Logic, Logic and Logic

Title......Page 001_0001.djvu
Copyright......Page 002_0001.djvu
Contents......Page 003_0001.djvu
Editorial Preface......Page 005_0001.djvu
Editor’s Acknowledgments......Page 007_0001.djvu
Part I: Studies on Set Theory and the Nature of Logic......Page 009_0001.djvu
Introduction......Page 011_0001.djvu
Set Theory......Page 11
Second-Order Logic......Page 014_0001.djvu
Plural Quantification......Page 018_0001.djvu
1 – The Iterative Conception of Set......Page 021_0001.djvu
2 – Reply to Charles Parson’s “Sets and Classes”......Page 038_0001.djvu
3 – On Second-Order Logic......Page 045_0001.djvu
4 – To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables)......Page 062_0001.djvu
5 – Nominalist Platonism......Page 081_0001.djvu
6 – Iteration Again......Page 096_0001.djvu
7 – Introductory Note to Kurt Gödel’s “Some Basic Theorems on the Foundations of Mathematics and their Implications”......Page 113_0001.djvu
8 – Must We Believe in Set Theory?......Page 128_0001.djvu
Part II: Frege Studies......Page 141_0001.djvu
Introduction......Page 143_0001.djvu
The Inconsistency in Frege¹s System......Page 143
Frege’s Theorem......Page 146_0001.djvu
Frege and His Contemporaries......Page 148_0001.djvu
The Philosophical Status of Hume’s Principle......Page 149_0001.djvu
9 – Gottlob Frege and the Foundations of Arithmetic......Page 151_0001.djvu
10 – Reading the Begriffsschrift......Page 163_0001.djvu
11 – Saving Frege from Contradiction......Page 179_0001.djvu
12 – The Consistency of Frege’s Foundations of Arithmetic......Page 191_0001.djvu
13 – The Standard of Equality of Numbers......Page 210_0001.djvu
14 – Whence the Contradiction?......Page 228_0001.djvu
15 – 1879?......Page 245_0001.djvu
16 – The Advantages of Honest Toil over Theft......Page 263_0001.djvu
17 – On the Proof of Frege’s Theorem......Page 283_0001.djvu
18 – Frege’s Theorem and the Peano Postulates......Page 299_0001.djvu
19 – Is Hume’s Principle Analytic?......Page 309_0001.djvu
20 – Die Grundlagen der Arithmetik, §§82-83 (with Richard G. Heck, Jr.)......Page 323_0001.djvu
21 – Constructing Cantorian Counterexamples......Page 347_0001.djvu
Part III: Various Logical Studies and Lighter Papers......Page 351_0001.djvu
Introduction......Page 353_0001.djvu
Mathematical Induction......Page 353
Lengths of Proofs......Page 355_0001.djvu
The Incompleteness Theorems and Semantic Paradoxes......Page 357_0001.djvu
22 – Zooming Down the Slippery Slope......Page 362_0001.djvu
23 – Don’t Eliminate Cut......Page 373_0001.djvu
24 – The Justification of Mathematical Induction......Page 378_0001.djvu
25 – A Curious Inference......Page 384_0001.djvu
26 – A New Proof of the Gödel’s Incompleteness Theorem......Page 391_0001.djvu
27 – On “Seeing” the Truth of the Gödel Sentence......Page 397_0001.djvu
28 – Quotational Ambiguity......Page 400_0001.djvu
29 – The Hardest Logical Puzzle Ever......Page 414_0001.djvu
30 – Gödel’s Second Incompleteness Theorem Explained in Words of One Syllable......Page 419_0001.djvu
Afterword......Page 423_0001.djvu
Fundamental Theorems of Provability Logic......Page 423
Further Topics in Provability Logic......Page 427_0001.djvu
Bibliography......Page 433_0001.djvu
B......Page 433
C-D......Page 437_0001.djvu
F-G......Page 438_0001.djvu
H......Page 439_0001.djvu
J-K-L......Page 440_0001.djvu
M-N-P-Q......Page 441_0001.djvu
R-S......Page 442_0001.djvu
T-V-W-Z......Page 443_0001.djvu
Index......Page 445_0001.djvu
A-B-C......Page 445
D-E-F-G......Page 446_0001.djvu
H-I......Page 447_0001.djvu
J-K-L-M-N......Page 448_0001.djvu
O-P-Q-R......Page 449_0001.djvu
S-T-U-V......Page 450_0001.djvu
W-Z......Page 451_0001.djvu