front cover of From Frege to Gödel
From Frege to Gödel
A Source Book in Mathematical Logic, 1879–1931
Jean van Heijenoort
Harvard University Press, 1967

The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded by Leibniz, may be said to have been initiated by Boole, De Morgan, and Jevons, but it was the publication in 1879 of Gottlob Frege’s Begriffsschrift that opened a great epoch in the history of logic by presenting, in full-fledged form, the propositional calculus and quantification theory.

Frege’s book, translated in its entirety, begins the present volume. The emergence of two new fields, set theory and foundations of mathematics, on the borders of logic, mathematics, and philosophy, is depicted by the texts that follow. Peano and Dedekind illustrate the trend that led to Principia Mathematica. Burali-Forti, Cantor, Russell, Richard, and König mark the appearance of the modern paradoxes. Hilbert, Russell, and Zermelo show various ways of overcoming these paradoxes and initiate, respectively, proof theory, the theory of types, and axiomatic set theory. Skolem generalizes Löwenheim’s theorem, and he and Fraenkel amend Zermelo’s axiomatization of set theory, while von Neumann offers a somewhat different system. The controversy between Hubert and Brouwer during the twenties is presented in papers of theirs and in others by Weyl, Bernays, Ackermann, and Kolmogorov. The volume concludes with papers by Herbrand and by Gödel, including the latter’s famous incompleteness paper.

Of the forty-five contributions here collected all but five are presented in extenso. Those not originally written in English have been translated with exemplary care and exactness; the translators are themselves mathematical logicians as well as skilled interpreters of sometimes obscure texts. Each paper is introduced by a note that sets it in perspective, explains its importance, and points out difficulties in interpretation. Editorial comments and footnotes are interpolated where needed, and an extensive bibliography is included.

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front cover of Working Women in Mexico City
Working Women in Mexico City
Public Discourses and Material Conditions, 1879-1931
Susie S. Porter
University of Arizona Press, 2003
The years from the Porfiriato to the post-Revolutionary regimes were a time of rising industrialism in Mexico that dramatically affected the lives of workers. Much of what we know about their experience is based on the histories of male workers; now Susie Porter takes a new look at industrialization in Mexico that focuses on women wage earners across the work force, from factory workers to street vendors. Working Women in Mexico City offers a new look at this transitional era to reveal that industrialization, in some ways more than revolution, brought about changes in the daily lives of Mexican women. Industrialization brought women into new jobs, prompting new public discussion of the moral implications of their work. Drawing on a wealth of material, from petitions of working women to government factory inspection reports, Porter shows how a shifting cultural understanding of working women informed labor relations, social legislation, government institutions, and ultimately the construction of female citizenship. At the beginning of this period, women worked primarily in the female-dominated cigarette and clothing factories, which were thought of as conducive to protecting feminine morality, but by 1930 they worked in a wide variety of industries. Yet material conditions transformed more rapidly than cultural understandings of working women, and although the nation's political climate changed, much about women's experiences as industrial workers and street vendors remained the same. As Porter shows, by the close of this period women's responsibilities and rights of citizenship—such as the right to work, organize, and participate in public debate—were contingent upon class-informed notions of female sexual morality and domesticity. Although much scholarship has treated Mexican women's history, little has focused on this critical phase of industrialization and even less on the circumstances of the tortilleras or market women. By tracing the ways in which material conditions and public discourse about morality affected working women, Porter's work sheds new light on their lives and poses important questions for understanding social stratification in Mexican history.
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