Bolzano's Logical System (Oxford Logic Guides)

This book is focused on the first three parts of Bolzano's Theory of Sciene and introduces a more systematic reconsideration of Bolzano's logial thought. In undertaking this task, the book is intended as an exploration, not so much of the more specifically discursive aspects of Bolzano's logial thought - already amply studied - as muh as on identifying the singularly coherent and systematic nature of the logic presented in Bolzano's work. Casari presents this within a formal system and adopts the approach of the predicate calculus with identity and choice operator by using Hilbert's epsilon calculus (the logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics). Content: Cover PREFACE ACKNOWLEDGEMENTS CONTENTS 1 Introduction 1.1 The Bolzanian Conceptual Universe 1.2 The Logic and the Language 1.3 General (Elementary) Principles of Ontology, Lectology, and Epistemology 1.4 Restricted Quantifiers 1.5 Variation 1.6 Ordered n-tuples 1.7 Relations (Relational Qualities) 2 Elementary Level (A): Ideas 2.1 Preamble 2.2 Properties of Ideas 2.3 Relations Between Two Ideas 2.4 Relations Among Several Ideas 2.5 The Idea of Something 2.6 Concretization 2.7 Concrete and Abstract Ideas 2.8 Intuitions 2.9 Sum of Quality Ideas 2.10 Another Lectological Operation on Quality Ideas2.11 Negation 3 Elementary Level (B): Propositions 3.1 Atomic Propositions 3.2 Aristotelian Universal Propositions with Existential Import 3.3 Material Proprieties and Relations of Propositions 3.4 Complex Propositions 3.5 Variation 3.6 Formal Properties and Relations of Ideas 3.7 Validity of Propositions 3.8 Analytic and Synthetic Truth and Falsity 3.9 Formal Relations Among Propositions 3.10 Formal Connectives 3.11 Probability 3.12 Probability of Events 4 Symbolic Level 4.1 Preliminary Remark: Properties of Things and Quality of Objects4.2 Bolzano's Conjecture 4.3 Restricted Symbolic Level-Ideas of Ideas 4.4 The Traditional Categorical Propositions 4.5 Extended Symbolic Level: Ideas of Propositions 4.6 Material Connectives 4.7 Formal Properties and Relations 4.8 Formal Properties of Collections of Propositions 4.9 Formal Relations Among Propositions 4.10 Generalization to a Finite Set of Ideas 4.11 Formal Connectives Among Finite Sets of Propositions 4.12 'Arbitrary Sets' of Ideas and Propositions 4.13 Generalization of Properties and Material Relations among Ideas4.14 Two Operations on Ideas of Object Ideas 4.15 New Formulation of the Material Relations among Ideas of Ideas 4.16 Bolzano's Thesis for Material Relations Among Sets of Ideas 4.17 Material Conjunctions and Disjunctions 4.18 Formal Properties of 'Arbitrary Sets' of Propositions 4.19 Formal Relations among 'Arbitrary Sets' of Propositions 4.20 Formal Connectives among 'Arbitrary Sets' of Propositions 5 Inferences 5.1 Preliminaries 5.2 Rules to Obtain Inferences from Inferences 5.3 Inferences with One or More Universal Premises5.4 Inferences with at Least One Negated Universal Premise 5.5 Inferences with One or More Existential or Inexistential Premises 5.6 Syllogistic Inferences 5.7 Inferences from Premises Containing Width Determinations 5.8 Inferences from Premises Enunciating Relations among Ideas 5.9 Inferences from Premises Enunciating Relations among Propositions 6 Higher Level 6.1 Preamble 6.2 The Problem of Vacuous Qualities 6.3 Truth as Enunciation of a Situation 6.4 Qualities of Qualities 7 Etiology 7.1 Consecutivity 7.2 Dependence A starting point of Bolzano’s logical reflection was the conviction that among truths there is a connection, according to which some truths are grounds of others, and these in turn are consequences of the former, and that such a connection is objective, i.e. subsisting independently of every cognitive activity of the subject. In the attempt to account for the distinction between subjective and objective levels of knowledge, Bolzano gradually gained the conviction that the reference of the subject to the object is mediated by a realm of entities without existence that, recalling the Stoic lectà, are here called ‘lectological’. Moreover, of the two main ways through which that reference takes place—psychic activity and linguistic activity—Bolzano favoured the first and traced back to it the problems of the second; i.e. he considered those intermediate entities first as possible content of psychic phenomena and only subordinately, on the basis of a complex theory of signs, as meanings of linguistic phenomena. This book follows this schema and treats, in great detail, first, lectological entities (ideas and propositions in themselves), second, cognitive psychic phenomena (subjective ideas and judgements), and, finally, linguistic phenomena. Moreover, it tries to bring to light the extraordinary systematic character of Bolzano’s logical thought and it does this showing that the main logical ideas developed principally in the first three parts of the Theory of Science , published in 1837, can be effortlessly formally presented within the well-known Hilbertian epsilon-calculus A unique new book exploring Bernard Bolzano's Wissenschaftslehre (Theory of Science) and introducing a formal system to examine the logic presented in Bolzano's work.