Quantum, Probability, Logic: The Work and Influence of Itamar Pitowsky (Jerusalem Studies in Philosophy and History of Science)

Preface
Itamar Pitowsky: Academic Genealogy and the Arrow of Time
Itamar Pitowsky: Selected Publications
Contents
Contributors
1 Classical Logic, Classical Probability, and Quantum Mechanics
	1.1 Introduction
	1.2 Boole\'s ``Conditions of Possible Experience\'\'
		1.2.1 An Example: The Bell Table
			1.2.1.1 Logical Analysis of the Bell Table
		1.2.2 The General Form
	1.3 From Correlation Polytopes to Non-contextual Polytopes
		1.3.1 Formalization
		1.3.2 The Non-contextual Polytope
		1.3.3 Completeness of Logical Bell Inequalities
	1.4 The Contextual Fraction
	1.5 Remarks on Complexity
	1.6 The ``Edge of Logical Contradiction\'\' vs. the ``Boundary of Paradox\'\'
	1.7 Concluding Remarks
	References
2 Why Scientific Realists Should Reject the Second Dogma of Quantum Mechanics
	2.1 Introduction
	2.2 The IT Account, the Two Dogmas, and the Measurement Problem
	2.3 The IT Approach as a Kinematic Theory
	2.4 Objections to the Explanatory Superiority of Kinematic Theories
	2.5 Accepting the Second Dogma: Wavefunction Realism
	2.6 Why Realists Should Reject the Second Dogma
	2.7 The Dogmas, Scientific Realism, and the Role of Explanation
	2.8 On the Status of the Wavefunction
	2.9 Objections Based on the Wavefunction Being Epistemic
	2.10 The Wavefunction Is as the Wavefunction Does
	2.11 Conclusion
	References
3 Unscrambling Subjective and Epistemic Probabilities
	3.1 Subjective or Epistemic Probabilities?
	3.2 Subjective vs Objective Probabilities
	3.3 Epistemic vs Ontic Probabilties
	3.4 Subjective Ontic Probabilities
	3.5 Epistemic Objective Probabilities
	3.6 Redrawing the Subjective-Objective Distinction
	3.7 Redrawing the Epistemic-Ontic Distinction
	3.8 Remarks on Time Symmetry
	3.9 Further Remarks on the Quantum State
	3.10 Hume and de Finetti
	References
4 Wigner\'s Friend as a Rational Agent
	4.1 Introduction
	4.2 Wigner, Friend and Contradictions
	4.3 Discussion
	Modified Born Rule ch4:baumann2017formalisms
	References
5 Pitowsky\'s Epistemic Interpretation of Quantum Mechanics and the PBR Theorem
	5.1 Introduction
	5.2 Born\'s Probabilistic Interpretation and Its Problems
	5.3 Pitowsky\'s Interpretation of QM
	5.4 The PBR Theorem
	5.5 Possible Responses by the Epistemic Theorist
	5.6 Instrumentalism
	References
6 On the Mathematical Constitution and Explanation of Physical Facts
	6.1 The Orthodoxy
	6.2 An Alternative Perspective
	6.3 On the Relationship Between Mathematics and Physics
	6.4 On Conceptions of Mathematical Constitution of the Physical
	6.5 On the Common View of How Mathematical Models Represent Physical Reality
	6.6 On the Notion of the Physical
	6.7 On the Scope of the Mathematical Constitution of the Physical
	6.8 A Sketch of a New Account of Mathematical Explanation of Physical Facts
