Set theory is concerned with the foundation of mathematics. In the original formulations of set theory, there were paradoxes contained in the idea of the "set of all sets". Current standard theory (Zermelo-Fraenkel) avoids these paradoxes by restricting the way sets may be formed by other sets, specifically to disallow the possibility of forming the set of all sets. In the 1930s, Quine proposed a different form of set theory in which the set of all sets - the universal set - is allowed, but other restrictions are placed on these axioms. Since then, the steady interest expressed in these non-standard set theories has been boosted by their relevance to computer science. The second edition still concentrates largely on Quine's New Foundations, reflecting the author's belief that this provides the richest and most mysterious of the various systems dealing with set theories with a universal set. Also included is an expanded and completely revised account of the set theories of Church-Oswald and Mitchell, with descriptions of permutation models and extensions that preserve power sets. Dr Foster here presents the reader with a useful and readable introduction for those interested in this topic, and a reference work for those already involved in this area.

This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.

For 30 years, Quine, a dominant figure in logical theory and philosophy of logic, has combined insights in methodology, language, epistemology, and ontology, to blur the boundaries of speculative metaphysics and natural sciences. This revised text contains two new essays with replies from Quine.

For more than two generations, W.V. Quine has contributed fundamentally to the substance, the pedagogy and the philosophy of mathematical logic. "Selected Logic Papers", long out of print and now reissued with eight additional essays, includes much of the author's important work on mathematical logic and the philosophy of mathematics from the past 60 years.

Hailed by the "Bulletin of the American Mathematical Society" as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. 1978 edition.

These nine essays are largely concerned with the theory of meaning and references—semantics. At the same time adjacent portions of phil osophy and logic are discussed. To the existence of what objects may a given scientific theory be said to be committed? And what considerations may suitably guide us in accepting or revising such ontological commitments? These are among the questions dealt with in this book, particular attention being devoted to the role of abstract entities in mathematics. There is speculation on the mechanism whereby objects of one sort or another come to be posited a process in which the notion of identity plays an important part.

内容提要 本卷包括两部论著：《威拉德·范·奥曼·蒯因自传》（1986）和《数理逻辑》（1940）。前者是蒯因为“在世哲学家文库”《蒯因哲学》卷所写的简明自传；后者是蒯因的一部重要的逻辑著作，在其中，他仍然坚持逻辑主义纲领，试图从逻辑中推导出数学，把先前在《数理逻辑的新基础》（1937）一文中提出的NF系统，修改为ML系统，这是一个把命题逻辑、量化理论和集合论集为一身的系统，结构简明、特性奇异。 目录 威拉德·范·奥曼·蒯因自传 数理逻辑 导言 第一章 句子 1 合取、析取和否定 2 条件句 3 多重复合 4 使用和谈论 5 谈论句子的句子 6 准引语 7 括号与黑点 8 归约为三个初始联结词 9 归约为一个初始联结词 10 重言式 11 某些重言的形式 第二章 量化 12 量词 13 公式 14 约束、自由、闭包 15 量化的公理 16 定理 17 元定理 18 等值代换 19 存在量词 20 量词的分配 21 字母变体 第三章 项 22 类和分子 23 逻辑公式 24 抽离 25 等同 26 再论抽离 27 摹状词和名字 第四章 关于类的进一步理论 28 层次 29 更进一步的从属关系公理 30 等同可代入性 31 变元的代入 32 进一步的结果 33 逻辑积、和、补 34 包含 35 单类 第五章 关系 36 对和关系 37 关系的抽离 38 逆、象、关系积 39 祖先 40 函数 41 函数的抽离 42 作为关系的等同和从属 第六章 数 43 零、一、后继 44 自然数 45 可数集合 46 有穷的和无穷的 47 关系的幂 48 算术和、积、幂 …… 第七章 句法 附录 参考文献 人名索引 主题词索引