Formal logic can be a challenge for many students. I recall my own struggles with trying to formulate an overall picture of what symbolic logic is all about and how it's relevant to natural language and other philosophical topics.
I wrote this section in response to a question from a linguistics student, and so had in mind an audience of students who are primarily interested in language, and who want to know what they will learn in a logic class that is relevant to understanding natural language.
I’ve tried to explain in broad terms what I think is relevant and useful about logic for the study of language. The details will always be contested, but the general idea, that natural language has a logical structure, and that formal logic offers tools for investigating this structure, should not be doubted.
However, I am critical of the way these ideas are often communicated (or not communicated) in textbooks, and I'm sympathetic to those students who feel confused and uncertain about the point of a logic class for linguistics majors.
My hope is that this discussion will also be helpful to anyone who is interested in formal logic. I certainly wish I had this perspective in my head when I was an undergraduate student.