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Logic

Course Description

Formal logic aims to represent and codify certain aspects of good reasoning.  The development and use of a formal language brings to the surface the logical connections between different claims, and enables us to use clear and precise techniques for evaluating arguments. And, as one of our central tasks is to sort the good arguments from the bad, this means that formal logic is a powerful and useful tool for any would-be philosopher.

This course serves as an introduction to formal logic. We particularly focus on two logical systems: Truth-Functional Logic (TFL) and First Order Logic (FOL). For each, we discuss the syntax (what it means to construct a well formed sentence in the logic), the semantics (how one decides whether or not a sentence in the logic is true), a proof theory (how, if you know some true things, you can figure out what else is true), and how to translate between natural languages (e.g., English) and these formal languages.

In this way, by successfully completing this course, students will be provided with certain skills and formal tools that will prove invaluable, regardless of their future course of study/career.

Learning Goals

On the basis of their knowledge and comprehension of techniques covered in class, students will be able to:

  • Identify, explain, and apply the notation and basic concepts of truth-functional and first-order formal logic
  • Translate natural language sentences (i.e., sentences of English) into truth-functional and first-order logic, translate truth-functional and first-order logic sentences into natural language, and evaluate said translations
  • Test the validity of arguments and the consistency of sets of sentences in truth-functional logic and first-order logic
  • Construct formal proofs in truth-functional and first-order logic

Required Literature

There is a textbook for the course:

  • Forallx: Cambridge, 2017, T. Button.

This book is printed under a Creative Commons license, meaning that students are able to freely download the book, and print as many copies as they like.

Course Documents

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