	6.9 On Mathematical Explanations of Physical Facts
		6.9.1 On a D-N Mathematical Explanation of the Life Cycle of `Periodical\' Cicadas
		6.9.2 On Structural Explanation of the Uncertainty Relations
		6.9.3 On Abstract Mathematical Explanation of the Impossibility of a Minimal Tour Across the Bridges of Königsberg
		6.9.4 On Explanations by Constraints that Are More Necessary than Laws of Nature
	6.10 Is the Effectiveness of Mathematics in Physics Unreasonable?
	References
7 Everettian Probabilities, The Deutsch-Wallace Theorem and the Principal Principle
	7.1 Introduction
	7.2 Quantum Probability and Gleason\'s Theorem
	7.3 The Riddle of Probability
		7.3.1 Chances
		7.3.2 Carbon-14 and the Neutron
		7.3.3 The Law of Large Numbers
		7.3.4 The Principal Principle
	7.4 Quantum Probability Again
		7.4.1 The Principle of Indifference
		7.4.2 Deutsch
		7.4.3 Wallace
	7.5 A Quantum Justification of the Principal Principle?
		7.5.1 Wallace and Saunders
		7.5.2 Earman
	7.6 The Refutability Issue for Everettian Probability
	7.7 Conclusions
	References
8 `Two Dogmas\' Redux
	8.1 Introduction
	8.2 The Information-Theoretic Interpretation
	8.3 Encapsulated Measurements and the Everett Interpretation
	8.4 A Clarification
	8.5 Concluding Remarks
	References
9 Physical Computability Theses
	9.1 Introduction
	9.2 Three Physicality Theses: Modest, Bold and Super-Bold
	9.3 Challenging the Modest Thesis: Relativistic Computation
	9.4 Challenging the Bold Thesis
	9.5 Challenging the Super-Bold Thesis
	9.6 Conclusion
	References
10 Agents in Healey\'s Pragmatist Quantum Theory: A Comparison with Pitowsky\'s Approach to Quantum Mechanics
	10.1 Introduction
	10.2 A Brief Review of PQT
	10.3 Is PQT Really Realist?
	10.4 The Incompatibility Between PQT and Agent Physicalism
	10.5 What Is an Agent in PQT?
	10.6 Why Pitowsky\'s Information-Theoretic Approach to Quantum Theory Also Needs Agents
		10.6.1 Realism
		10.6.2 Probability
		10.6.3 Information
	References
11 Quantum Mechanics As a Theory of Observables and States (And, Thereby, As a Theory of Probability)
	11.1 Introduction
	11.2 Restatement of Thesis 1
	11.3 The Relation Between Quantum States and Quantum Probabilities
		11.3.1 Quantum States
		11.3.2 From States to Probabilities, and from Probabilities to States
		11.3.3 The Born Rule and a Challenge for T2 and T2
	11.4 Justifying Normality/Complete Additivity
		11.4.1 Normality and the Practice of QM
		11.4.2 Justifying Normality: T2
		11.4.3 Justifying Normality: T2
		11.4.4 Finitizing
	11.5 Ontological Priority of States: State Preparation and Objective Probabilities
	11.6 Fighting Back: An Alternative Account of `State Preparation\'
		11.6.1 Updating Quantum Probabilities
		11.6.2 `State Preparation\' According to T2
	11.7 State Preparation in QFT
		11.7.1 The Conundrum
		11.7.2 The Buchholz, Doplicher, and Longo Theorem
	11.8 Taking Stock
	11.9 The Measurement Problem
	11.10 Conclusion
