-
161Handbook of the history of logic (edited book)Elsevier. 2004.Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, includ…Read more
-
222000 Annual Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 6 (3): 361-396. 2000.
-
The Proceedings of the Twentieth World Congress of PhilosophyThe Proceedings of the Twentieth World Congress of Philosophy 6. 2000.Analytic philosophy, a dominant tradition of twentieth-century philosophy, can be informatively cast as the outgrowth of the investigations of logic and language of Gottlob Frege, Bertrand Russell, and Ludwig Wittgenstein, and in the next generation, of Rudolf Carnap and W.V. Quine. As such, it is a specific historical development, one that featured subtle dialectical interactions among its propounders, interactions that have been reflected or reenacted in later developments. Whatever its herita…Read more
-
45
-
24Shelah Saharon. Cardinal arithmetic. Oxford logic guides, no. 29. Clarendon Press, Oxford University Press, Oxford and New York1994, xxxi + 481 pp (review)Journal of Symbolic Logic 62 (3): 1035-1039. 1997.
-
11José Ferreirós. Labyrinth of thought. A history of set theory and its role in modern mathematics. Science networks, vol. 23. Birkhäuser Verlag, Basel, Boston, and Berlin, 1999, xxi + 440 pp (review)Bulletin of Symbolic Logic 7 (2): 277-278. 2001.
-
19
-
Putnam’s Constructivization ArgumentIn John Burgess (ed.), Hilary Putnam on Logic and Mathematics, Springer Verlag. 2018.
-
19Mathias and set theoryMathematical Logic Quarterly 62 (3): 278-294. 2016.On the occasion of his 70th birthday, the work of Adrian Mathias in set theory is surveyed in its full range and extent.
-
23The Mathematical Infinite as a Matter of MethodAnnals of the Japan Association for Philosophy of Science 20 3-15. 2012.
-
28Mathematical Knowledge : Motley and Complexity of ProofAnnals of the Japan Association for Philosophy of Science 21 21-35. 2013.
-
The Infinite as Method in Set Theory and MathematicsOntology Studies: Cuadernos de Ontología 31-41. 2009.Este artículo da cuenta de la aparición histórica de lo infinito en la teoría de conjuntos, y de cómo lo tratamos dentro y fuera de las matemáticas. La primera sección analiza el surgimiento de lo infinito como una cuestión de método en la teoría de conjuntos. La segunda sección analiza el infinito dentro y fuera de las matemáticas, y cómo deben adoptarse. This article address the historical emergence of the infinite in set theory, and how we are to take the infinite in and out of mathematics.Th…Read more
-
17Review: Saharon Shelah, Cardinal Arithmetic (review)Journal of Symbolic Logic 62 (3): 1035-1039. 1997.
-
81In praise of replacementBulletin of Symbolic Logic 18 (1): 46-90. 2012.This article serves to present a large mathematical perspective and historical basis for the Axiom of Replacement as well as to affirm its importance as a central axiom of modern set theory.
-
91The empty set, the Singleton, and the ordered pairBulletin of Symbolic Logic 9 (3): 273-298. 2003.For the modern set theorist the empty set Ø, the singleton {a}, and the ordered pair 〈x, y〉 are at the beginning of the systematic, axiomatic development of set theory, both as a field of mathematics and as a unifying framework for ongoing mathematics. These notions are the simplest building locks in the abstract, generative conception of sets advanced by the initial axiomatization of Ernst Zermelo [1908a] and are quickly assimilated long before the complexities of Power Set, Replacement, and Ch…Read more
-
23Review: Jon Barwise, H. J. Keisler, K. Kunen, Y. N. Moschovakis, A. S. Troelstra, Handbook of Mathematical Logic; J. R. Shoenfield, B.1. Axioms of Set Theory (review)Journal of Symbolic Logic 49 (3): 971-975. 1984.
-
24On Gödel incompleteness and finite combinatoricsAnnals of Pure and Applied Logic 33 (C): 23-41. 1987.
-
108Zermelo and set theoryBulletin of Symbolic Logic 10 (4): 487-553. 2004.Ernst Friedrich Ferdinand Zermelo transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framewo…Read more
-
14G ödel has emphasized the important role that his philosophical views had played in his discoveries. Thus, in a letter to Hao Wang of December 7, 1967, explaining why Skolem and others had not obtained the completeness theorem for predicate calculus, Gödel wrote: This blindness (or prejudice, or whatever you may call it) of logicians (review)Bulletin of Symbolic Logic 11 (2). 2005.
-
53Bernays and set theoryBulletin of Symbolic Logic 15 (1): 43-69. 2009.We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higher-order reflection principles
-
Boston UniversityRegular Faculty
Boston, Massachusetts, United States of America
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |