# Language, Proof and Logic

SOHS-XLPL-SP

### Description

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.

## Instructors

John Etchemendy, Professor of Philosophy and Symbolic Systems

Dave Barker-Plummer, Senior Research Scientist

Delivery Option: Online
 Online Course Free
Notes:

#### Statement of Accomplishment

You can earn a Statement of Accomplishment if you score at least 70% on the graded assignments. To complete the assignments, you will need to purchase the courseware package for \$55US.

#### Textbook

If you do not wish to earn the Statement of Accomplishment, you do not need to purchase the textbook or courseware package. However, in order to complete the course and earn a Statement of Accomplishment you must purchase the Language, Proof and Logic courseware package (including the Grade Grinder assessment service). 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.

You can obtain it from the Language, Proof and Logic online store for \$55US. You may purchase the courseware package from other online retail sites and their prices may vary. Make sure the courseware package you purchase is new (not used) and includes the software as a CD. The courseware package is required to complete the course.

This course may not currently be available to learners in some states and territories.