Phil 76600

Phil 76600, Spring 2023

First-Order Modal Logic

Class Schedule: Thursday, 11:45 - 1:45, Room 7395.

Textbook: A pdf of the second edition of the Fitting/Mendelsohn book First-Order Modal Logic is available by clicking here. Please download it to your own device rather than working from the web page; it's not an industrial strength site. This is a work in progress, intended for publication with Springer. It is not for distribution. A password will be supplied to decrypt it.

Instructors: Melvin Fitting and Richard L. Mendelsohn

Description/Syllabus: Modal logic is usually thought of as the logic of qualified truth: necessarily true, true at all times, and so on. From at least Montague on, quantified modal logic has also been thought of as the natural setting for a logic of intensions. This course will cover the whole range.

We begin with propositional modal logic, presented semantically via Kripke models, and proof theoretically using both tableaus and axiom systems. First-order modal logic will be studied in considerable detail, using possible-world semantics and tableau systems, but not axiom systems. Various philosophical issues will be discussed, amongst which are: the nature of possible worlds, possibilist and actualist quantification, rigid and non-rigid designators, intensional and extensional objects, existence and being, equality, synonymy, designation and non-designation, and definite descriptions in a modal context.

The prerequisites for the course: a familiarity with classical logic, both propositional and first-order.

[Counts towards course satisfaction of Group E]

Course Learning Goals: By the end of the course students will be expected to:
Added Material:

Some additional material has been added to the book manuscript, covering in more detail how constant domain tableaus can simulate varying domain tableaus. This material can be accessed here: Additional Material.

More additional material has been added, containing a better intuitive discussion of some of the definite description tableau rules than was given in class. this can be accessed at: Additional Material About Definite Descriptions


The homework is not to be handed in. It will be discussed in class.

  1. February 9, 2023: Exercises 5.3.2, 5.3.3, 5.4.3, 5.4.5, 5.4.6
  2. February 16, 2023: Exercises 7.1.1, 7.1.3, 7.2.1, 7.2.2, 7.2.3, 7.2.4
  3. February 23, 2023: Exercises 7.4.1, 7.6.4, 7.6.5, 7.6.6
  4. March 2, 2023: Exercises 8.6.1, 8.7.1
  5. March 9, 2023: Exercises 9.1.2
  6. March 16, 2023: Exercises 11.9.1, 11.9.2
  7. March 23, 2023: Exercises 8.9.1, 8.10.4, 12.2.3, 12.2.4
  8. March 30, 2023: Exercises 14.2.1, 14.2.2, 14.4.2
  9. April 20, 2023: Exercise 15.4.1, and also the following,
    This continues Exercise 14.2.2. Each of the formulas in that exercise is an equivalence. Break it into two implications. You now have eight formulas. For each of at least four of them: provide a K tableau proof assuming constant symbols might not designate, or provide a counter-model assuming constant symbols might not designate.
  10. April 27, 2023: Exercises 17.2.6, 18.1.3, 18.1.4
  11. May 4, 2023: Exercises 20.4.4, 20.5.4, 20.5.5

Final Exam:

The final exam is a take-home series of problems. It will be made available by the final meeting of the class and is due one week later. In addition a student might, if he or she wishes, instead of taking the final examination, submit for a grade a term paper. The paper should be 10-20 pages and have as a topic any philosophical issue connected in some way with modal logic. If you think you might want to do this, discuss it with Prof. Mendelsohn.

Here are some practice test questions., similar to what will be on the take-home final.

There was a request during our final class meeting that answers to the Sample Test Questions be posted. Here they are. Answers,

Here is the final exam. It is due May 18. Send it to me by email.