# Language, Proof and Logic

Date:
Tuesday, September 2, 2014 to Friday, December 19, 2014
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Course topic:

The ability to reason is fundamental to human beings. Whatever the discipline or discourse it is important to be able to distinguish correct reasoning from incorrect reasoning. The consequences of incorrect reasoning can be minor, like getting lost on the way to a birthday party, or more significant, for example launching nuclear missiles at a flock of ducks, or permanently losing contact with a space craft.

The fundamental question that we will address in this course is "when does one statement necessarily follow from another" --- or in the terminology of the course, "when is one statement a logical consequence of another". This is an issue of some importance, since an answer to the question would allow us to examine an argument presented in a blog, for example, and to decide whether it really demonstrates the truth of the conclusion of the argument. Our own reasoning might also improve, since we would also be able to analyze our own arguments to see whether they really do demonstrate their conclusions.

In this course you will be introduced to the concepts and techniques used in logic. We will start right from the beginning, assuming no prior exposure to this or similar material, and progress through discussions of the proof and model theories of propositional and first-order logic.

We will proceed by giving a theory of truth, and of logical consequence, based on a formal language called FOL (the language of First-Order Logic). We adopt a formal language for making statements, since natural languages (like English, for example) are far too vague and ambiguous for us to analyze sufficiently. Armed with the formal language, we will be able to model the notions of truth, proof and consequence, among others.

While logic is technical in nature, the key concepts in the course will be developed by considering natural English statements, and we will focus the relationships between such statements and their FOL counterparts. The goal of the course is to show how natural English statements and arguments can be formalized and analyzed.

## Prerequisites

This course has no prerequisites except an interest in the way in which we use language to construct arguments and justify conclusions. If that interests you, then you're all set! Go sign up.

## Textbook

You will need to purchase the MOOC edition of the Language, Proof and Logic courseware package. The package contains software applications that you will use to complete exercises during the course. You will also get access to the Grade Grinder, an Internet-based assessment service for these exercises.

The MOOC edition of the courseware is offered at \$10, a significantly reduced cost from the regular edition, but can only be used in conjunction with this course. You can obtain it from the Language, Proof and Logic online store. We guarantee to refund the cost of the MOOC edition of the textbook up until the end of the fourth week of the course (Oct 1 2014), so you can try the course out with no risk.

If purchasing the textbook would cause financial hardship, please write a note to the Language, Proof and Logic team, to request a free copy of the courseware.

## Instructors

### John Etchemendy

#### Professor of Philosophy and Symbolic Systems

John Etchemendy has been on the faculty of Princeton University and Stanford University where he was chairman of the Department of Philosophy and is currently Provost. He has has also served as the director of the Center for the Study of Language and Information.

### Dave Barker-Plummer

#### Senior Research Scientist

I'm Dave Barker-Plummer. Since 1995 I have managed the Openproof project's work on educational software for teaching logic at Stanford University. I have a background in Artificial Intelligence, and have taught computer science and logic at Stanford, Swarthmore College and Duke University. In my spare time I indulge my rock-star fantasies with PAN!C, a San Franciso based reggae/pop/jazz band.

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