The Theory of Indistinguishables: A Search for Explanatory Principles Below the Level of Physics / Edition 1

The Theory of Indistinguishables: A Search for Explanatory Principles Below the Level of Physics / Edition 1

by A.F. Parker-Rhodes

Product Details

Springer Netherlands
Publication date:
Synthese Library Series, #150
Edition description:
Product dimensions:
6.14(w) x 9.21(h) x 0.56(d)

Table of Contents

I: Theory.- I/Introduction.- 1.A. The Concept of Indistinguishability.- 1.B. Primary and Secondary Indistinguishables.- 1.C. Classes of Indistinguishables.- 1.D. Correlation and Predication.- 1.E. The Triparity of Notations.- 1.F. Levels of Notation.- 1.G. Syntactic Specification of the Notations.- II/Semantic Theory of the Notation F.- 2.A. The Meaning of Meaning.- 2.B. The Pair Functors of U.- 2.C. Classifying Functors.- 2.D. Initial Theorems in U.- 2.E. Indistinguishable Arguments — Cases (a) & (b).- 2.F. Enchained Functors — Cases (c) & (d).- 2.G. Classifying Functors — Cases (e) to (g).- 2.H. Declassifying & Confounding Functors.- 2.J. Concurrence of Symbols.- 2.K. Concurrence in V.- 2.L. Compound Statements and Quantification.- 2.M. Comparison of Biparitous and Triparitous Quantification.- 2.N. Quantification of Definiends.- III/The Physical Relevance of Indistinguishables.- 3.A. The Concept of ‘Planes’.- 3.B. The Inchoative Plane.- 3.C. Observability of the Inchoative.- 3.D. Methodology.- 3.E. Types of Indistinguishables.- 3.F. The Principle of Coherence.- 3.G. Valid Representations.- 3.H. The Construction of Representations.- 3.J. The Irreducibility of the Physical Plane.- 3.K. The Combinatorial Hierarchy.- IV/Sort Theory — Axioms and Definitions.- 4.A. Indefinables of T.- 4.B. Method of Verifying Concurrence.- 4.C. Definitions in the Inferential System.- 4.D. Definitions in T — Basics.- 4.E. The Conditional Quantification Functor.- 4.F. Definition and Classification of Sorts.- 4.G. Some Classifying Functors.- 4.H. Ordered Pairs.- 4.J. Some Confounding Functors.- 4.K. Miscellaneous Functors over Sorts.- V/Sort Theory — Mappings.- 5.A. Mappings and Functions.- 5.B. Mappings from and to Perfect Sorts.- 5.C. The Closure of a Sort.- 5.D. A Classification of Sort Mappings.- 5.E. Cardinality of Perfect Sorts.- 5.F. The Invariant Subdomain Theorem.- 5.G. Functions of Two Arguments over a Perfect Sort.- 5.H. Values of the Functions.- 5.J. Properties of the Functions.- 5.K. Two-Argument Functions over Derived Perfect Domains.- 5.L. Functions of More than Two Arguments.- 5.M. Infinite Perfect Sorts.- 5.N. Operational Tables of the Functors.- VI/Representations of Initial Sorts.- 6.A. Initial and Superstruct Sorts.- 6.B. Complexes on an Initial Sort.- 6.C. Representation of $$\bar D$$20 by Pairs.- 6.D. Representation of Functors over $$\bar D$$20.- 6.E. Representing the Symmetry of the Functions.- 6.F. Representation of $$\bar D$$30.- 6.G. Representation of Functors over $$\bar D$$30.- 6.H. Symmetry of the Functions over $$\bar D$$30.- 6.J. Representation of $$\bar D$$40.- 6.K. Representation of Infinite Sorts.- 6.L. Conspectus of Representations of Initial Sorts.- VII/Representation of Superstruct Sorts.- 7.A. Sorts of Bivalent Functors.- 7.B. Families of Endomorphisms.- 7.C. Functions over Superstructs.- 7.D. The Cedilla Functor.- 7.E. The Hex Functor X.- 7.F. The Auxiliary Functor X.- 7.G. Pair Trees.- 7.H. General Definition of X over Pair-Trees.- 7.J. Representation of $$\bar D$$22 &c., by Hex Formulae.- 7.K. Are there Alternatives to Hex?.- 7.L. Representation of the Family D3.- 7.M. Representation of the Family D?.- 7.N. Rational Sorts.- 7.O. Catalogue of Rational Sorts.- II: Application.- VIII/Hypothesis and Principles.- 8.A. The Role of the Observer.- 8.B. Formulation of the Hypothesis.- 8.C. Some General Principles.- 8.D. The Pattern of the Families.- 8.E. The Nature of Observation.- 8.F. Unconditional Observables.- 8.G. Perfect and Mixed RSs.- IX/Events in the Void.- 9.A. The Void.- 9.B. Events.- 9.C. Orderings of a Segment of U.- 9.D. Specification of Particular Events.- 9.E. Ordinators.- 9.F. Dimensions.- 9.G. The Initial RSs.- X/The Texture of Space-Time.- 10.A. The Interpretation of D?0.- 10.B. Disordinate Statistics.- 10.C. The Action Metric.- 10.D. The Distinction Metric.- 10.E. The Chain of Measurement.- 10.F. The Concept of a Particle.- 10.G. The Polarity of Time.- 10.H. The Limiting Velocity.- 10.J. The Big Bang.- 10.K. The Connectivity of Space.- XI/The Constitution of Matter.- 11.A. The Finiteness of Information.- 11.B. Quantization and Conservation.- 11.C. Some Problems of Correlation.- 11.D. Partons.- 11.E. A Rudimentary Chromodynamics.- 11.F. Interpretation.- 11.G. Parton Descriptors.- 11.H. Reconstruction of Particles.- 11.J. Summary of Kinds of Particles.- XII/States of Particles.- 12.A. The Family D3.- 12.B. States in a Disordinate Space.- 12.C. The Proton-Electron Mass Ratio.- 12.Ca. The Fine Structure Constant.- 12.D. States Distinguishing Particles.- 12.E. Location and Orientation States.- 12.F. Interaction-Field States.- 12.G. The Chromodynamic Contribution.- 12.H. The Mean Density of the Universe.- 12.J. Discussion.- XIII/General Assessment.- 13.A. Characteristics of the Theory.- 13.B. New Paradoxes for Old.- 13.C. A Mendeleevian Presentation.- 13.D. Summary of Evidence.- 13.E. Assessment of the Results.- 13.F. Limits of Interpretation.- 13.G. General Conclusions.- References.- Index of Terms Defined.- Index of Symbols.

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