Fall 2026
PHIL3038M Philosophical Logic

Course information

Instructor Dr. Bruno Bentzen

TA Zixin Fang

Office Location Chengjun Complex 4, 306

Office Hours by appointment

Email bbentzen at zju.edu.cn

Credits 32 hours (8 weeks)

Language English

Course description

This course is an introduction to philosophical logic focusing on a wide selection of logical systems that either extend, restrict, or deviate from classical first-order logic as established by Frege, Peirce, Russell, Hilbert, and others. After a brief review of classical propositional and predicate logic, we will study the introduction of identity, definite descriptions, function symbols, and generalized quantifiers like "most" or "there are as many as"; you will also learn about second-order logic and how its expressive power goes beyond that of first-order logic, and how substitutional quantifiers and free logic can be adopted to address the alleged ontological commitment of classical first-order logic; among the other non-classical logics overviewed in this course are modal propositional logic and quantified modal logic, intuitionistic logic, relevant logic and paraconsistent logic, and many-valued logic.

Course materials and resources

This course is based on a series of lecture notes which will be made available in advance here. Please note that the document might occasionally be updated for corrections, minor revisions, or the addition of new material. Motivated students interested in complementary readings are especially encouraged to check out some of the following textbooks on logic for philosophers:

• John MacFarlane. Philosophical Logic: A Contemporary Introduction (2020). Routledge.

• Ted Sider. Logic for Philosophy (2010). OUP.

• Graham Priest. An Introduction to Non-Classical Logic (2008). CUP.

• John L. Bell, David DeVidi & Graham Solomon. Logical Options: An Introduction to Classical and Alternative Logics (2001). Peterborough: Broadview Press

Course objectives

Upon the successful completion of this course, you will:

1. distinguish between the semantic and proof-theoretic accounts of logical consequence;

2. become familiar with classical logic with identity and definite descriptions;

3. gain command of substitutional quantifiers, second-order logic, and free logic;

4. have a basic understanding of the K, T, D, B, S4, and S5 modal logics;

5. acquire a better understanding of intuitionistic logic;

6. understand some of the motivations for relevant and paraconsistent logic;

7. learn the basics of many-valued logic.

Course prerequisites

Ideally, you should have taken an introduction to logic or an equivalent course. We will overview basic propositional and predicate logic in our first week, but if this is your very first time learning formal logic, you will find this course very challenging and might not be able to keep up. 

Assessment and grades

• In-class problem sets 90%

• Participation 10%

Grades are awarded on a scale from 0 to 100, where 100 is the best grade and 60 is the minimum passing grade.

Problem sets: There will be 6 in-class problem sets assigned every Wednesday between the first and last teaching weeks. Problem sets are important because learning logic properly takes effort and constant practice. Your problem set grade will be determined by your five best-graded solutions of the total six. The problem sets will be posted in class and must be handed in to our TA by the end of class. We will try our best to make sure your solutions will be graded and returned to you by the following Wednesday in class. Your solutions must be written legibly, and you must name your document. In general, no late solutions will be accepted; but if you missed the deadline because you were ill or for another valid reason, please contact us as soon as possible for an arrangement. I might require documentation of serious personal emergencies.

Participation: I will not require you to speak up in class, but any form of engagement with the lectures is highly encouraged. The use of mobile phones, computers, and other portable devices is permitted for taking notes and class-related activities only.

Attendance policy

You are expected to attend every lecture in person and be on time. If you cannot come to class due to an emergency, please let our TA 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.

Plagiarism and AI policies

I wish to evaluate your performance, so your work should reflect your own efforts. You can discuss the problem sets with other students, but do not copy their solutions and submit them as your own. Any form of cheating and plagiarism is prohibited and will be taken as a serious offense by the university. The use of AI editing tools as language aids is permitted. However, submission of assignments based on AI-generated solutions is considered cheating. I will reserve the right to run AI writing detectors and request an impromptu oral explanation of your solutions whenever the suspicion arises.

Feedback

I always 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, either positively or negatively. But it will help me to see my lectures from different angles and develop new ways of improving them.

Special Accommodations

Please contact me if you have a disability or other circumstances that require special accommodations.

Schedule

The following schedule is tentative and subject to change with fair notice:

Lecture 1: Classical propositional semantics

Lecture 2: Classical propositional natural deduction

Lecture 3: Classical predicate semantics

Lecture 4: Classical predicate natural deduction

Lecture 5: Identity, function symbols, and definite descriptions 

Lecture 6: Generalized quantifiers 

Lecture 7: Second-order logic

Lecture 8: Expressive power of second-order logic 

Lecture 9: Substitutional quantifiers

Lecture 10: Free logic

Lecture 11: Propositional modal logics K, D, T, B, S4, S5

Lecture 12: Fitch-style natural deduction in modal logic

Lecture 13: Overview of Gödel's ontological proof

Lecture 14: Intuitionistic logic

Lecture 15: Relevance and paraconsistent logic

Lecture 16: Many-valued logics

Past instances

• Fall 2025, Winter 2024, 2023, 2022

Please let me know if you find any broken links.