UMass Philosophy 110 — Introduction to Logic

Spring 2024 – Prof. Kevin Klement

Tuesdays and Thursdays 1:00–2:15pm in Integrative Learning Center S240

Course description and goals

An introduction to symbolic logic, including sentential and predicate logic. Its purpose is to familiarize you with certain formal methods for representing and evaluating arguments and reasoning. These methods can be used not only for philosophy, but for any subject matter. Like mathematics, the methods you will learn are highly abstract, formal and symbolic. If math can be tricky for you, be prepared to devote extra time to this course. This is an analytical reasoning (R2) course, and 3 credits.

Contact information

Prof. Klement’s office is South College E319. Email: Office hours are Tuesdays and Thursdays 11am–12pm. You can also schedule an appointment at, or click here to schedule an appointment.


The textbook for this course is Gary M. Hardegree’s Symbolic Logic: A First Course. You can download this text from his website here or from within Canvas.

Camvas page

Most course content can be found on our page on the UMass Canvas LMS ( There you can find interactive lecture notes, homework exercises, check your grades, and more.


The course content is divided into twelve parts, “sections” or “units”. Each one usually represents about one week’s worth of lecture material. The Canvas page is divided up similarly. For each, there is an interactive lecture notes page, and a Credit Exercise set.

Online exercises

Credit exercises (CEs)

Most of the work for the class consists in online exercises which are accessed through Canvas. In general, each of the 12 Credit Exercise sets consists of three kinds of problems:

  1. Warm up problems: These problems are designed to introduce you to the kinds of problem in the set and give you an idea of what a correct answer looks like. Some will offer to give you hints as you complete the problem. Some even allow you to blatantly cheat and see correct answers. Still, for learning purposes it is best to try to answer them yourself and only use the hints and cheat mechanisms to check your answers and correct them as needed. These usually make up about 20% of the problems for each exercise set.
  2. Standard/honing problems: These problems are designed to help hone your skills in advance of doing the testing problems. They do not show you the answers in advance, or provide you with many hints, but the website will immediately tell you if your answer is incorrect, and you can change it until it is correct. These usually make up about 40% of the problems for each exercise set.
  3. Testing problems: The problems here will be similar to the others except the website will not tell you if your answer is right or wrong. You will only find out once the deadline passes. Hence you are on your own in determining the right answer. These usually make up about 40% of the problems for each exercise set.

All types of problems allow you to change your answer as many times as you wish at any point prior to the deadline passing for the exercise set. Answers may no longer be saved once the deadline passes. Your grade will typically be posted to Canvas within 24 hours after the deadline.

In general, each Credit Exercise is due around a week and a half after the lectures for the corresponding material are completed. The last two are due at the end of finals week. See the schedule below.

It is strongly recommended to start each exercise well ahead of its due date. This way you will have time to get help if you need it. Do not spend hours trying over and over to get a question right!

You are expected to work on your own on the Credit Exercises. (You may collaborate with peers on Textbook exercises.)

It is recommended that you do the online exercises on a traditional laptop or desktop computer rather than a smaller portable device. Use an up-to-date browser: Firefox or Chromium is recommended. Do not use Safari, as the exercises can malfunction on Safari.

Textbook exercises (TBEs)

If you need additional practice before finishing the Credit Exercises, you may complete online versions of the exercises at the end of each chapter of the textbook (or complete them on paper). These do not contribute to your grade, and are completely optional. These all work like the warm up exercises in that you can see the answers and get hints when available. These have no due date. Answers can also be found at the end of the corresponding chapter in the textbook.

Requirements and grading

Grade scale
93–100% = A
90–92.99%= A−
87–89.99%= B+
83–86.99%= B
80–82.99%= B−
77–79.99%= C+
73–76.99%= C
70–72.99%= C−
67–69.99%= D+
60–66.99%= D
0–59.99% = F

Your final grade in the course will be determined by your scores on the 12 Credit Exercises (see above) done through Canvas. In particular, your final grade will be determined by your 10 best scores on these 12 exercises; your two lowest scores are dropped, whatever they are (even if they are zero). The grade for each exercise will be listed on Canvas as a percentage/score out of 100. Your final grade will be based on the average (arithmetical mean) of your ten best of these scores, and you will be given a final grade according to the scale on the right. Each exercise set is weighed equally.

Academic honesty

Academic honesty is defined in the University Academic Regulations document (page 5), available at Plagiarism and cheating are serious offenses that strike at the very heart of academic life, and will result in serious penalties, including minimally (but not limited to) receiving an F in the course.


The course has no specific attendance requirements, but students who attend class regularly have historically done significantly better on average than those who did not.

Common courtesy demands that you come to class on time, and refrain from leaving early without special permission. Phones must be silenced for the duration of class.

I would like to hear from anyone who has a disability and may require special accommodations regarding note-taking, exercises or similar. Please obtain the appropriate paperwork from Disability Services and inform me far enough ahead of time to make the appropriate arrangements.


Subject to change.

Day Material CE TBEs CE Due
Th Feb 1 Course introduction
1. Logic, Arguments and the Basics of Sentential Logic
Tu Feb 6 Chap. 1, §§1–6CE11A
Th Feb 8Chap. 1, §§7–9CE11B, 1C
Tu Feb 13Chap. 2, §§1–11CE12A, 2B
2. Truth Tables
Th Feb 15Chap. 2, §§12–13CE22C/3A
Tu Feb 20Chap. 3, §§1–5CE23B, 3C
Th Feb 22Monday class schedule. No class.
3. Sentential Logic Translations
Tu Feb 27Chap. 4, §§1–15CE34A, 4BCE1 due
Th Feb 29Chap. 4, §§16–25CE34C, 4D
4. Translating Whole Arguments
Tu Mar 5 Combining the aboveCE4CE2 due
Th Mar 7 Review and catch upCE4
5. Direct Derivations
Tu Mar 12Chap. 5, §§1–8CE55BCE3 due
Th Mar 14Chap. 5, §§9–10CE55C
Mar 18–22Spring break. No class.
6. Conditional and Indirect Derivations
Tu Mar 26Chap. 5, §11CE65DCE4 due
Th Mar 28Chap. 5, §§12–14CE65E, 5F
7. Strategies for Derivations
Tu Apr 2 Chap. 5, §§15–16CE75GCE5 due
Th Apr 4Chap. 5, §§17–20CE75H
8. Monadic Predicate Logic Translations
Tu Apr 9Chap. 6, §§1–12CE86A–6DCE6 due
Th Apr 11Chap. 6, §§13–19CE86E–6H
9. Polyadic Predicate Logic Translations
Tu Apr 16Chap. 7, §§1–5CE97A–7CCE7 due
Th Apr 18Chap. 7, §§6–12CE97D, 7E
10. Predicate Logic Derivations
Tu Apr 23Chap. 8, §§1–7CE108A, 8BCE8 due
Th Apr 25Chap. 8, §§8–10CE108C, 8D
11. Derivations with Multiple Quantifiers
Tu Apr 30Chap. 8, §11CE118E, 8FCE9 due
Th May 2 Chap. 8, §12CE118G, 8H
12. Derivation Strategies and Review
Tu May 7Chap. 8, §§13–14CE12CE10 due
Th May 9Catch up dayCE12
Fr May 17End of finals week CE11 & CE12 due