Phil 455: Symbolic Logic


Course Number Phil 455.001 (spring 2024)
Title Symbolic Logic
Credit Hours 3 credits
Course Description See below
Prerequisites Phil 155, or permission of the instructor
Target Audience Graduate students in Philosophy, and others with comparable preparation and instructor’s permission
Class Times and Location Mon Wed 11:15 – 12:30 in Caldwell (CW) 208
Instructional Format In-person, mix of lectures and tutorials/group problem-solving
Instructor Professor Jim Pryor (he/him), email
Teaching Assistants None
Course Website
Instructor’s Office Hours Mon 3–4:30 and Wed 1:30–3 in Caldwell 108A, or by appointment
Course Texts Readings provided by web links

Canvas Site, Zoom, and Regular Updates

UNC students enrolled in the course (or otherwise authorized by the instructor) can access the Canvas site.

Those pages include the Zoom links for any course meetings you need to attend remotely, and for my office hours. These can also be retrieved from this restricted page.

Most of the information for the course will be published here, outside of the Canvas system, and can also be viewed by people not enrolled in the course.

This front web page won’t be updated frequently. Regular announcements, readings, and lecture notes will be posted at this page instead.

Table of Contents

Course Description

This course aims to provide solid foundations to deal with reading and writing papers that deal with logic in philosophy and related disciplines. We will cover a range of issues in logic and metalogic, and some in math and formal semantics. Our emphasis will be equipping you with a broad understanding of the field, rather than refining your proof skills. Important metalogical results we discuss include the completeness, compactness, and undecidability of first-order predicate logic.


The course is offered by Professor Jim Pryor (he/him). Undergrads generally address me as “Professor Pryor,” and grad students address me as “Jim.”

Professor Pryor’s office is Caldwell 108A. He can best be reached by email, at

Professor Pryor’s office hours are on Mondays from 3–4:30 and Wednesdays from 1:30–3. (On both days, I can sometimes go later. If you have a quick question, you can also ask just after class.) If you’re unable to meet in person or at these times, we can also arrange to meet by Zoom. The Zoom link for office hours can be found on this restricted page.

Feel free to drop into office hours to discuss anything you like about our course. I’m happy to talk about your homeworks, continue discussion, and so on. If you do come to my office and I’m already speaking with someone, make sure that we know that you’re waiting for us to finish.

Target Audience and Course Goals

This course is aimed at grads and undergrads in Philosophy, Linguistics, and related disciplines like Math and Computer Science.

As stated in the catalog listing, it’s expected that you have taken Phil 155 or its equivalent. Understanding that material well will be essential for being able to keep up with this course.

Goals for the course include:

Philosophy Courses

All our philosophy courses aim at the acquisition and nurturing of basic philosophic skills. One of the main goals of our philosophy curriculum is to instill and enable the development of skills that are distinct to philosophy, but which are foundational to all forms of knowledge.

These basic philosophical skills involve being able to:

In addition, this course satisfies our logic and philosophy of science requirement for the philosophy major and minor and thereby aims at developing the following learning outcomes:

IDEAs in Action General Education Curriculum

This course satisfies the Quantitative Reasoning Focus Capacity (FC-QUANT).

These courses address questions like these:

As an FC-QUANT course, we will aim at the following learning outcomes:

Every Focus Capacity course includes the following activities:

These elements — referred to as “recurring capacities” — will help you repeatedly practice crucial skills for future study, life, and career success.


All readings for the course will be provided by web links. Some of these are in a restricted section of the course website. The username and password for these will be emailed to you, and also announced in class.

Course Requirements and Expectations

The University says that a 3 credit course should be expected to demand 9–12 hours of work per week on average, including the time for classroom meetings. This course should be in the middle of that range.

It is essential that you attend class meetings consistently. Material not in the readings will often be presented in class, and useful background and framing for many of the readings will also be provided.

