elementary Sentences91.- 3. Extrinsic Negation94.- 4. Terms95.- 5. Definitions97.- 6. Rules of Substitution of Terms99.- 7. Individualization of Terms100.- 8. Sentences on n-Tuples of Objects100.- 9. Transformation Rules and Terms102.- 10. Definitions103.- 11. Existential Predicate103.- 12. Two Types of Objects and Attributes104.- 13. Truth-Values105.- 14. Theory of Predication107.- Nine/Empirical And Abstract Objects.- 1.Empirical Objects109.- 2. Abstract Objects110.- 3. Interpretation112.- 4. Calculus113.- 5. Empirical and Exact Sciences113.- 6. States114.- 7. Situation115.- 8. The Collection of Situations115.- 9. Derivative Sentences116.- 10. Variation118.- 11. Variation of Attributes119.- 12. Magnitude120.- 13. Range of Truth121.- Ten/Sentences with Quantifiers.- 1. Quantifiers123.- 2. The Structure of Quantified Sentences123.- 3. Indeterminacy126.- 4. Quantification of Terms126.- 5. Extrinsic Negation127.- 6. Definitions of Quantifiers128.- 7. Other Quantifiers130.- 8. A Number of Quantifiers131.- 9. Truth-Values132.- 10. Quantifiers and Existence133.- 11. Rules of Logical Entailment134.- 12. Introduction and Elimination of Quantifiers134.- 13. Quantifiers and the Signs “and” and “or”135.- 14. Syllogistics of Properties137.- 15. Implicit Quantifiers138.- 16. Terms139.- 17. Partial Quantification139.- 18. Construction of Sentences139.- 19. Definitions and Assertions143.- 20. Classical and Non-Classical Relations Between Sentences144.- Eleven/Theory of Quantifiers.- 1. Paradoxes of Theory of Quantifiers 146.- 2. Classical and Non-Classical Cases147.- 3. Restriction of the Classical Calculus of Predicates147.- 4. Classical Strong Theory of Quantifiers148.- 5. Other Systems of Classical Theory of Quantifiers152.- 6. Classical Theory of Quantifiers and Classical Predicate Calculus153.- 7. Non-Classical Theory of Quantifiers154.- 8. Intuitionist Logic and Non-Classical Theory of Quantifiers155.- 9. Weakening of Intuitive Requirements156.- Twelve/Conditional Sentences.- 1. Conditional Sentences157.- 2. The Construction of Conditional Sentences157.- 3. Truth-Values158.- 4. Logical Conditions158.- 5. Deductive Properties of Conditional Sentences159.- 6. Contrafactual Sentences161.- 7. Explanation161.- 8. Conditionality and Quantifiers161.- Thirteen/Theory of Terms.- Fourteen/Classes.- 1. Classes166.- 2. Inclusion in a Class168.- 3. Classes of Classes168.- 4. Paradox of the Class of Normal Classes170.- 5. Limitations of the Concept of Class171.- 6. Empty and Non-Empty Classes172.- 7. Universal Classes172.- 8. Derivative Classes173.- 9. Relations Between Classes174.- 10. Terms175.- 11. The Number of Elements of a Class176.- 12. Composition and Power of a Class178.- 13. Functions179.- 14. Functions with Sentences180.- 15. Definitions181.- 16. Models181.- 17. Logic of Classes182.- 18. Quasi-Classical Cases in Theory of Quantifiers184.- Fifteen/ Existential Logic.- 1. Non-Classical Cases185.- 2. Classical Cases186.- 3. Interpretation186.- Sixteen/ Modal Sentences.- 1. Events187.- 2. Basic Modalities188.- 3. Introduction of Modality189.- 4. The Logical Limits of Modality191.- 5. Prediction192.- 6. The Meaning of Modal Predicates193.- 7. The Modality of Individual and Recurrent Events195.- 8. The Logical Properties of Modal Predicates195.- 9. Randomness197.- 10. Modality and Existence197.- 11. Modality of a Higher Order198.- 12. Modality and Quantifiers199.- 13. Modality and Entailment200.- 14. Modality and Conditionality200.- 15. Linguistic Transformations201.- 16. Terms201.- 17. Truth-Values202.- 18. Probability203.- 19. The Actual and the Potential204.- 20. Basic Modal Logic204.- 21. Normative Sentences206.- 22. Modalities and Norms209.- Seventeen/ Relations.- 1. Sentences About Relations210.- 2. Logical Types of Relations211.- 3. Simple and Complex Relations211.- 4. Elementary and Derivative Relations211.- 5. Binary and n-ary Relations212.- 6. Universal and Local Relations213.- 7. Pseudorelations213.- 8. Comparison214.- 9. Relations of Order216.- 10. The Logic of Relations217.- 11. The Relation “Between”219.- 12. Interval219.- 13. Ordered Series220.- 14. The Length of an Interval and of a Series221.- 15. Structure223.- 16. Relation and Function224.- Eighteen/ Physical Entailment.- 1. Empirical Objects226.- 2. Order of Events226.- 3. Ordered Conjunctions228.- 4. Physical Entailment229.- 5. Truth-Values231.- 6. Deductive Properties of Physical Entailment232.- 7. Physical Entailment and Functions233.- 8. Two-Valued and Many-Valued Functions234.- 9. Empirical Connections235.- 10. Contrafactual Sentences237.- 11. Sentences on Connections and Individual Events238.- Nineteen/ Theories.- 1. Theory239.- 2. Theoretical Assumptions242.- 3. Properties and Relations Between Theories243.- 4. Theory and Experience245.- 5. Theory and Formal System245.- 6. Non-Deductive Principles246.- Twenty/ Logic and Ontology.- 1. Ontological Assertions in Logic247.- 2. Paradoxes of Motion248.- 3. Space and Time249.- 4. Part and Whole254.- 5. Cause255.- Twenty-One/ the Universality of Logic.- 1. Doubts About the Universality of Logic257.- 2. Examples of the “Non-Universality” of Logic258.- 3. Many-Valued Logic and the Universality of Logic260.- 4. Differences in Logical Systems261.- Conclusion.- Append.- Proof of the Basic Theorems of the Theory of Logical.- Entailment.- G. A. Smirno.- Independence in the Systems of Logical Entailment.- E. A. Sidorenko.- Some Variants of the Systems of Logical Entailment.- E. A. Sidorenko.- Completeness of the Systems of Logical Entailment.- A. M. Fedina.- Completeness of Systems of Degenerate Entailment and Quasi-Entailment.- L. A. Bobrova.- Index of Names.