Question:

I’m a linguistics student and I’m confused about something. In linguistics we study the syntax, semantics and pragmatics of language, which is pretty comprehensive. But in our program we also have to take a course in symbolic logic taught by the philosophy department. I’m a little afraid of this course (I’m not the only one), but I also don’t understand why it’s important enough to be a requirement. I see how diagramming sentences is helpful for understanding language, but symbolic logic just looks like math or computer programming to me. I don’t see how it’s relevant to real human languages. Is there something I’m missing?

- Kylie

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Wow, this is a great question.

I’m actually one of those philosophy professors who has taught symbolic logic to a class of mostly linguistics majors, many of whom don’t know why they’re in the class other than to fulfill a degree requirement.

I’m also keenly aware that if you just teach the standard introductory symbolic logic curriculum it’s easy for students to walk away wondering why the course was required. Logic textbooks usually don’t do a good job of explaining the relevance of logic to linguistics.

And linguistics departments often don’t do a good job of explaining the relevance either, unless they have at least one formal linguist on faculty - someone who specializes in formal semantics. And even then, you can get formal linguists who defend the relevance of symbolic logic and others who are skeptical of its relevance. So students often hear nothing, or conflicting things, about the importance of symbolic logic to linguistics.

I’m no expert on the historical development of formal semantics in linguistics. And that discussion would get technical quickly and wouldn’t be helpful to folks who are primarily interested in logic as it relates to critical thinking in everyday contexts.

But I do have a few things to say about the relationship between logic and language that I think are important for general “logic literacy”. So I’m going to take this opportunity to share that with you here.

The Short Version

The short version of I what I want to say comes down to three theses:

1. Natural language has a logical structure. This structure is important for understanding the symbolic and semantic capacities of language.
2. The historical development of formal logic was motivated by a desire to understand the nature of deductive reasoning and deductive proof, not the logical structure of natural language.
3. However, different systems of formal logic can be used to model different fragments of the logical structure of natural language, and thereby shed light on this structure.

In the lectures in this section I’ll try to elaborate on each of these points.