Knowledge and Time; Editor's Preface; Contents; Part I: Knowledge; Chapter 1: Introduction; 1.1 A Full Understanding of Time Requires a Non-Boolean Framework; 1.2 Two Modes of Understanding; 1.3 Two Modes of Learning; 1.4 Two Notions of Time; 1.4.1 Chronos and Kairos; 1.4.2 Time Is Neither Material Nor Mental; 1.4.3 Sequential and Non-Sequential Processing; 1.5 Parts of the Universe of Discourse; Chapter 2: Boolean Descriptions; 2.1 On the Necessity of Distinctions; 2.2 Boolean Logic; 2.3 On the Biological Basis of Binary Distinctions; 2.4 Boolean Worldviews; 2.4.1 Boolean Frames of Reference

2.4.2 Incompatible Boolean Descriptions2.4.3 Simultaneously Undecidable Propositions; 2.5 Boolean Classi cations; Chapter 3: Non-Boolean Descriptions; 3.1 Vagueness; 3.1.1 Eliminable Vagueness; 3.1.2 Intrinsic Vagueness; 3.2 Non-Classical Logic; 3.2.1 Some Examples; 3.3 Fuzzy Sets and Fuzzy Logic; 3.3.1 Fuzzy Sets; 3.3.2 Fuzzy Logic and Fuzzy Classi cations; 3.3.3 Example: Bandpass Filters; 3.3.3.1 Ideal Bandpass Filters; 3.3.3.2 Fuzzy Bandpass Filters; 3.3.3.3 Butterworth Filters; 3.3.3.4 The Küpfmüller-Wiener Fuzzyness Principle; 3.4 Partial Boolean Descriptions

3.4.1 Partial Boolean Algebras3.4.2 Logical Structures in Partial Boolean Algebras; 3.4.3 Partial Boolean Classi cations; 3.4.4 Algebras Generated by Classi cations; 3.4.5 Boolean Manifolds; 3.4.6 A Simple Geometric Analogy; 3.5 Mathematical Models of Complementarity; 3.5.1 Incompatible Classi cations Generate Weyl Systems; 3.5.2 Complementary Commutative Algebras; 3.5.3 Complementarity in Quantum Mechanics; 3.5.4 Coexistent Effects; Chapter 4: Rationality and Creativity; 4.1 Modes of Reasoning; 4.1.1 The Fascination of Science; 4.1.2 Intuitive Knowledge and Logical Knowledge

4.1.3 Verbalization and Mental Pictures4.1.4 Hertz's Metaphor Conception of Theories; 4.1.5 Ludwik Fleck's Thought Collectives; 4.2 Neuropsychological Aspects; 4.3 Time and the Modes of Knowing; 4.4 Modes of Comprehending Art; 4.5 Modes of Learning; 4.6 Complementary Modes of Knowing; 4.7 Where Do Ideas Come From?; Chapter 5: Modes of Knowing in Mathematics; 5.1 Truth in Mathematics; 5.2 On the Origin of the Concept of Integers; 5.3 Is Mathematics Discovered or Invented?; 5.4 Formalism; 5.5 Gödel's Theorems; 5.6 Constructivism; 5.7 Platonism; 5.8 Complementarity in Mathematics

5.9 Birds and Frogs in Mathematics5.10 Mathematical Intuition; 5.10.1 Logic Versus Creativity; 5.10.2 The Intuition of Srinivasa Ramanujan; 5.10.3 The Intuition of Kurt Gödel; Chapter 6: Bottom-Up Approaches in Physics; 6.1 Atomistic Physics; 6.2 Bottom-Up Quantum Mechanics; 6.2.1 Quantum Mechanics Is a Non-Boolean Theory; 6.2.2 Building Blocks in Bottom-Up Quantum Mechanics; 6.2.3 Traditional Hilbert-Space Quantum Mechanics; 6.2.4 Superselection Rules; 6.2.5 Non-Pure States Versus Classical Mixtures; 6.2.6 Measurements of the First Kind; 6.2.7 The Expectation-Value Postulate