Winter 2023
04124880 Philosophical Logic

Tue 1:25–3:00 PM / Thu 4:15–5:50 PM at 3 North Hall, 319

Course Information

Instructor Dr. Bruno Bentzen

TA Huayu Guo

Office Location Chengjun Complex 4, 306

Office Hours by appointment

Email bbentzen at

Credits 32 hours (8 weeks)

Course Description

This course focuses on the philosophical examination of the fundamental concepts and motivation behind the development of different logical systems that extend, restrict, or deviate from classical logic as established by Frege, Peirce, Russell, Hilbert and others. It covers an overview of classical propositional and first-order logic, the theory of generalized quantifiers and second-order logic, modal propositional logic, quantified modal logic, conditionals, Tarski's account of logical consequence, intuitionistic logic and Prawitz's proof-theoretic semantics, relevant logic and paraconsistent logic, and many-valued logic and fuzzy logic.

Course Materials and Resources

This course is roughly based on the textbook:

Some lectures draw on notes on additional material which will be made available in advance. Students interested in complementary readings are also encouraged to check the following textbooks on logic for philosophers and non-classical logics:

Course objectives

Upon the successful completion of this course, you will:

Assessment and grades

Final paper

There will be one major writing assignment at the end of the course. Your paper must have one page (around 500 words) and must be written in English. You should name and date your paper — it must also contain a title, introduction, exposition of your problem and ideas, and conclusion. You will be graded based on the clarity and structure of your exposition:

Your English level will NOT be subject to evaluation, only the content of your paper. But you should at least be able to communicate your ideas clearly and effectively. Detailed information about the content of the final paper will be provided as it approaches.


Each homework assignment must be completed and turned in on time. I wish to evaluate your performance, so your homework should reflect your own efforts. Homework will be assigned weekly every Thursday and will be due on the following Thursday in class. No late homework will be accepted. If you missed the deadline because you were ill or for some other valid reason, please send me an email. Your solutions must be written legibly. The corrected homework will be returned to you on the Tuesday that follows the due date.

Attendance policy

You are expected to attend every lecture and be on time. If you cannot come to class due to an emergency please let me know as soon as possible. If you miss a class it is your responsibility to make up the material missed and catch up with your classmates.


I welcome feedback, be it positive or negative. If you wish, you can do this by speaking to me directly after class, sending me an email, or, if you prefer, sending me an anonymous note. Giving feedback will not have any effect on your grade, neither positively nor negatively. But it will help me to see my lectures from different angles and develop new ways of improving them.

Schedule (tentative)

Lecture 1: Classical propositional logic

Lecture 2: Classical predicate logic

Lecture 3: Identity and definite descriptions

Lecture 4: Generalized quantifiers and second-order logic

Lecture 5: Proofs in second-order logic

Lecture 6: Substitutional quantifiers

Lecture 7: Free logic

Lecture 8: Propositional modal logic

Lecture 9: Kripke semantics for K, D, T, B, S4, S5

Lecture 10: Fitch-style natural deduction in modal logic

Lecture 11: Quantified modal logic with constant and varied domains

Lecture 12: Intuitionistic propositional logic

Lecture 13: Proof-theoretic semantics

Lecture 14: Intuitionistic predicate logic

Lecture 15: Relevance and paraconsistent logic

Lecture 16: Many-valued logics

Past instances

Please let me know if you find any broken links.