## About the Program

Logical reasoning is essential in most areas of human inquiry. The discipline of Logic treats logical reasoning itself as an object of study. Logic has been one of the main branches of philosophy since Aristotle; it revolutionized the foundations of mathematics in the 20th century; and it has been called “the calculus of computer science,” with applications in many areas. Logic has also played an important role in the investigation of language and the mind, as the basis for formal semantics in linguistics and automated reasoning in artificial intelligence. With these interdisciplinary connections, Logic serves as a bridge between the humanities and STEM (Science, Technology, Engineering, and Mathematics) fields. Studying logic enhances students’ abilities to reason and argue rigorously, to read and write analytically, to discern patterns amidst complexity, and to understand abstract structures. The Logic Minor (offered through the Philosophy Department) consists of three core courses in symbolic logic, which may be pursued in parallel tracks within Philosophy or Mathematics, plus a choice of three upper division electives from an array of courses in Philosophy, Mathematics, Linguistics, and Computer Science. This minor is currently open to students in the College of Letters & Science.

## Minor Requirements

The Logic Minor at Berkeley consists of three core courses in symbolic logic, which may be pursued in parallel tracks within Philosophy or Mathematics, plus a choice of three upper division electives from a list of courses across Philosophy, Mathematics, Linguistics, and Computer Science.

### Course Requirements for Logic Minors

Code | Title | Units |
---|---|---|

Introductory | ||

PHILOS 12A | Introduction to Logic ^{1} | 4 |

or MATH 55 | Discrete Mathematics | |

Mathematical Logic | ||

PHILOS 140A | Intermediate Logic | 4 |

or MATH 125A | Mathematical Logic | |

Computability and Logic | ||

PHILOS 140B | Intermediate Logic ^{2} | 4 |

or MATH 136 | Incompleteness and Undecidability | |

Electives: Choose Three | 10-12 | |

At least two of these electives must be at the undergraduate level (unless an exception is granted by petition to the Logic Minor Committee). Note also that undergraduate enrollment in graduate seminars requires the consent of the instructor. | ||

Computability and Complexity [4] | ||

Formal Semantics [4] ^{3} | ||

Advanced Formal Semantics I [3] | ||

Introduction to the Theory of Sets [4] | ||

Metamathematics and Metamathematics | ||

Theory of Recursive Functions [4] | ||

Theory of Models [4] | ||

Theory of Sets [4] | ||

Metamathematics of Set Theory [4] | ||

Form and Meaning [4] | ||

Philosophical Logic [4] | ||

Modal Logic [4] | ||

Philosophy of Mathematics [4] | ||

Special Topics in Philosophy of Logic and Mathematics [4] | ||

Seminar [3] ^{4} | ||

Students may optionally fulfill (at most) one of their electives with a course on related formal methods and reasoning, or other courses approved by petition: PHILOS 141, PHILOS 148, and COMPSCI 188. |

^{1} | Please note that PHILOS 140A and PHILOS 140B are typically not offered in the same academic year, but rather in alternate years. Also note that MATH 125A and MATH 136 may have additional prerequisites, determined by the instructor. |

^{2} | LINGUIS 121 requires LINGUIS 120 as a prerequisite. |

^{3} | The Logic Minor Committee will decide which instances of PHILOS 290 count as “Graduate Seminars in Logic” for the Logic Minor. |

*Please note: It is a policy of the College of Letters & Sciences that no more than one upper-division course may be included in both your minor and major program.*

## Faculty and Instructors

**+ **Indicates this faculty member is the recipient of the Distinguished Teaching Award.

#### Faculty

**Lara Buchak, Associate Professor. **Game theory, decision theory, epistemology, philosophy of religion.

Research Profile

**Wesley H. Holliday, Associate Professor. **Philosophy, logic.

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**John Macfarlane, Professor. **Ancient philosophy, philosophical logic, philosophy of language, epistemology.

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**Paolo Mancosu, Professor. **Philosophy, philosophy of mathematics and its history, philosophy of logic, mathematical logic.

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**Antonio Montalban, Associate Professor. **Mathematical logic.

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**George Necula, Assistant Professor. **Software engineering, programming systemsm, security, program analysis.

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**Stuart Russell, Professor. **Artificial intelligence, computational biology, algorithms, machine learning, real-time decision-making, probabilistic reasoning.

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**Thomas Scanlon, Professor. **Mathematics, model theory, applications to number theory.

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**Sanjit Seshia, Associate Professor. **Electronic design automation, theory, computer security, program analysis, dependable computing, computational logic, formal methods.

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**Theodore A. Slaman, Professor. **Mathematics, recursion theory.

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**Hans Sluga, Professor. **Political philosophy, recent European philosophy, history of analytic philosophy, Frege, Wittgenstein, Foucault.

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**John Steel, Professor. **Mathematics, descriptive set theory, set theory, fine structure.

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**Umesh Vazirani, Professor. **Quantum computation, hamiltonian complexity, analysis of algorithms.

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**Seth Yalcin, Associate Professor. **Philosophy of language, logic, philosophy of mind, cognitive science, semantics, metaphysics.

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#### Emeritus Faculty

**John W. Addison, Professor Emeritus. **Mathematics, theory of definability, descriptive set theory, model theory, recursive function theory.

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**Robert Anderson, Professor Emeritus. **Finance, probability theory, mathematical economics, nonstandard analysis.

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**Charles S. Chihara, Professor Emeritus. **

**Alan D. Code, Professor Emeritus. **

**Leo A. Harrington, Professor Emeritus. **Mathematics, model theory, recursion theory, set theory.

Research Profile

**+ Richard Karp, Professor Emeritus. **Computational molecular biology, genomics, DNA molecules, structure of genetic regulatory networks, combinatorial and statsitical methods.

Research Profile

**Paul Kay, Professor Emeritus. **Linguistics, sociolinguistics, linguistic anthropology, pragmatics, syntax, semantics, lexicon, grammar, color naming, lexical semantics, grammatical variation, cross-language color naming, the encoding of contextual relations in rules of grammar.

Research Profile

**Ralph N. McKenzie, Professor Emeritus. **Mathematics, logic, universal algebra, general algebra, lattice theory.

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**W. Hugh Woodin, Professor Emeritus. **Mathematics, set theory, large cardinals.

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**Lotfi A. Zadeh, Professor Emeritus. **Artificial intelligence, linguistics, control theory, logic, fuzzy sets, decision analysis, expert systems neural networks, soft computing, computing with words, computational theory of perceptions and precisiated natural language.

Research Profile

## Contact Information

### Department of Philosophy

314 Moses Hall

Phone: 510-642-2722

Fax: 510-642-4164

#### Undergraduate Student Affairs Officer

Janet Groome

314 Moses Hall

Phone: 510-642-2722