On the Sea Battle Tomorrow That May Not Happen: A Logical and Philosophical Analysis of the Master Argument

Description

This book is devoted to the problem of the Master Argument – a historical argument of the Greek philosopher Diodorus Cronus. Since the original argument was lost, many contemporary logicians have tried to recreate it, using modern tools of logic. The objective of Diodorus’ argument was to evidence the correctness of the temporarily defined modalities: necessity and probability. They took a deterministic form and challenged the indeterministic approach of Aristotle included in the Sea-Battle Tomorrow. In this study, the author shows that some of the reconstructions of the Master Argument allowed for the branched time structures. This is the crowning argument to prove that despite the acceptance of Diodorus’ notions, the Aristotelian Sea-Battle Tomorrow may still not happen, or may as well happen. Cover Copyright information Foreword Contents Part I Philosophical framework of the topic 1 Introduction 2 Truth and Sentences 2.1 Syntactic approach 2.2 Meanings of expressions 2.2.1 Propositions as meanings of sentences 2.2.2 Pragmatic components of a statement 2.2.3 Sentences that are temporarily determined 2.2.4 Sentences that are temporarily undetermined 2.3 Sentences vs. logical value 2.3.1 Requirements for the concept of truth 2.3.2 Historical background 2.3.3 What owns the truth? 2.3.4 What makes sentences true 2.3.5 The concept of truth employed in the study, concept of false controversy 2.3.6 Presuppositions of sentences 2.3.7 Sentences with modalities and other 2.3.8 Truth, time vs. epistemic concepts 3 Determinism 3.1 The extent of determinism 3.2 Modal components of determinism 3.3 Ontological determinism 3.3.1 Physical determinism 3.3.2 Metaphysical determinism 3.4 The consequences of determinism 3.4.1 Logical determinism 3.4.2 Epistemological determinism 3.4.3 Temporal determinism 3.4.4 Anthropological aspects of determinism 3.5 Determinism vs. the Reasoning of Diodorus Cronus 4 Time 4.1 Cultural time 4.2 Psychological and phenomenological time 4.3 Physical time 4.3.1 From psychological time to physical time 4.3.2 Time in scientific physics 4.3.3 Absolute time 4.3.4 Relative time 4.3.5 Properties of the physical time 4.4 Time measurement, its accuracy and units 4.5 Philosophy of time and its problems 4.5.1 Substantial time vs. attributive time 4.5.2 The direction of an arrow of time 4.5.3 McTaggart's problematique 4.6 Formal representation of time 4.6.1 Attempts to define moments of time: moments as points vs. moments without points Part II The issues 5 The problem 5.1 Aristotle and The Sea Battle Tomorrow 5.1.1 Primary problems concerning modality 5.1.2 Interpretations of De Interpretatione 5.1.3 On Interpretation, IX vs. The Reasoning of Diodorus Cronus 5.2 The reasoning of Diodorus Cronus 5.2.1 The definitions of modality vs. Diodorus' reasoning 5.2.2 Diodorus' conditional sentences 5.2.3 Conclusions and indications for a reconstruction 5.3 The issue of futura contingentia 5.4 Research problem and the method used 6 Dates, tenses, sentences vs. time structures 6.1 Dates 6.1.1 Dates and the pseudo-dates 6.1.2 Denotations of the dates 6.2 Grammatical tenses 6.3 Logical values of the sentences within the time structures 7 Logic 7.1 Temporal logics 7.1.1 Temporal interpretation of the positional logic 7.2 Time for the point moments 7.2.1 The similarity of the moments, branches and time 7.3 Axioms of the logical structures of time 7.4 The outline of logics of time Rn+ 7.4.1 Grammar 7.4.2 Axioms and rules of deduction 7.4.3 Semantics 7.5 Tense logic Part III Solutions 8 Reconstructions with operator R 8.1 The Reconstruction of F. S. Michael 8.1.1 Preliminaries 8.1.2 Reasoning 8.1.3 Definitions of modality 8.1.4 Time structure 8.2 Reconstruction of N. Rescher 8.2.1 Preliminaries 8.2.2 Reasoning 8.2.3 Definitions of modality 8.2.4 Time structure 8.3 Calculation of moments 8.3.1 Preliminaries 8.3.2 Reasoning 8.3.3 Definitions of modality 8.3.4 Time structure 9 Other reconstructions 9.1 Reconstruction of A. N. Prior 9.1.1 Preliminaries 9.1.2 Reasoning 9.1.3 Definitions of modality 9.1.4 Time structure 9.2 Reconstruction of P. Øhrstrøm 9.2.1 Preliminaries 9.2.2 Reasoning 9.2.3 Definitions of modality 9.2.4 Time structure Conclusion Summary Bibliography Index