Contents

• 1. Overture
  • 1.1 Revolution
  • 1.2 History
  • 1.3 Themes
  • 1.4 Logical Truth
    • 1.4.1 Kinds of Truth
    • 1.4.2 Rationalism and Empiricism
  • 1.5 Revolutions
    • 1.5.1 Scepticism and Speculation
  • 1.6 Rationality
    • 1.6.1 Epistemology
    • 1.6.2 Epistemic Standards
    • 1.6.3 Language and Logic
      • 1.6.3.1 Pathologies of Natural Language
      • 1.6.3.2 Oracular Evolution
      • 1.6.3.3 Scientific Language
      • 1.6.3.4 Formalisation
      • 1.6.3.5 The Tractarian Denial
      • 1.6.3.6 Semantics and Usage
      • 1.6.3.7 Formal Leakage
      • 1.6.3.8 Formality in Science
      • 1.6.3.9 More Leakage
  
  
• 2. Prelude
  • 2.1 The First Revolution
  • 2.2 Pythagoras: c 532 b.c
  • 2.3 Aristotle: 384-322 b.c.
    • 2.3.1 Epistemological Dichotomies
  • 2.4 Chrysippus: c.280-c.207 b.c
  • 2.5 Phyrro: -275 b.c.
  • 2.6 Galileo: 1564-1642
  • 2.7 Hobbes: 1588-1679
  • 2.8 Descartes: 1596-1650
  • 2.9 Locke: 1632-1704
    • 2.9.1 Empiricism
  • 2.10 Leibniz: 1646-1716
    • 2.10.1 Rationalism
    • 2.10.2 Dichotomies
    • 2.10.3 Sufficient Reason
    • 2.10.4 Universal Language
  • 2.11 Berkeley: 1685-1783
  • 2.12 Hume: 1711-1776
  • 2.13 Kant
  • 2.14 The Status of Mathematical Truths
  
  
• 3. Revolution in Logic
  • 3.1 The Vision of Leibniz
  • 3.2 Mathematical Rigour
    • 3.2.1 Numbers
    • 3.2.2 Functions
  • 3.3 Frege's Logicism
  • 3.4 Foundation Systems
    • 3.4.1 Frege's Foundations
    • 3.4.2 Foundations to Follow
  • 3.5 Expressiveness and Strength
  • 3.6 Expressiveness
    • 3.6.1 Definitions
    • 3.6.2 Conservative Extension
    • 3.6.3 Flexible Syntax
    • 3.6.4 Semantic Embedding
  • 3.7 Strength
    • 3.7.1 Completeness of First Order Logic
    • 3.7.2 Incompleteness of Arithmetic
    • 3.7.3 Measures of Strength
  
  
• 4. Abortive Coup
  • 4.1 Analytic Philosophy
  • 4.2 Plan
  • 4.3 Philosophical Logicism
  • 4.4 The Vacuum
  • 4.5 Logical Atomism
    • 4.5.1 Tractatus Logico-Philosophicus
    • 4.5.2 Russell's Atomism
  • 4.6 Logical Positivism
  • 4.7 Linguistic Reaction
    • 4.7.1 Wittgenstein
    • 4.7.2 Linguistic Philosophy
  • 4.8 Post Positivism
  
  
• 5. Logic and Computation
  • 5.1 Proof
    • 5.1.1 Proof as Syntax
    • 5.1.2 Computability and Proof
    • 5.1.3 The LCF Paradigm
    • 5.1.4 Oracles
    • 5.1.5 Compiler Integration
    • 5.1.6 Reflection Principles
    • 5.1.7 Computers in Mathematical Proofs
  • 5.2 Logic Technology
  
  
• 6. Perfect Cadence
  • 6.1 Technological Hypotheses
  • 6.2 Formalised Science and Engineering
    • 6.2.1 Language and Logic
    • 6.2.2 Mathematics
    • 6.2.3 Metaphysics
    • 6.2.4 Empirical Hard Science
    • 6.2.5 Engineering Design
  • 6.3 Epistemology
  • 6.4 Return to Leibniz
  
  
• Bibliography
• Index