**Education**

University of Pennsylvania B. A. in Mathematics, summa cum laude, 1969.

University of California, Berkeley M. A. in Mathematics 1971.

Ph. D. in Mathematics 1973.

**Fellowships**

Postdoctoral Fellow in Mathematics and Philosophy

1975–77 Victoria University of Wellington, New Zealand

U. S. National Academy of Sciences Exchange Scholar

1981 Polish Academy of Sciences, Warsaw

Fulbright Fellow

1987 Center for Logic and Epistemology, University of Campinas, Brazil

CNPQ Fellow

1991 Philosophy Department, University of Paraíba, Brazil

(CNPQ is the Brazilian government’s research funding foundation.)

**Academic Employment**

Iowa State University

1978–1981 Assistant Professor of Mathematics

1981–1982 Associate Professor of Mathematics with tenure

University of California, Berkeley

1982–1984 Visiting Associate Professor of Mathematics

California State University, Hayward

1985–1986 Temporary Associate Professor in Mathematics and Computer Science

San Jose State University

1988 Visiting Associate Professor in Mathematics and Computer Science

University of Auckland, New Zealand

1993 Visiting Lecturer in Philosophy

University of Nevada, Las Vegas

1995–1998 Lecturer in Philosophy

Advanced Reasoning Forum

1999– Head

**Books and Monographs**

Minimal Degrees of Unsolvability and the Full Approximation Construction

Memoirs of the American Mathematical Society, no. 162, 1975.

Degrees of Unsolvability: Structure and Theory

Lecture Notes in Mathematics, 759, Springer-Verlag, 1979.

Initial Segments of the Degrees Below 0´

Memoirs of the American Mathematical Society, no. 241 (2), 1981.

Computability: Computable Functions, Logic, and the Foundations of Mathematics

with Walter Carnielli, Wadsworth & Brooks/Cole, 1989.

2nd edition, including Computability and Undecidability, a Timeline,Wadsworth, 1999.

3rd edition, Advanced Reasoning Forum, 2008.

The Semantic Foundations of Logic

Propositional Logics

Kluwer, 1990. 2nd edition, Oxford University Press, 1995.

2nd edition with corrections, Wadsworth, 2000.

Predicate Logic

Oxford University Press, 1994. Reprinted, Wadsworth, 2000.

Classical Mathematical Logic

Princeton University Press, 2006.

Critical Thinking

Wadsworth, 1998. 4th edition, with Michael Rooney, Advanced Reasoning Forum, 2013.

The Pocket Guide to Critical Thinking

Wadsworth, 1999. 5th edition, Advanced Reasoning Forum, 2016.

Five Ways of Saying “Therefore”

Wadsworth, 2001.

The Guide to Critical Thinking in Economics

with Carolyn Kernberger, South-Western, 2004.

Essays on Logic as the Art of Reasoning Well

Cause and Effect, Conditionals, Explanations

Advanced Reasoning Forum, 2011

Reasoning in Science and Mathematics

Advanced Reasoning Forum, 2012

Prescriptive Reasoning

Advanced Reasoning Forum, 2013

Reasoning and Formal Logic

Advanced Reasoning Forum, 2015

The Fundamentals of Argument Analysis

Advanced Reasoning Forum, 2013

The Guide to Writing Introductory College Textbooks Advanced Reasoning Forum, 2013. Conventional Gestures: Meaning and Methodology. Advanced Reasoning Forum, 2014. An Introduction to Formal Logic. Advanced Reasoning Forum, 2016.

__Books in Preparation__

An American Gestuary with Alex RaffiIllustrated dictionary of gestures, 2013. Draft available at www.ARFbooks.org. Logic, Language, and the WorldVolume 1: The Internal Structure of Predicates and NamesTypescript, 2015.Volume 2: Time and Space in Formal LogicVolume 3: The World as Process Essays on Language and the World

**Articles**

Diagonalization in degree constructions (with David Posner)

Journal of Symbolic Logic, 43, no. 2, 1978, 280–283.

Relatedness and implication

Relatedness and interpretability (with L. Szczerba)

Philosophical Studies, 36, no. 2, 1979, 137—175, 225—231.