The University’s Class Attendance Policy can be found here. In brief, they authorize absences only for some University activities, religious observances, disabilities, significant health conditions including pregnancy, and personal or family emergencies. If these include your situation, then consult these links:

  1. The University Approved Absence Office (UAAO) provides information and FAQs for students related to University Approved Absences.

  2. Students can be excused because of disability, pregnancy, or religious observance, as required by law and approved by Accessibility Resources and Service (ARS) and/or the Equal Opportunity and Compliance Office (EOC).

  3. Students can be excused for significant health conditions (generally, these will require you to miss classes for five or more days) and/or personal/family emergencies, as approved by the Office of the Dean of Students (ODOS), Gender Violence Service Coordinators, and/or the Equal Opportunity and Compliance Office (EOC).

If you need to miss class because of a more temporary illness, just email to let me know. If you need to miss class for other kinds of reasons (like a job interview or to attend a wedding), ask me about it well in advance. If you do miss a class, you will be responsible for catching up with missed content; and permission to miss a class doesn’t excuse you from deadlines for work due before or after the class.

If you need to stay home during any of our class meetings, try to attend the meeting by Zoom instead.

See the Policies section below about using laptops or other devices in class.

When you join our class meetings, you are expected to have read any material assigned for that day, and to be ready to ask questions about it.

It is essential that you ask questions when things in the readings or my presentations are unclear.

As required for IDEAs in Action courses, this course has presentation and collaboration components that are counted towards your participation grade. These will consist in our solving problems as a group in class. When we are doing this, and you don’t understand what’s happening, or why some strategy is or isn’t being used, it is also essential that you ask questions.

Talking through your confusions and lack of understanding is enormously helpful in overcoming them. Your overall participation and engagement with the class, which includes asking questions and contributing to our group problem-solving, will make up 15% of your grade for the course. There are also other ways to be engaged, such as pursuing matters further in office hours.

There will be reading assignments for most class meetings. Sometimes these will be selections from published texts; other times my own webnotes. I’ll often also post summaries of materials I presented in class. You should read these materials carefully when they’re posted, and expect that you’ll have to read many of them more than once.

These resources should be of some use in helping you keep up if you have to miss some class. But you can not rely on everything discussed in class also being summarized online. And you should not expect that the online materials fully make up for attending class meetings, nor for reading assigned texts.

There will be homeworks due most weeks during the semester. There will also be a final homework due on Thursday May 2 at 4 pm, which is the time scheduled for our final exam. Instead of the exam, we will meet at that time to review the final homewok and discuss outstanding philosophical issues that emerged during the semester.

Some of the homework exercises will ask you to define a specified function or predicate (as you might do in a computer programming course). Many will ask you to argue for some conclusion, in a mathematically rigorous way but not in a formal proof system. (Only occasionally will you be asked to prove things in a formal system like first-order logic or extensions of it; instead most of this course will involve reasoning about formal systems.) Some homework exercises will ask you to explain why some mathematical fact does/doesn’t obtain (as an educator or philosopher might, to a student who is stuck or confused). Taken together, the homeworks will constitute (substantially more than) the University requirement of the intellectual equivalent of ten pages of writing.

Homeworks cannot be turned in late, as I’ll be posting sample solutions after you submit them. Your grade for the course will mostly be based on the quality of your homeworks. The weakest two homeworks you submit will be ignored. Ordinarily I’ll expect you to at least attempt every homework; but if emergencies arise you can count a missed/skipped homework as one of the ones to be ignored. Having a lot of work for other courses etc doesn’t qualify as an “emergency” in this sense; and the final homework cannot be skipped.

All students are expected to follow the University Honor Code, which applies to all course assignments and petitions for absences or rescheduling. In brief, this means students are expected to refrain from “lying, cheating, or stealing” in the academic context. For more information or to clarify which actions violate the honor code, consult with your instructors,, and/or The Instrument of Student Judicial Governance.

What constitutes “lying, cheating, or stealing” depends on the academic activity.

