Eidomorphism: The Philosophy of Ontological Mathematics 9781074086138

Table of contents :
Contents

0  Apologia
1  Introduction
 1.1  References
2  First Principles
  2.0.1  Grounding the PSR
  2.0.2  The Law of Identity
 2.1  References
3  Epistemology
 3.1  Provable and Hypothetical Knowledge
  3.1.1  Folk Knowledge
  3.1.2  Coherence
  3.1.3  Reliability
  3.1.4  Epistemic Confidence
 3.2  Reworking Epistemology
 3.3  Mathematics and Science
 3.4  The Possibility of Knowledge
 3.5  References
4  Ontological Substance
 4.1  Basic Ideas About Substance
  4.1.1  Necessary Properties
  4.1.2  The Centrality of Experience
 4.2  Ontology of the Fundamental Substance
  4.2.1  No Two Substances Share Attributes
 4.3  Derived Principles and Definitions
  4.3.1  Spinoza’s First Principles
  4.3.2  Spinozist Doctrines in Eidomorphism
  4.3.3  Modifications to Rationalist Doctrines
  4.3.4  Necessary Properties Reducible to Two
 4.4  Auxiliary Principles
  4.4.1  First Law of Thermodynamics
  4.4.2  Concluding Laws on Matters of Ontology
  4.4.3  Other Auxiliaries
 4.5  Double-Aspect Monism
  4.5.1  Immaterialism Reconcilable With Physicalism
 4.6  References
5  Ontic Status of Math
 5.1  The Basis of Mathematical Ontology
  5.1.1  The Ontology of Euler’s Formula
 5.2  The Advantages of the Ontological Euler Formula Over Other Conceptions of Math
  5.2.1  Contra Locke
  5.2.2  Contra Formalism
  5.2.3  Contra Informalism
  5.2.4  The Limitations of Intuitionism and Category Theory
  5.2.5  The Problem With Platonism and Realism
  5.2.6  Eidetic Mathematics
  5.2.7  Definition of Number
 5.3  Monads
  5.3.1  Cellular Automata
  5.3.2  The Monad
  5.3.3  Monadic Space and Time
  5.3.4  Information
  5.3.5  Ontological Operations versus Mathematical Operations
  5.3.6  Eidetic Mathematics as Physics
  5.3.7  Conclusion
 5.4  References
6  Monads and Eidetic Mathematics
 6.1  Flowing Points
 6.2  Recursive Definition
 6.3  Wave Structure of Monadic Contents
 6.4  Definition of the Monad
 6.5  Composition of the Monadic Continuum
 6.6  Monadic Array
  6.6.1  The Monadic Collective as Riemann Sphere
 6.7  Monadic Functions
 6.8  Transformations
  6.8.1  Rotations
  6.8.2  Affine Transformations
  6.8.3  Quaternions
 6.9  Extended Complex Plane
 6.10  References
7  Monadic Physics
 7.1  Spacetime Structure
  7.1.1  Speed of Light
  7.1.2  Particles, Energy, and Causality
 7.2  Lorentz Transformations
  7.2.1  Contra Principle of Relativity
  7.2.2  Beyond Relativity
  7.2.3  Photons and the Ether
 7.3  Relational Standard Units
 7.4  Gaussian Six-Dimensional Curved Spacetime
  7.4.1  Time and Motion Decoupled
  7.4.2  Phenomenology of Three-Time
  7.4.3  Anomalous Precession of Mercury’s Perihelion
 7.5  Null Lines
  7.5.1  Lorentz Invariance
  7.5.2  Locality and Non-Locality
  7.5.3  3D Complex Lorentz Transformations
 7.6  Spin Rotation
  7.6.1  Spin and Rotational Angles
 7.7  Quantum Mechanics as Wave Effects
  7.7.1  Ultrahyperbolic Wave Equation
  7.7.2  Six-Dimensional Electromagnetism
  7.7.3  Schrödinger, Klein-Gordon, and Dirac Equations
  7.7.4  Heisenberg’s Uncertainty Relations in 6D Spacetime
  7.7.5  Six Dimensional Bohmian Mechanics?
 7.8  Wavefunction Collapse, Uncertainty, and the Arrow of Time
  7.8.1  Uncertainty and Time
 7.9  The Standard Model & QFT
 7.10  Quantum Gravity and Supersymmetry
  7.10.1  Details Concerning Distributive Quantum Gravity
  7.10.2  Supersymmetry
  7.10.3  Dark Energy and Emanation
 7.11  The Significance of Fields
  7.11.1  Light and Fields
 7.12  Phase Spheres
 7.13  Conclusion
 7.14  References
8  The Monadic Universe
 8.1  The Monad
  8.1.1  Physical and Non-Physical Structure
  8.1.2  Compossibility
  8.1.3  Bodies as Collections of Flowing Points
  8.1.4  Thermodynamic Entropy and Information Entropy
  8.1.5  A Law of Eternal Return?
 8.2  Cosmology
  8.2.1  Monadic Evolution
  8.2.2  How Monads Evolve
  8.2.3  The Inevitability of Life
  8.2.4  Directed Chance and the Mechanism of Mutation
  8.2.5  Four Forms of Causation
  8.2.6  Evolution and Functions
  8.2.7  Bisection and the Hegelian Dialectic
 8.3  Conclusion
 8.4  References
9  Towards A Formal Philosophy
 9.1  Formal Ontology of the Monadic System
  9.1.1  Logic of Form, Logic of Content
  9.1.2  Basic Terms of Formal Ontology
  9.1.3  Extensionality and Intensionality
  9.1.4  Ontological Semantics and Ontological Syntax
  9.1.5  Abstraction vs. Concreteness
  9.1.6  The Problem of Universals
  9.1.7  Time
  9.1.8  Mereological Essentialism
  9.1.9  Primary and Secondary Qualities and their Ideas
  9.1.10  Kant’s Antinomies
  9.1.11  Aristotle’s Causes
  9.1.12  Monadic Causation and Free Will
 9.2  Formal Epistemology of the Monadic System
  9.2.1  The System of Sciences
  9.2.2  Epistemic Logic and Game Theory
  9.2.3  Levels of Consciousness and Accessibility
  9.2.4  Epistemic Information Games
  9.2.5  A Note on Epistemic Reliability
 9.3  Phenomenology of the Monadic System
  9.3.1  Towards a Well-Founded Phenomenology
  9.3.2  Spinoza’s Psychological Theory in Eidomorphism
  9.3.3  The Definitions of the Emotions
 9.4  References
10  Ethics
 10.1  The Law of Optimal Compossibles
  10.1.1  The Categorical Imperative
 10.2  Rational Enlightenment
11  Conclusion