Relatedness and dependence in propositional logics

Abstract of talk to the Association of Symbolic Logic, 1979 Spring Meeting,

Journal of Symbolic Logic, 6, no. 1, 1981, p. 202.

A hierarchy of sets and degrees below 0´ (with R. Kramer and R. Haas)

in Logic Year 1979–1980, eds. Lerman, Schmerl, and Soare, Lecture Notes in Mathematics,

no. 859, Springer–Verlag, 1981, 32–48.

A mistaken theorem on degrees of f-r.e. sets

Abstracts of the American Mathematical Society, 3, no. 1, 1982,p. 129

(correction to Degrees of Unsolvability above).

The algebra of dependence logic

Reports on Mathematical Logic, 21, 1987, 19–34.

Complementing below recursively enumerable degrees (with S. B. Cooper)

Annals of Pure and Applied Logic, 34, no. 1, 1987, 15–34.

A general framework for semantics for propositional logics

Text of invited address to the VII Latin American Symposium on Mathematical Logic,

in Methods and Applications of Mathematical Logic, eds. W. Carnielli and L. P. de Alcantara,

Contemporary Mathematics, no. 69, 1988, 149–168.

A paraconsistent many-valued logic: J3 (with Itala M. L. D’Ottaviano)

Reports on Mathematical Logic, 22, 1988, 89–103.

A theory of truth based on a medieval solution to the liar paradox

History and Philosophy of Logic, 13, 1992, 149-177.

Valid deductions for falsity-default logics

Reports on Mathematical Logic, 26, 1992, 89–95.

The metaphysical basis of logic

Manuscrito, vol. 22, no. 2, 1999, 133–148.

Arguments and explanations

Bulletin of Advanced Reasoning and Knowledge, 1: Proceedings of the Advanced Reasoning

Forum meeting in Bucharest, Romania, 2000,New Europe College, 2001.

(Also at .)

Relatedness predicate logic (with Stanislaw Krajewski)

Bulletin of Advanced Reasoning and Knowledge, vol. 2, 2004, pp. 19–38.

(Also at .)

On models and theories, with applications to economics

Bulletin of Advanced Reasoning and Knowledge, vol. 2, 2004, pp. 77–98.

(Also at .)

Classical predicate logic with non-referring names

Logique et Analyse, vol. 189–192, 2005, pp. 71–86.

Paraconsistent logics with simple semantics

Logique et Analyse, vol. 189–192, 2005, pp. 189–207.

Mathematics as the Art of Abstraction In The Argument of Mathematics, eds. Andrew Aberdein and Ian Dove, Springer-Verlag, 2013, pp. 257–289. Valid Inferences In Logic without Frontiers:Festschrift for Walter Alexandre Carnielli on the Occasion of his 60th Birthday, eds. J.-Y. Béziau and M. E. Coniglio, College Publications, pp. 105–12, 2012. A Propositional Logic of Temporal Connectives (with Esperanza Buitrago-Díaz) Logic and Logical Philosophy, vol. 24, no. 2, pp. 155–200, DOI 10.12775/LLP.2014.015, 2014. Reflections on Temporal and Modal Logic Logic and Logical Philosophy, DOI 10.12775/LLP.2014.020, 2014.

**Edited Volumes**

Relatedness and Dependence in Propositional Logics,

Research Report of the Iowa State University Logic Group, 1982.

Bulletin of Advanced Reasoning and Knowledge 1, 2001.

Available at .

Bulletin of Advanced Reasoning and Knowledge 2, 2005.

Available at .

**Reviews**

Review of “Degrees of unsolvability complementary between r.e. degrees” by S. B. Cooper

Journal of Symbolic Logic, 40, no. 1, 1975, p. 86.

Truth Is beauty

Essay review of John Buridan on Self-reference by G. Hughes,

History and Philosophy of Logic, 6, no. 1, 1985, 117–125.

Review of Logic Made Easy by Deborah J. Bennett

Bulletin of Symbolic Logic, vol. 10, no. 4, 2004, p. 577.

Review of Logics by John Nolt

Bulletin of Symbolic Logic, vol. 12, no. 2, 2006, p. 290.

**Newspaper column**

They’re not like you and me

Published weekly in El Defensor Chieftain, Socorro, NM, from July, 2006 to May, 2008.