Your grades for the different components of the course will be weighted as follows:

15% for overall participation/engagement, including questions and group problem-solving in class 10% for final homework (due before our scheduled final exam session on May 2) 75% for regular homeworks during term

Should it be necessary to convert between numeric and letter grades, I assume the following correspondences:

F 0 or 50 D 63.3 and higher D+ 66.7 and higher C- 70.0 and higher C 73.3 and higher C+ 76.7 and higher B- 80.0 and higher B 83.3 and higher B+ 86.7 and higher A- 90.0 and higher A 93.3 and higher

Grade Appeals: If you feel you have been given an incorrect grade for any part of the course, we can review together how I applied the announced standards. If this doesn’t resolve the issue, you have the right to discuss with our department’s Director of Undergraduate Studies (currently Professor Markus Kohl), or to appeal through a formal University process. You’ll be expected to make a case that the grade reflects an arithmetic/clerical error, arbitrariness, discrimination, harassment, or personal malice. To learn more, consult the Academic Advising Program website, or this summary of University policies.

Most requests that I and other professors hear for changing grades are based on how good/bad it would be for a student to get a given grade; but it would be unfair and inappropriate for justifications like that to succeed.


This schedule lists the rough order of our topics. See this other page for course announcements, context for the main readings, links to optional further reading, lecture notes, and any minor tweaks to the schedule. Check that page frequently.

Meeting 1 / Wed Jan 10
Overview of course
Notion of effective decidability
Mon Jan 15
MLK Day, No classes
Meeting 2 / Wed Jan 17
Sets, tuples, functions
Meeting 3 / Mon Jan 22
Meeting 4 / Wed Jan 24
Meeting 5 / Mon Jan 29
Order Relations
Meeting 6 / Wed Jan 31
More on orders and lattices
Meeting 7 / Mon Feb 5
Graphs and trees
Meeting 8 / Wed Feb 7
Algebras and morphisms
Mon Feb 12
Wellness Day, No classes
Meeting 9 / Wed Feb 14
Strings and patterns
Meeting 10 / Mon Feb 19
Formal languages and grammars
Meeting 11 / Wed Feb 21
More on formal languages and grammars
Meeting 12 / Mon Feb 26
Meeting 13 / Wed Feb 28
Syntax, formula complexity
Normal forms
Bound/free variables, substitution
Meeting 14 / Mon Mar 4
Semantics for sentential and predicate logic
Logical truth and consequence
Meeting 15 / Wed Mar 6
Extensions of orthodox logic
Spring Break
Meeting 16 / Mon Mar 18
Relations between semantics and proofs
Meeting 17 / Wed Mar 20
Normal modal logic
Uses/extensions of modal sentential logic
Meeting 18 / Mon Mar 25
More on modal logic
Meeting 19 / Wed Mar 27
Completeness of predicate logic, and its corollaries
Meeting 20 / Mon Apr 1
More on completeness and corollaries
Meeting 21 / Wed Apr 3
Models and theories
Meeting 22 / Mon Apr 8
Standard/nonstandard models
Meeting 23 / Wed Apr 10
More on arithmetics
Meeting 24 / Mon Apr 15
Gödel’s Incompleteness Theorems
Meeting 25 / Wed Apr 17
More on Gödel
Meeting 26 / Mon Apr 22
More on Gödel
Meeting 27 / Wed Apr 24
More on Gödel
Meeting 28 / Mon Apr 29
Catchup, review
Thu May 2
Final homeworks due before Final Exam Session at 4 pm

More Information

Missing/rescheduling deadlines

Devices in the classroom

Other Policies and Resources

The following is information that the University mandates we include on every syllabus. (So you will see a lot of overlap with your syllabi for other courses.)

Syllabus Updates

I reserve the right to make changes to the syllabus, including assignment due dates. These changes will be announced as early as possible so that students can adjust their schedules.


I welcome your input about the course at any time. You are welcome to approach me directly. I’ll also provide opportunities for anonymous evaluation and feedback during the term.