04124880 Philosophical Logic
Tue 1:25–3:00 PM / Thu 4:15–5:50 PM at 3 North Hall, 319
Instructor Dr. Bruno Bentzen
TA Huayu Guo
Ofﬁce Location Chengjun Complex 4, 306
Ofﬁce Hours by appointment
Email bbentzen at zju.edu.cn
Credits 32 hours (8 weeks)
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:
MacFarlane, J. (2020). Philosophical Logic: A Contemporary Introduction. Routledge.
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:
Sider, T. (2010). Logic for Philosophy. Oxford University Press.
Priest, G. (2008). An Introduction to Non-Classical Logic. Cambridge University Press.
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
Assessment and grades
Final exam 50%
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:
How well you can understand the issues you are writing about
How good the arguments you offer are
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.
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.
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
Please let me know if you find any broken links.