	Appendix 1 The Lattice of Projections
	Appendix 2 Locally Normal States in Algebraic QFT
	Appendix 3 No Filters for Mixed States
	Appendix 4 Belief Filters Are State Filters
	Appendix 5 The Buchholz-Doplicher-Longo Theorem
	Appendix 6 Interpreting the Buchholz-Doplicher-Longo Theorem
	References
12 The Measurement Problem and Two Dogmas About Quantum Mechanics
	12.1 Introduction
	12.2 Two Dogmas and Two Problems
	12.3 Incompatible Predictions in Black-Box Approaches
	12.4 QBism
	12.5 Bub\'s Information-Theoretic Interpretation of QT
	12.6 Pitowsky\'s Information-Theoretic Interpretation
	12.7 A Bohrian Escape
	12.8 Conclusions
	References
13 There Is More Than One Way to Skin a Cat: Quantum Information Principles in a Finite World
	13.1 In Memory
	13.2 Introduction
	13.3 Knowledge, or Lack Thereof
		13.3.1 How Slow Is Slow Enough
		13.3.2 How Fast Is Fast Enough
	13.4 Moral
	References
14 Is Quantum Mechanics a New Theory of Probability?
	14.1 Introduction
	14.2 Quantum Measure Theory
	14.3 Quantum Gambles
	14.4 Objective Knowledge of Quantum Events
	14.5 A Pragmatist View of Quantum Probability
	14.6 Conclusion
	References
15 Quantum Mechanics as a Theory of Probability
	15.1 Introduction
	15.2 The Bub-Pitowsky Approach
	15.3 The Role of Decoherence in the Consistency Proof
	15.4 From Subjectivism to Idealism
	References
16 On the Three Types of Bell\'s Inequalities
	16.1 Introduction
	16.2 Case 1: Bell\'s Inequalities for Classical Probabilities
	16.3 Case 2: Bell\'s Inequalities for Classical Conditional Probabilities
	16.4 Relating Case 1 and Case 2
	16.5 Case 3: Bell\'s Inequalities for Quantum Probabilities
	16.6 The EPR-Bohm Scenario
	16.7 Conclusions
	References
17 On the Descriptive Power of Probability Logic
	17.1 Introduction: Logic as a Descriptive Tool
	17.2 Continuous Logic
	17.3 Probability Logic
	17.4 The Recognition of Space
	17.5 Unary and Monadic
	17.6 Nothing But Space
	References
18 The Argument Against Quantum Computers
	18.1 Introduction
	18.2 Basic Models of Computation
		18.2.1 Pitowsky\'s ``Constructivist Computer,\'\' Boolean Functions, and Boolean Circuits
		18.2.2 Easy and Hard Problems and Pitowsky\'s ``Finitist Computer\'\'
		18.2.3 Quantum Computers
		18.2.4 Noisy Quantum Circuits
		18.2.5 Quantum Supremacy and NISQ Devices
	18.3 The Argument Against Quantum Computers
		18.3.1 The Argument
		18.3.2 Predictions on NISQ Computers
		18.3.3 Non-interacting Bosons
		18.3.4 From Boson Sampling to NISQ Circuits
		18.3.5 The Scope of the Argument
		18.3.6 Noise Stability, Noise Sensitivity, and Classical Computation
		18.3.7 The Extended Church–Turing Thesis Revisited
	18.4 The Failure of Quantum Computers: Underlying Principles and Consequences
		18.4.1 Noise Stability of Low-Entropy States
		Principle 1: Probability Distributions Described by Low-Entropy States Are Noise Stable and Can Be Expressed by Low-Degree Polynomials
