Library of Congress Cataloging-in-Publication Data
Barker-Plummer, Dave.
Language, proof, and logic. – 2nd ed. / Dave Barker-Plummer, Jon
Barwise, and John Etchemendy in collaboration with Albert Liu, Michael
Murray, and Emma Pease.
p. cm. –
Rev. ed. of: Language, proof, and logic / Jon Barwise & John Etchemendy.
Includes index.
ISBN 978-1-57586-632-1 (pbk. : alk. paper)
1. Logic. I. Barwise, Jon. II. Etchemendy, John, 1952- III. Barwise, Jon.
Language, proof, and logic. IV. Title.
BC71.B25 2011
160–dc23
2011019703
CIP
∞ The acid-free paper used in this book meets the minimum requirements of the
American National Standard for Information Sciences—Permanence of Paper for
Printed Library Materials, ANSI Z 39.48-1984.
, Acknowledgements
Our primary debt of gratitude goes to our main collaborators on this project:
Gerry Allwein and Albert Liu.They have worked with us in designing the
entire package, developing and implementing the software, and teaching from
and refining the text.Without their intelligence, dedication,
and hard work,
LPL would neither exist nor have most of its other good properties.
In addition to the five of us, many people have contributed directly and in-
directly to the creation of the package. First, over two dozen programmers have
worked on predecessors of the software included with the package, both earlier
versions of Tarski’s World and the program Hyperproof, some of whose code
has been incorporated into Fitch. We want especially to mention Christopher
Fuselier, Mark Greaves, Mike Lenz, Eric Ly, and Rick Wong, whose outstand-
ing contributions to the earlier programs provided the foundation of the new
software. Second, we thank several people who have helped with the develop-
ment of the new software in essential ways: Rick Sanders, Rachel Farber, Jon
Russell Barwise, Alex Lau, Brad Dolin,Thomas Robertson, Larry Lemmon,
and Daniel Chai. Their contributions have improved the package in a host of
ways.
Prerelease versions of LPL have been tested at several colleges and univer-
sities. In addition, other colleagues have provided excellent advice that we have
tried to incorporate into the final package. We thank Selmer Bringsjord, Rens-
selaer Polytechnic Institute; Tom Burke, University of South Carolina; Robin
Cooper,Gothenburg University; James Derden,Humboldt State University;
Josh Dever, SUNY Albany; Avrom Faderman, University of Rochester; James
Garson, University of Houston; Christopher Gauker, University of Cincinnati;
Ted Hodgson, Montana State University; John Justice, Randolph-Macon Wom-
en’s College;Ralph Kennedy,Wake ForestUniversity;MichaelO’Rourke,
University ofIdaho;Greg Ray,University ofFlorida; Cindy Stern,Califor-
nia State University, Northridge; Richard Tieszen, San Jose State University;
Saul Traiger, Occidental College; and Lyle Zynda, Indiana University at South
Bend. We are particularly grateful to John Justice, Ralph Kennedy, and their
students (as wellas the students at Stanford and Indiana University),
for
their patience with early versions of the software and for their extensive com-
ments and suggestions. We would also like to thank the many instructors and
students who have offered useful feedback since the initial publication of LPL.
We would also like to thank Stanford’s Center for the Study of Language
v
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