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.
The book aims to formalise tableau methods for the logics of propositions and names. The methods described are based on Set Theory. The tableau rule was reduced to an ordered n-tuple of sets of expressions where the first element is a set of premises, and the following elements are its supersets.