Applications of Formal Philosophy: The Road Less Travelled (Logic, Argumentation & Reasoning Book 14)

Annotation This book features mathematical and formal philosophers' efforts to understand philosophical questions using mathematical techniques. It offers a collection of works from leading researchers in the area, who discuss some of the most fascinating ways formal methods are now being applied. It covers topics such as: the uses of probable and statistical reasoning, rational choice theory, reasoning in the environmental sciences, reasoning about laws and changes of rules, and reasoning about collective decision procedures as well as about action. Utilizing mathematical techniques has been very fruitful in the traditional domains of formal philosophy - logic, philosophy of mathematics and metaphysics - while formal philosophy is simultaneously branching out into other areas in philosophy and the social sciences. These areas particularly include ethics, political science, and the methodology of the natural and social sciences. Reasoning about legal rules, collective decision-making procedures, and rational choices are of interest to all those engaged in legal theory, political science and economics. Statistical reasoning is also of interest to political scientists and economists Contents 6 1 Applied Formal Philosophy: Some Reflections on the Program 8 Part I Human Affairs 11 2 The Logic of Guilt, Innocence and Legal Discourse 12 2.1 Introduction 12 2.2 ``Not Guilty'' and ``Innocent'' 13 2.3 New Vocabulary 15 2.4 Logical Relationships 16 2.5 Norms, Values and Legal Principles 19 2.6 Idealizations 21 2.7 Constructive Models for Legal Deliberation 23 2.8 Nelson Logic 24 2.9 Modeling the Burden of Proof 26 2.10 Future Work 27 References 28 3 Counterfactuals, Logic Programming and Agent Morality 30 3.1 Introduction 31 3.2 Preliminaries 33 3.2.1 Abductive Logic Programs 37 3.2.2 Pearl's Structure-Based Counterfactuals 39 3.3 LP-Based Counterfactuals 40 3.3.1 Causal Model and LP Abduction 40 3.3.2 Intervention and LP Updating 41 3.3.3 Evaluating Counterfactuals in LP 41 3.3.4 Some Properties 45 3.3.5 Implementation 47 3.4 Counterfactuals in Morality 47 3.5 Related Work 53 3.6 Conclusion and Future Work 55 References 56 4 The Wisdom of the Multitude: Diversity Versus Size 59 4.1 Introduction 59 4.2 Size and Diversity 61 4.3 Comparing Size and Diversity 64 4.4 Monte Carlo Simulation 66 4.5 Conclusion 72 References 74 5 A Logic for Human Actions 76 5.1 Introduction 76 5.2 Logic Categorically Conceived 77 5.2.1 Preliminaries 77 5.2.2 Deductive Systems and Categories 78 5.2.3 Summing Up 84 5.3 A Survey of Action Logics 84 5.3.1 Dynamic Logic 84 5.3.2 Pratt 92 5.3.3 Linear Logic 94 5.3.4 Boolean Algebras of Actions 95 5.3.5 Stit Logics 97 5.3.6 Thierry Lucas 98 5.3.7 Summing Up 99 5.4 Philosophical Analysis of Action Connectives 100 5.4.1 Preliminaries 100 5.4.2 Action Conjunction and Sequence 102 5.4.3 The Without Connective 103 5.4.4 Action Negation 104 5.5 A Logic for Human Actions 108 5.6 Closing Remarks 112 References 113 6 Reasoning with Comparative Moral Judgements: An Argument for Moral Bayesianism 116 6.1 Introduction 116 6.2 Moral Bayesianism 117 6.3 Reasoning with CMJs 124 6.4 Non-Bayesian Reasoning with CMJs Is Impossible 128 6.5 What Can the Bayesian do? 132 6.6 Conclusion 138 References 138 Part II Epistemology 140 7 Is Theory Choice Using Epistemic Virtues Possible? 