# Open Logic Project

Richard Zach, University of Calgary

Andrew Arana, University of Paris

Jeremy Avigad, Carnegie Mellon University

Walter Dean, University of Warwick

Gillian Russell, University of North Carolina

Nicole Wyatt, University of Calgary

Audrey Yap, University of Victoria

Copyright Year: 2016

Publisher: Open Logic Text

Language: English

## Formats Available

## Conditions of Use

Attribution

CC BY

## Reviews

The text covers formal meta-logic and formal methods at an intermediate level. Given that starting point, this text covers just about any topic you want to cover including model theory, computability, Turing machines, incompleteness results,... read more

The text covers formal meta-logic and formal methods at an intermediate level. Given that starting point, this text covers just about any topic you want to cover including model theory, computability, Turing machines, incompleteness results, second-order logic, modal logic, intuitionistic logic, naive set theory, and many other topics.

I haven't found any bias in the text.

The text is up-to-date and should be easy to update.

While the text is quite technical in places, the concepts are explained quite well. Students might benefit from some more examples in places, though the authors have already highlighted sections that can benefit from additional examples.

The text does a good job of using consistent notation throughout.

The project lists different logic courses and the book that was compiled from chapters of the main text.

As befitting a book on logic, the topics are presented in a clear, logical manner.

I have not encountered any interface issues.

I have not found any grammar errors.

I did not find any examples that were culturally insensitive.

I hope this text continues to expand and cover other topics such as many-valued logics, relevance logics, and perhaps Zermelo-Fraenkel set theory.

## Table of Contents

- I Naıve Set Theory
- II Propositional Logic
- III First-order Logic
- IV Model Theory
- V Computability
- VI Turing Machines
- VII Incompleteness
- VIII Second-order Logic
- IX The Lambda Calculus
- X Many-valued Logic
- XI Normal Modal Logics
- XII Intuitionistic Logic
- XIII Counterfactuals
- XIV Set Theory
- XV Methods
- XVI History

## Ancillary Material

## About the Book

The Open Logic Text is an open-source, collaborative textbook of formal meta-logic and formal methods, starting at an intermediate level (i.e., after an introductory formal logic course). Though aimed at a non-mathematical audience (in particular, students of philosophy and computer science), it is rigorous.

The Open Logic Text is a collaborative project and is under active development. Coverage of some topics currently included may not yet be complete, and many sections still require substantial revision. We plan to expand the text to cover more topics in the future. We also plan to add features to the text, such as a glossary, a list of further reading, historical notes, pictures, better explanations, sections explaining the relevance of results to philosophy, computer science, and mathematics, and more problems and examples. If you find an error, or have a suggestion, please let the project team know.

The project operates in the spirit of open source. Not only is the text freely available, we provide the LaTeX source under the Creative Commons Attribution license, which gives anyone the right to download, use, modify, re-arrange, convert, and re-distribute our work, as long as they give appropriate credit.

## About the Contributors

### Authors

**Richard Zach** is a logician working at the University of Calgary (Canada) where he is Professor of Philosophy. He works on the history of logic, the philosophy of logic and mathematics, and mathematical logic. He has recently used the Open Logic Text in a course on Intermediate Logic at McGill University.

**Andrew Arana** is a logician working at the University of Paris 1 Panthéon-Sorbonne (France) where he is maître de conférences (associate professor) of philosophy. He works on the history and philosophy of mathematics and logic. At Paris 1 his logic teaching includes model theory, philosophy of logic, and elementary logic. In his previous appointment as Associate Professor of Philosophy and Mathematics at the University of Illinois at Urbana-Champaign and at other institutions he has taught logic at many different levels as well. He looks forward to using this text in logic courses this academic year.

**Jeremy Avigad** is a logician at Carnegie Mellon University, where he is Professor of Philosophy and Mathematical Sciences. He works in mathematical logic, history and philosophy of mathematics, and formal verification. At Carnegie Mellon, he teaches logic to students in mathematics, computer science, and philosophy, from undergraduate freshmen to advanced graduate students. Sections on computability and incompleteness are based on his notes.

**Walter Dean** is Associate Professor of Philosophy at the University of Warwick (UK). He works in philosophy of mathematics, mathematical and philosophical logic, theoretical computer science, and the philosophy and history of computation. He regularly teaches intermediate and advanced undergraduate logic.

**Gillian Russell** is Professor of Philosophy at the University of North Carolina, Chapel Hill. She writes on the philosophy of language and the philosophy of logic, and often teaches advanced logic courses to philosophers.

**Nicole Wyatt** is a philosopher working at the University of Calgary, where she is also Head of the Department of Philosophy. She works on the philosophy of logic and language, as well as the history of computational theory. She regularly teaches Logic II, as well as Philosophy of Logic, at Calgary. She has used the Open Logic Text twice in Logic II, and contributed material to the sections on first-order logic and Turing computability.

**Audrey Yap** is Associate Professor of Philosophy at the University of Victoria (Canada). She works in epistemic logic, history and philosophy of mathematics, and more recently in feminist epistemology. She teaches logic from the intro level onward.