Winter 2025
04124880 Philosophical Logic

Mon 4:15–5:50 PM / Wed 4:15–5:50 PM at 3 North Hall, 405

Course information

Instructor Dr. Bruno Bentzen

TA TBD

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, many-valued logic, and fuzzy 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:

Course objectives

Upon the successful completion of this course, you will:

Course prerequisites

You must have taken an introduction to logic or 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

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 take-home problem sets assigned weekly every Thursday and due on the following Wednesday before class starts. The problem sets will be posted on the class' Dingtalk group. Please hand in your hard copy assignment to our TA in class. In general, no late homework will be accepted, but if you missed the deadline because you were ill or for another valid reason, please contact our TA as soon as possible. I might require documentation of serious personal emergencies. We will try our best to make sure your homework will be graded and returned to you on the Monday that follows the due date. Your solutions must be written legibly and you must name your document. Problem sets are important because learning logic properly takes effort and constant practice. 

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 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. 

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 such as Grammarly or Hemingway Editor as language aids is permitted. However, the submission of assignments based on AI-generated solutions (such as those generated by ChatGPT prompts) is considered cheating. To submit AI-generated text as your own is no different from plagiarism and 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 logic

Lecture 2: Classical predicate logic

Lecture 3: Classical predicate logic with identity 

Lecture 4: Function symbols and definite descriptions 

Lecture 5: Generalized quantifiers 

Lecture 6: Second-order logic

Lecture 7: Expressive power of second-order logic 

Lecture 8: Substitutional quantifiers

Lecture 9: Free logic

Lecture 10: Propositional modal logics K, D, T, B, S4, S5

Lecture 11: Fitch-style natural deduction in modal logic

Lecture 12: Quantified modal logic with constant and varied domains

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

Please let me know if you find any broken links.