Language, Proof and Logic
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.
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Language, Proof and Logic
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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.
All learners receive a complete textbook and software package ($55.00 value).
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.
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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.
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Who should take this course?
This course is for you if you are interested in how to use language to construct and analyze arguments. The course has no prerequisites.
How is the course structured?
In addition to watching highly entertaining video lectures, you will complete assignments approximately weekly, using software applications and an automated TA who will give you feedback on your progress whenever you want it.
How will I be assessed?
Assessment is based on a combination of weekly assignments, and midterm and final exams. All assignments are graded automatically.
Do I need to buy a textbook?
No. The textbook and software for this course are provided free-of-charge ($55.00 value) to all registered learners.
If you are on the verified track you will additionally receive access to the Grade Grinder automated assessment service. This service is used to grade your work for this course.
Can I get Stanford University credit for this class?