This book develops a philosophical and logical interpretation of the concept of information within the formal structure of Constructive Type Theory (CTT), in a manner concurrent with a diverse range of contemporary perspectives on the philosophy of information. It presents a newly formulated and conceptually developed presentation of the Problem of Analyticity, and a new interesting perspective on the constructive interpretation of knowledge processes.
Author(s): Giuseppe Primiero
Series: Logic, Epistemology, and the Unity of Science, 10
Publisher: Springer
Year: 2007
Language: English
Pages: 215
Contents......Page 7
Introduction......Page 10
1.1 Philosophical Foundation......Page 16
1.2 Basic Epistemic Notions......Page 17
1.3.1 Constructive Notion of Type......Page 20
1.3.2 Definition......Page 25
1.3.3 Conceptual Priority......Page 27
1.3.4 Method......Page 29
1.4 Identity......Page 34
1.4.1 Definitional Identity vs. Syntactically Induced Identity......Page 36
1.4.2 Identity as Theoretical Notion......Page 38
1.5.1 Formalizing the Forms of Judgement......Page 40
1.5.2 Formalizing Equality Rules......Page 42
1.5.3 Categories......Page 43
1.5.4 Type set......Page 46
1.5.5 Type prop......Page 47
1.5.6 The Notion of Proposition for CTT......Page 49
1.5.7 Propositions as Sets......Page 55
1.6 Dependent Objects: Hypothetical Judgements......Page 56
1.6.1 Judgements Depending on One Assumption......Page 59
1.6.2 Judgements Depending on More Assumptions......Page 60
1.7 Introducing Functions......Page 61
1.8 Computational Rules......Page 63
1.8.1 The System of Rules and Some Examples for set and prop......Page 64
1.8.2 Rules for the type Func......Page 66
1.9 Introducing Information......Page 69
2. Analyticity and Information......Page 72
2.1.1 The Modern Origin of Analyticity: Kant......Page 73
2.1.2 Elements of the Bolzanian Doctrine of Science......Page 79
2.1.3 A New Concept of Analyticity (Against the Critical View)......Page 82
2.1.4 Analyticity in Question: The Possibility of Knowledge......Page 86
2.2 Analysis and Synthesis......Page 93
2.2.1 Act and Content: A Foundational Distinction......Page 96
2.2.2 Content and Meaning......Page 97
2.2.3 Analyticity Reconsidered: From Meaning to Information......Page 102
2.2.4 Rejecting the Analytic/Synthetic Distinction: Quine......Page 104
2.2.5 Towards a Constructive Notion of Analyticity......Page 108
2.3 Informativeness of Derivations......Page 110
2.3.1 Individuals and Degrees: Computing Information of Sentences......Page 112
2.4 Different Notions of Information......Page 118
2.4.2 Surface Information: Probability and Possible Worlds......Page 120
2.4.3 Increasing Logical Information: Depth Information......Page 122
2.5.1 Reconsidering the Semantic Approach......Page 124
2.5.2 Recollecting Perspectives on Information......Page 128
2.5.3 Knowledge: What, That, How......Page 129
3.1 CTT as the General Framework: Informal Description......Page 133
3.1.1 Formalization of Knowledge and Information......Page 137
3.1.2 Contexts: Formal Explanation......Page 138
3.2 Representation of Knowledge and Information......Page 143
3.2.1 Presuppositions......Page 144
3.2.2 Assumptions......Page 147
3.2.3 Types and Meaning Declarations......Page 149
3.2.4 Truth and the Role of Assumptions......Page 152
3.2.5 Defining Information......Page 156
3.3 Contexts as Constructive PossibleWorlds......Page 158
3.3.1 Introducing Orderings: Kripke Models......Page 160
3.4.1 Updating Information, Extending Knowledge......Page 162
3.4.2 The Structure of Knowledge......Page 166
4.1 An Extension for the Constructive Epistemology......Page 172
4.2 Information and Mathematics......Page 175
4.2.1 From Analytic Method to the Analyticity of Logic......Page 177
4.3 The Role of Constructions......Page 178
4.4.1 Overview on Presuppositions Theory and Dynamic Logics......Page 182
4.4.2 Declaring and Explaining Meanings......Page 186
4.4.3 Meaning and Predication......Page 191
4.5 Information and Logical Knowledge......Page 195
4.6 Final Epistemic Foundation for Information......Page 198
Bibliography......Page 201
K......Page 213
W......Page 214
