Gödel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added to produce a modified version of Montague/Gallin intensional logic. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Parts of the book are mathematical, parts philosophical.
Author(s): Melvin Fitting
Series: Trends in Logic, Volume 12
Publisher: Kluwer Academic Publishers
Year: 2002
Language: English
Pages: 198
Cover......Page 1
Series......Page 3
Volumes of the Series......Page 198
Title......Page 4
Copyright......Page 5
Contents......Page 6
Epigraph......Page 10
Preface......Page 12
Part I: Classical Logic......Page 18
1. Terms and Formulas......Page 20
2. Substitutions......Page 25
1. Classical Models......Page 28
2. Truth in a Model......Page 29
3.1 Compactness......Page 32
3.3 Weak Completeness......Page 33
3.4 And Worse......Page 34
4. Henkin Models......Page 36
5. Generalized Henkin Models......Page 41
6.2 Extensional Models......Page 46
6.3 Language Extensions......Page 47
1. A Different Language......Page 50
2. Basic Tableaus......Page 52
3. Tableau Examples......Page 54
1. Soundness......Page 60
2. Completeness......Page 63
2.1 Hintikka Sets......Page 64
2.2 Pseudo-Models......Page 65
2.3 Substitution and Pseudo-Models......Page 69
2.4 Hintikka Sets and Pseudo-Models......Page 76
2.5 Pseudo-Models are Models......Page 79
2.6 Completeness At Last......Page 80
3. Miscellaneous Model Theory......Page 83
2. Derived Rules and Tableau Examples......Page 86
3. Soundness and Completeness......Page 90
2. A Derived Rule and an Example......Page 94
3. Soundness and Completeness......Page 96
Part II: Modal Logic......Page 98
1. Introduction......Page 100
2. Types and Syntax......Page 103
3. Constant Domains and Varying Domains......Page 106
4. Standard Modal Models......Page 107
5. Truth in a Model......Page 109
6. Validity and Consequence......Page 111
7. Examples......Page 112
8. Related Systems......Page 118
9. Henkin/Kripke Models......Page 119
1.1 Prefixes......Page 122
1.3 Modal Rules......Page 124
1.4 Quantifier Rules......Page 125
1.6 Atomic Rules......Page 126
1.7 Proofs and Derivations......Page 127
2. Tableau Examples......Page 128
3. A Few Derived Rules......Page 130
1.1 Equality Axioms......Page 132
1.2 Extensionality......Page 134
2. De Re and De Dicto......Page 135
3. Rigidity......Page 138
4. Stability Conditions......Page 141
5. Definite Descriptions......Page 142
6. Choice Functions......Page 145
Part III: Ontological Arguments......Page 148
1. Introduction......Page 150
3. Descartes......Page 151
4. Leibniz......Page 154
5. Gödel......Page 155
6. Gödel’s Argument, Informally......Page 156
2. Positiveness......Page 162
3. Possibly God Exists......Page 167
4. Objections......Page 169
5. Essence......Page 173
6. Necessarily God Exists......Page 177
7.2 Positive Properties are Necessarily Instantiated......Page 179
8. More Objections......Page 180
9. A Solution......Page 181
10. Anderson’s Alternative......Page 186
11. Conclusion......Page 188
A-B-C......Page 190
D-F-G......Page 191
H-K......Page 192
L-M-O-P-R......Page 193
S-T......Page 194
A-C-D-E-F-G-H......Page 196
I-K-L-M-N-O-P-Q-R-S-T-V-W-Z......Page 197