141 7.1 Introduction 141 7.2 The Epistemic Virtue Account 143 7.3 Arrow's Theorem 145 7.3.1 Premises of Arrow's Theorem 145 7.3.2 Proof of Arrow's Theorem for Two Epistemic Virtues 146 7.3.3 The Impossibility Result Is Fatal to EVA 150 7.4 Weakening the Informational Assumption 151 7.5 No Rules are Permissible for Cardinal-Cardinal Theory Choice 155 7.6 No Rules are Permissible for Unit-Cardinal Theory Choice or Ratio-Cardinal Theory Choice 156 7.6.1 Unit-Cardinal Theory Choice 156 7.6.2 Ratio-Cardinal Theory Choice 159 7.6.3 Intermediate Conclusions 161 7.7 No Rules for Unit-Unit Theory Choice, Ratio-Ratio Theory Choice and Unit-Ratio Theory Choice 163 7.7.1 Two Assumptions Plausible to the EVA-Supporter 163 7.7.2 All Rules Compatible with Trade-Off 164 7.7.3 These Rules are Impermissible to the EVA-Supporter 166 7.8 Conclusion 169 References 170 8 Abduction Logics: Illustrating Pitfalls of Defeasible Methods 171 8.1 Aim of This Article 171 8.2 Historical Note 172 8.3 Abduction: Introductory Comments 174 8.4 Exact Methods as Logics 176 8.5 The Standard Format 179 8.6 Variant Elements for Abduction 186 8.7 More Properties of Adaptive Logics 189 8.8 What It Is All About 192 References 193 9 A Multimodal Pragmatic Analysis of the Knowability Paradox 196 9.1 Introduction 196 9.2 The Knowability Paradox 197 9.3 An Outline of mathcalLP 199 9.4 mathcalL,KP and Its Interpretations 200 9.5 Semantic and Pragmatic Validity for mathcalL,KP 203 9.6 The Paradox of Knowability in mathcalL,KP 206 9.7 Conclusions 208 References 209 Part III Closer to the Core 211 10 Philosophical Aspects of an Alleged Connection Between the Axiom of Choice and Predicting the Future 212 10.1 Introduction 212 10.1.1 Mathematical Background 213 10.2 Problems with Randomness and Predicting 214 10.3 Problems with the Concept of Knowledge 217 10.4 A Few Words About Computability 218 10.5 Conclusions 219 References 219 11 Counterpossibles, Impossible Worlds, and the Notion of Similarity 220 11.1 Introduction 220 11.2 Counterfactuals 222 11.3 Troubles with Similarity 223 11.4 Abduction and the Notion of Similarity 227 11.5 Organized and Chaotic Worlds 231 11.6 A Priori Implication and the Structure of Worlds 234 11.7 Possible Objections 236 11.8 Summary 239 References 239 12 Grzegorczyk's Non-Fregean Logics and Their Formal Properties 241 12.1 Introduction 241 12.2 Paraconsistency 245 12.3 The Delusion Axiom 247 12.4 Reformulating LD in Terms of Implication 250 12.5 Logics LD and LE 251 12.6 The Logic LDS 254 12.7 Extensionality 256 12.8 Conclusions 260 References 261 Front Matter ....Pages i-vi Applied Formal Philosophy: Some Reflections on the Program (Gillman Payette, Rafal Urbaniak)....Pages 1-3 Front Matter ....Pages 5-5 The Logic of Guilt, Innocence and Legal Discourse (Andreas Kapsner)....Pages 7-24 Counterfactuals, Logic Programming and Agent Morality (Luís Moniz Pereira, Ari Saptawijaya)....Pages 25-53 The Wisdom of the Multitude: Diversity Versus Size (Peter C. Stone, Koji Kagotani)....Pages 55-71 A Logic for Human Actions (Clayton Peterson)....Pages 73-112 Reasoning with Comparative Moral Judgements: An Argument for Moral Bayesianism (Ittay Nissan-Rozen)....Pages 113-136 Front Matter ....Pages 137-137 Is Theory Choice Using Epistemic Virtues Possible? (Kit Patrick, Kate Hodesdon)....Pages 139-168 Abduction Logics: Illustrating Pitfalls of Defeasible Methods (Diderik Batens)....Pages 169-193 A Multimodal Pragmatic Analysis of the Knowability Paradox (Massimiliano Carrara, Daniele Chiffi, Davide Sergio)....Pages 195-209 Front Matter ....Pages 211-211 Philosophical Aspects of an Alleged Connection Between the Axiom of Choice and Predicting the Future (Pawel Pawlowski)....Pages 213-220 Counterpossibles, Impossible Worlds, and the Notion of Similarity (Maciej Sendłak)....Pages 221-241 Grzegorczyk’s Non-Fregean Logics and Their Formal Properties (Joanna Golińska-Pilarek, Taneli Huuskonen)....Pages 243-263