			18.4.1.1 Learnability
			18.4.1.2 Reaching Ground States
		18.4.2 Noise and Time-Dependent Evolutions
		Principle 2: Time-Dependent (Local) Quantum Evolutions Are Inherently Noisy
		18.4.3 Noise and Correlation
		Principle 3: Entangled Qubits Are Subject to Positively Correlated Noise
		18.4.4 A Taste of Other Consequences
	18.5 Conclusion
	18.6 Itamar
	References
19 Why a Relativistic Quantum Mechanical World Must Be Indeterministic
	19.1 Introduction
	19.2 The Hidden Variable Model (HVM) Framework
		19.2.1 Basic Definitions
		19.2.2 Definitions of Properties of Hidden Variable Models (HVM)
		19.2.3 Existence Theorems and Relations Between HVM Properties
	19.3 Properties of Empirical Models and Their Relations
	19.4 Contextuality
	19.5 Empirical Models and Special Relativity
	19.6 Application of Our No-Go Proof to Interpretations of QM
	19.7 Conclusion
	References
20 Subjectivists About Quantum Probabilities Should Be Realists About Quantum States
	20.1 Introduction
	20.2 Credence and Action: Some Preliminary Considerations
	20.3 Constructing a Framework
	20.4 Ontic Distinctness of Non-orthogonal States
	20.5 The QBist Response
	20.6 An Argument from Locality?
	20.7 Conclusion
	References
21 The Relativistic Einstein-Podolsky-Rosen Argument
	21.1 Preliminaries
	21.2 The Crux of the Argument
	21.3 The Thesis of Myself and La Rivière\'s Paper
	21.4 But there Is a Catch…
	21.5 Conclusion
	A.1 Appendix
		A.1.1 Realist Interpretations
		A.1.2 Anti-Realist Interpretations
	References
22 What Price Statistical Independence? How Einstein Missed the Photon
	22.1 Overview
	22.2 The Gibbs Paradox and `Mutual Independence\'
	22.3 Einstein\'s `Miraculous Argument\'
	22.4 Gibbs\' Generic Phase as the Limit of Bose-Einstein Statistics
	22.5 Locality and Entanglement
	22.6 Particle Trajectories and the Gibbs Paradox
	References
23 How (Maximally) Contextual Is Quantum Mechanics?
	23.1 Introduction
	23.2 How Robust Can Quantum Maximal Contextuality Be?
		23.2.1 Triangle-Free Graphs
	23.3 Higher-Rank PVMs
	23.4 Conclusion and Future Work
	References
24 Roots and (Re)sources of Value (In)definiteness VersusContextuality
	24.1 Introduction
	24.2 Stochastic Value Indefiniteness/Indeterminacy by Boole-Bell Type Conditions of Possible Experience
	24.3 Interlude: Quantum Probabilities from Pythagorean ``Views on Vectors\'\'
	24.4 Classical Value Indefiniteness/Indeterminacy by Direct Observation
	24.5 Classical Value Indefiniteness/Indeterminacy Piled Higher and Deeper: The Logical Indeterminacy Principle
	24.6 The ``Message\'\' of Quantum (In)determinacy
		24.6.1 Simultaneous Definiteness of Counterfactual, Complementary Observables, and Abandonment of Context Independence
		24.6.2 Abandonment of Omni-Value Definiteness of Observables in All But One Context
	24.7 Biographical Notes on Itamar Pitowsky
	References
25 Schrödinger\'s Reaction to the EPR Paper
	25.1 Introduction
	25.2 The Argumentation of the EPR Paper
	25.3 Schrödinger\'s Objections to the EPR Argument
	25.4 Einstein\'s Reply to Schrödinger
	25.5 What Did Schrödinger Make of the EPR Argument?
		25.5.1 Schrödinger\'s Interpretation of the Wave Function
		25.5.2 Schrödinger\'s Take on the EPR Problem
	25.6 The Origins of the Cat Paradox
	References
26 Derivations of the Born Rule
	26.1 Introduction
	26.2 Frequentist Approach
	26.3 The Born Rule and the Measuring Procedure
	26.4 Symmetry Arguments
	26.5 Other Approaches
	26.6 Summary of My View
	References
27 Dynamical States and the Conventionality of (Non-) Classicality
	27.1 Introduction
	27.2 Probability Theory vs Probabilistic Theories
		27.2.1 Test Spaces, Probability Weights, and Probabilistic Models
		27.2.2 Some Examples
		27.2.3 Probabilistic Models Linearized
		27.2.4 Probabilistic Theories
	27.3 Classicality and Classical Representations
		27.3.1 Classical Models and Classical Embeddings
		27.3.2 Classical Extensions
		27.3.3 Semiclassical Covers
		27.3.4 Discussion
	27.4 4
		27.4.1 Models with Symmetry
		27.4.2 A Representation in Terms of Dynamical States
	27.5 Composite Models, Entanglement and Locality
		27.5.1 Composites of Probabilistic Models
		27.5.2 Entanglement
		27.5.3 Locality and Hidden Variables
		27.5.4 Composites of Dynamical Models
	27.6 Conclusion
	Appendix A Common Refinements
	Appendix B Semiclassical Test Spaces
	Appendix C Constructing Fully G-Symmetric Models
	References