Interactions of metaphysical and epistemic concepts [PhD Thesis]

Introduction 1
1 Plug-ins: possibility and knowledge 28
1.1 Fusions of modal logics and Fitch’s paradox . . . . . . . . . . 35
1.1.1 Church or Fitch? . . . . . . . . . . . . . . . . . . . . . 36
1.1.2 The verification principle . . . . . . . . . . . . . . . . 36
1.1.3 The collapse principle . . . . . . . . . . . . . . . . . . 38
1.1.4 The nature of Fitch’s paradox . . . . . . . . . . . . . . 38
1.1.5 Somany people . . . . . . . . . . . . . . . . . . . . . . 45
1.2 Other formulations . . . . . . . . . . . . . . . . . . . . . . . . 47
1.2.1 Philosophical foundations of the paradox . . . . . . . 48
1.3 Products of modal logics and the limits of knowledge . . . . . 50
1.3.1 The logic for knowability . . . . . . . . . . . . . . . . 52
1.3.2 Combined modality? . . . . . . . . . . . . . . . . . . . 57
1.4 Imagination and possible knowledge . . . . . . . . . . . . . . 58
2 Interplays: knowledge and contingency 63
2.1 Logical skepticism . . . . . . . . . . . . . . . . . . . . . . . . 65
2.2 Combining knowledge and contingency . . . . . . . . . . . . . 70
2.2.1 Two notions of contingency . . . . . . . . . . . . . . . 71
2.2.2 Contingency logics . . . . . . . . . . . . . . . . . . . . 74
2.2.3 Mixing knowledge and contingency . . . . . . . . . . . 78
2.3 Logical skepticism revisited . . . . . . . . . . . . . . . . . . . 90
2.3.1 Knowledge and reality . . . . . . . . . . . . . . . . . . 90
2.3.2 Two basic criteria . . . . . . . . . . . . . . . . . . . . 91
2.4 Fusions, skepticism and the border of concepts . . . . . . . . 98
3 Connections: belief and contingency 100
3.1 Shaking knowledge and belief . . . . . . . . . . . . . . . . . . 102
3.2 Different conceptions of belief . . . . . . . . . . . . . . . . . . 105
3.3 Interactions of knowledge and belief . . . . . . . . . . . . . . 110
3.3.1 The knowledge-belief reduction . . . . . . . . . . . . . 115
3.4 Combining belief and contingency . . . . . . . . . . . . . . . . 118
3.5 Fusions, skepticism and the border of concepts II . . . . . . . 123
4 Combinations: contradictions, contingency, knowledge and belief 125
4.1 Can contradictions be object of knowledge and belief? . . . . 130
4.2 Paraconsistentization of logics . . . . . . . . . . . . . . . . . . 134
4.2.1 The case of modal logics . . . . . . . . . . . . . . . . . 137
4.2.2 The problem of a paraconsistent negation . . . . . . . 141
4.2.3 Desparaconsistentization of logics? . . . . . . . . . . . 143
4.3 Paraconsistentization of classical propositional logic . . . . . 143
4.3.1 Fusions and paraconsistentization . . . . . . . . . . . . 149
4.4 Paraconsistentizing fusions . . . . . . . . . . . . . . . . . . . . 151
5 Network: a universal approach to concepts 154
5.1 Philosophical categorification . . . . . . . . . . . . . . . . . . 157
5.1.1 A categorial approach . . . . . . . . . . . . . . . . . . 157
5.1.2 Logic applied to philosophy . . . . . . . . . . . . . . . 158
5.1.3 Category theory and philosophy . . . . . . . . . . . . 162
5.1.4 Categories and logics . . . . . . . . . . . . . . . . . . . 163
5.1.5 Categories and philosophy . . . . . . . . . . . . . . . . 165
5.1.6 A system of philosophy based on category theory? . . 167
5.2 The universal approach to modalities . . . . . . . . . . . . . . 167
5.2.1 Structuralist theory of modalities . . . . . . . . . . . . 168
5.2.2 The n-dimensional modal logics . . . . . . . . . . . . . 168
5.2.3 The n-opposition theory . . . . . . . . . . . . . . . . . 169
5.3 The duality of reality . . . . . . . . . . . . . . . . . . . . . . . 173
Conclusion 176
History and Interview 182
Bibliography 192