andrew-bacon

PHIL 350: Intermediate Logic

Time and place

Tuesdays and Thursdays 12:30-1:50. MHP B7B

Contact

office: 224 STO

email: abacon@usc.edu

in person office hours: Tuesdays 2-3

zoom office hours: Wednesday 9-10 (by appointment)

Texts

Material will be drawn primarily from lectures and notes. The two books listed below are useful supplements. It is recommended that you take handwritten notes during class, so you will need a notepad. This can be supplemented by the first few chapters of

• For the first part of the course on inductive structures:
  • Chapter two of The Limits of Logic by Jeff Russell (free, and available in the dropbox folder).
• Later portions of the course on propositional and modal logics:
  • chapters 1-3 of Ted Sider’s Logic for Philosophy.

Links

dropbox

signup sheet

notes and exercises

Course description

In this course students will learn fundamental results in metalogic. The course begins with an introduction to mathematical reasoning about inductive structures, such as natural numbers, sequences, trees and sentences. Using these tools we will then study the model theory and proof theory for classical and non-classical propositional logics allowing us to establish various soundness, completeness, and indepedence results. If time permits we will look at propositional modal logic, and first-order and higher-order logics,

Prerequisites

There are no prerequisites.

Grading

• Participation
  • Students are encouraged to ask questions or ask for clarification at any point.
• Grading
  • You will be assessed entirely on the basis of weekly exercises (20%), participation and in-class exercises (20%), two exams (30% and 30%).
• Weekly exercises
  • These will be graded on a pass fail basis. Note that a pass does not mean that you got the exercise correct – it means that you gave the exercise an honest try. Solutions to exercises will be covered in class.
  • You have two free passes: you may miss up to two weekly exercises without it affecting your grade, which should be reserved for illness or family emergencies. Further absences will need proper documentation.
  • Feedback on solutions is always verbal. Make sure you prepare any questions you had for the in-class discussion of solutions, and come to office hours if necessary.

• In-class exercises

  • You will present a solution to an exercise of your choice on the board. The signup sheet for these presentations can be found here.
• Midterm
  • Thursday, October 3rd. In class exam.
• Final
  • Thursday December 5th, in class.
  • Exams cannot be rescheduled except in a very limited set of circumstances (you may consult the universities regulations and policies here ).

Schedule of topics

1. Inductive structures: natural numbers, lists, trees.

2. Definitions by recursion.

3. Proof by induction.

4. Propositional languages.

5. Semantics for propositional languages.

6. Hilbert axiom systems.

7. Soundness and statement of completeness.

8. First-order languages.

9. Semantics for first-order languages.

10. Non-classical propositional logics.

11. If we have time: Modal languages.

12. If we have time: Hilbert axiom systems.

13. If we have time: Semantics for modal languages.

Statement on academic conduct and support services

Academic Conduct

Plagiarism - presenting someone else’s ideas as your own, either verbatim or recast in your own words - is a serious academic offense with serious consequences. Please familiarize yourself with the discussion of plagiarism in SCampus in Part B, Section 11, Behavior Violating University Standards. Other forms of academic dishonesty are equally unacceptable. See additional information in SCampus and university policies on scientific misconduct.

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