Logical Physics

In this stimulating study of the logical character of selected fundamental topics of physics, Zinov'ev has written the first, and major, stage of a general semantics of science. In that sense he has shown, by rigorous examples, that in certain basic and surprising respects we may envision a reducibility of science to logic; and further that we may detect and eliminate frequent confusion of abstract and empirical objects. In place of a near chaos of unplanned theoretical languages, we may look toward a unified and epistemologically clarified general scientific language. In the course of this work, Zinov'ev treats issues of continuing urgency: the non-trivial import of Zeno's paradoxes; the residually significant meaning of 'cause' in scientific explanation; the need for lucidity in the conceptions of 'wave' and 'particle', and his own account of these; the logic of fields and of field propagation; Kant's antimonies today; and, in a startling aper~u, an insightful note on 'measuring' consciousness. Logical physics, an odd-appearing field of investigation, is a part of logic; and as logic, logical physics deals with the linguistic expressions of time, space, particle, wave, field, causality, etc. How far this may be taken without explicit use of, or reference to, empirical statements is still to be clarified, but Zinov'ev takes a sympathetic reader well beyond a realist's expectation, beyond the classical conventionalist. Zinov'ev presents his investigations in four chapters and an appendix of technical elucidation.

Inhalt
One / The General Theory of Inference and Terms.- 1. The Rules of Logic.- 2. Terms.- 3. Two Types of Terms.- 4. Simple and Complex Terms.- 5. Complex Terms.- 6. Occurrence of Terms and Statements in Other Terms and Statements.- 7. Metaterms and Metastatements.- 8. The Meaning of Terms.- 9. Terms Including Statements.- 10. Definitions.- 11. Statements.- 12. The Meaning of Statements.- 13. Definitions with Statements.- 14. The Definition of Predicates.- 15. The Truth Values of Statements.- 16. The Number of Truth Values.- 17. The Coordinates of Statements.- 18. Truth Value for Statements with Conjunction, Disjunction and Negation Operators.- 19. Truth Values of Other Forms of Statements.- 20. Tautology, Contradictions, Realizable Statements.- 21. Deduction.- 22. Logical Inference.- 23. The General Theory of Deduction.- 24. Classical and Non-Classical Cases in the Theory of Inference.- 25. The Rules of Inference and the Truth Values of Statements.- 26. Identity by Meaning and Entailment.- 27. The General Theory of Terms.- 28. The Coordinates of Statements.- 29. Consequences of Definitions.- 30. Implicit Definitions.- 31. Incomplete Definitions.- 32. Pseudodefinitions.- 33. Operational Definitions.- 34. Intuitively Obvious Statements.- 35. Variables.- 36. Definitions with Variables.- 37. The Multiple Meanings of Linguistic Expressions.- 38. Explication.- 39. Consistency of Terms.- Two / The Special Theory of Inference and Terms.- 1. The Logical Explication of Terms.- 2. Empirical and Abstract Objects.- 3. Individuals.- 4. Classes (Sets).- 5. Clusters.- 6. States, Events.- 7. Existence.- 8. Quantifiers and Existence.- 9. Modal Predicates.- 10. Possibility.- 11. Contingent Events.- 12. Fatalism.- 13. Modal Operators.- 14. The Actual, the Existential, the Potential.- 15. The Measurement of Possibility.- 16. Relations.- 17. Comparison Relations.- 18. Order Relations.- 19. The Relation'Between'.- 20. The Existence of Relations.- 21. Ordered Series.- 22. Contact.- 23. Continuity and Discontinuity of an Empirical Series.- 24. The Beginning and End of a Series.- 25. Interval.- 26. Length.- 27. Abstract Series.- 28. Finite and Infinite Series.- 29. Structure.- 30. Existence of a Structure.- 31. The Dimensions and Order of Structures.- 32. Correspondence.- 33. Correspondence of Classes.- 34. Functions.- 35. Ordered States.- 36. Conditional Statements with an Order-Relation.- 37. Functional Dependence.- 38. Connections.- 39. Ordering of Classes.- Three / Number, Magnitude, Quantity.- 1. Numbers in the Language.- 2. Numbers as Terms.- 3. Base Arithmetic.- 4. The Abbreviated Form of NB.- 5. The Universal Nature of Arithmetic.- 6. Expanded Arithmetic (EA).- 7. Infinite Numbers.- 8. Formal Arithmetic with Metastatements.- 9. Formal Arithmetic and the Theory of Numbers.- 10. Number-Terms.- 11. The Existence of Numbers.- 12. Number as a Part of a Subject.- 13. Quantity.- 14. The Degrees and Range of Truth.- 15. Measurement and Definition.- 16. Number-Quantifiers.- 17. Amount.- 18. The Standard Classes of Numbers.- 19. The Cardinality of Classes of Numbers.- 20. Comparison of Cardinalities of Classes.- 21. Other Definitions.- 22. Reducibility to Logic.- 23. A Remark on the Class of Positive Integers.- 24. A Remark on a Paradox with the Number Terms.- Four / Logical Physics.- 1. On the Method of Presentation of Logic.- 2. Empirical Individuals.- 3. Variation.- 4. The Transition State.- 5. Space and Time.- 6. Spatial and Temporal Relations.- 7. The Time and Space of Existence of an Empirical Individual.- 8. The Existence of Space and Time.- 9. TheSpatial and Temporal Location of an Individual.- 10. One and the Same Individual.- 11. Change in Space and Time.- 12. The Irreversibility of Time.- 13. On the Relation of Generation.- 14. The Continuity of Space and Time.- 15. In variance of Space and Time.- 16. Identity and Difference of Location and Time.- 17. The Predication of Variations.- 18. Translation, Change of Place (Movement).- 19. The Paradox of Motion.- 20. Process.- 21. Minimal Dimensions.- 22. On Infinite Dimensions.- 23. Rate.- 24. Zeno's Paradoxes.- 25. Quanta of Space, Time and Motion.- 26. The Relativity of Motion.- 27. On the Existence and Motion of Clusters.- 28. The Beam.- 29. The Universe as a Whole.- 30. Empirical Geometry.- 31. Empirical Connections.- 32. The Predicates of Tendencies.- 33. Paradoxes of Connections.- 34. Conditional Predicates.- 35. Influence.- 36. Cause.- 37. Forms of Causal Relations.- 38. Determinism and Indeterminism.- 39. Other Forms of Connections.- 40. On the Logical Situation in Microphysics.- 41. The Wave-Particle Duality.- 42. The Trajectory.- 43. The Part and the Whole.- 44. Forecasts.- 45. The Hypothetical Ontology.- 46. General Assertions Concerning the Universe and Physical Assumptions.- 47. Generalizations of the Results of Science.- I. Epistemic Expressions.- II. On the Concept of Belief.- III. On the Notion of Preference.- IV. On the Logic of Norms and Questions.- V. On the Logic of Estimates.- VI. On the Theory of Proof.- VII. On Complete (Rigorous) Induction.- VIII. On Logical Consistency.- IX. On the Systems of the Logic of Classes.- Glossary of Symbols.