UMass Philosophy 110 — Introduction to Logic

Spring 2023 – 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 Moodle.

Moodle page

Most course content can be found on our page on the UMass Moodle in the Cloud 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 Moodle 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 Moodle. 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 Moodle 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 Brave is recommended.

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 Moodle. 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 Moodle 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.

Schedule (Revised Feb 23 2023)

Subject to change.

Day Material CE TBEs CE Due
Tu Feb 7 Course introduction
1. Logic, Arguments and the Basics of Sentential Logic
Th Feb 9 Chap. 1, §§1–6 CE1 1A
Tu Feb 14Chap. 1, §§7–9 CE1 1B, 1C
Th Feb 16Chap. 2, §§1–11 CE1 2A, 2B
2. Truth Tables
Tu Feb 21Chap. 2, §§12–13 CE2 2C/3A
Th Feb 23Snow day. Class cancelled.
Tu Feb 28Chap. 3, §§1–5 CE2 3B, 3CCE1 due
3. Sentential Logic Translations
Th Mar 2Chap. 4, §§1–15 CE3 4A, 4B
Tu Mar 7 Chap. 4, §§16–25 CE3 4C, 4D
4. Translating Whole Arguments
Th Mar 9 Combining the above CE4 CE2 due
Mar 12–19Spring break. No class.
5. Direct Derivations
Tu Mar 21Chap. 5, §§1–8 CE5 5B CE3 due
Th Mar 23Chap. 5, §§9–10 CE5 5C
6. Conditional and Indirect Derivations
Tu Mar 28Chap. 5, §11 CE6 5D CE4 due
Th Mar 30Chap. 5, §§12–14 CE6 5E, 5F
7. Strategies for Derivations
Tu Apr 4 Chap. 5, §§15–16 CE7 5G CE5 due
Th Apr 6 Chap. 5, §§17–20 CE7 5H
8. Monadic Predicate Logic Translations
Tu Apr 11Chap. 6, §§1–12 CE8 6A–6D CE6 due
Th Apr 13Chap. 6, §§13–19 CE8 6E–6H
Tu Apr 18Patriot’s day break. No class.
9. Polyadic Predicate Logic Translations
Th Apr 20Chap. 7, §§1–5 CE9 7A–7C CE7 due
Tu Apr 25Chap. 7, §§6–12 CE9 7D, 7E
10. Predicate Logic Derivations
Th Apr 27Chap. 8, §§1–7 CE108A, 8BCE8 due
Tu May 2 Chap. 8, §§8–10 CE108C, 8D
11. Derivations with Multiple Quantifiers
Th May 4 Chap. 8, §11 CE118E, 8F
Tu May 9 Chap. 8, §12 CE118G, 8HCE9 due
12. Derivation Strategies and Review
Th May 11Chap. 8, §§13–14 CE12
Tu May 16Catch up day CE12 CE10 due
Th May 25End of finals week CE11 & CE12 due