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:
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:
gain a deeper understanding of second-order quantifiers;
be familiar with the central concepts of logic;
have a basic understanding of the K, T, D, B, S4, and S5 modal logics;
distinguish between the semantic and proof-theoretic accounts of logical consequence;
acquire a better understanding of intuitionistic logic;
understand some of the motivations for relevant and paraconsistent logic;
learn the basics of many-valued and fuzzy logic.
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
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 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
Winter 2022, 2023, 2024
Please let me know if you find any broken links.