See full syllabus here.
What makes an argument good? How do you show that someone has reasoned invalidly? In this course we will study arguments and reasoning both informally as well as with the tools and techniques of formal deductive logic. We will learn the syntax and semantics of propositional and first-order logic (polyadic with identity and functions), and we will use them to explicate the intuitive notion of a valid argument. We then apply our formal logical techniques to a variety of domains, such as the domain of sets (abstract collections of objects). Topics include syntax, semantics, pragmatics, consistency, proof, logical consequence, logical equivalence, logical truth, analyticity, logical form, sets, set theory, infinity, paradoxes, truth functionality, logic gates, truth tables, quantification, relations, functions, interpretations, models, soundness, and completeness. We will also discuss connections between formal logic and computability theory, philosophy of language, cognitive science, foundations of mathematics, and metalogic (theorems about logical systems themselves).
Grading and Course Requirements
There are four components of your grade:
- Participation: 5%
- Homework: 25%
- Midterm exam: 30%
- Final exam: 40%
Here is an explanation of each of these parts:
- Participation will be measured by your involvement on the online discussion board on Canvas. We will use the discussion board as a place for you to ask and answer questions—about specific homework problems that you are struggling with, or course content in general. The main point of the discussion board is for you to help each other with the course material, so you are expected to answer as well as ask questions (though I will help answer questions too). You must use the board at least 5 times by July 19 (1% point for each time).
- Homework assignments will have two parts; one part is called “written” and the other part is called “electronic.” In fact, though, both parts will be submitted online. The “written” part will be submitted via file upload to Canvas, and the “electronic” part will be submitted with the program Submit (part of the software package that comes with the textbook). For directions on how to submit homework and manage your workflow for the course, please see both the video posted on Canvas called “Submitting Homework” as well as the directions on the first problem set. Problem sets will start to be due the first week! They will be due on the assigned days by 11 p.m. (See Late Policy below regarding late homework.)
- The midterm will occur in class on July 1 from 1:10 to 2:10 p.m. It is closed note/book/computer (unless allowed by Disability Resources for Services). It will be multiple choice, true/false, proofs, etc. Directions and a study guide will be provided before the exam. You must bring a PURPLE (not green) Scantron answer card and a no. 2 pencil in order to take the test.
- The final exam will occur on our last day, July 20, from 1:10-3:20 p.m. It is closed note/book/computer (unless allowed by Disability Services). Like the midterm, it will be multiple choice, true/false, proofs, etc. Directions and a study guide will also be provided during the last week of class. The test in cumulative, but the emphasis will be on new material since the midterm. You must bring a PURPLE (not green) Scantron answer card and a no. 2 pencil in order to take the test.
What makes an argument good? How do you show that someone has reasoned invalidly? In this course we study arguments and reasoning with the tools and techniques of formal deductive logic. We will learn the syntax and semantics of propositional and first-order logic, and we will use them to explicate the intuitive notion of a valid argument. We then apply our formal logical techniques to answer questions in a variety of areas. Is there only one size of infinity, or can one infinity be bigger than another? Can there be a set of all sets? How does a computer work? How could water running through hoses implement a computer?
TEXT: Language, Proof and Logic, David Barker-Plummer, Jon Barwise and John Etchemendy.