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.