Introduction | vii | |
1 | The functions of logic and the problem of truth definition | 1 |
2 | The game of logic | 22 |
3 | Frege's fallacy foiled: Independence-friendly logic | 46 |
4 | The joys of independence: Some uses of IF logic | 72 |
5 | The complexities of completeness | 88 |
6 | Who's afraid of Alfred Tarksi? Truth definitions for IF first-order languages | 105 |
7 | The liar belied: Negation in IF logic | 131 |
8 | Axiomatic set theory: Fraenkelstein's monster? | 163 |
9 | IF logic as a framework for mathematical theorizing | 183 |
10 | Constructivism reconstructed | 211 |
11 | The epistemology of mathematical objects | 235 |
Appendix (by Gabriel Sandu) | 254 | |
References | 271 | |
Index of names | 281 | |
Index of subjects and titles | 285 |
`... storm clouds begin to gather as soon as logicians venture beyond the enchanted land of first-order logic. And they have to do so, for unfortunately first-order logic soon turns out to be too weak for most mathematical purposes. Its resources do not suffice to characterize fully such crucial concepts as mathematical induction, well-ordering, finiteness, cardinality, power set, and so forth. First-order logic is thus insufficient for most purposes of actual mathematical theorizing.'