click image for Canvas textbook link
Last updated 04/24/2025 — accessed:
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Meets 2:00-3:15 Mon/Wed PHELP 1160
+ sections with TA scheduled Mon 4:00-4:50 PHELP 1445 and Wed 5:00-5:50 387 1015 |
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(Prof.) Colin Allen
<colinallen@ucsb.edu> |
Teaching Assistant:
Flavio Tisi
<flaviotisi@ucsb.edu> |
| Canvas site: https://ucsb.instructure.com/courses/26222 | |
Course Description
This class introduces students to formal techniques for evaluating arguments. We cover a natural deduction system of sentential logic, truth-tables, a natural deduction system of first-order predicate logic, and the basic ideas of model theory. The application of these systems for analyzing arguments is discussed. Exams are designed to test skill with the formal systems, particularly translation from English to formulas, proof techniques, and methods for showing invalidity. There are no prerequisites for the course.
Learning Objectives
By the end of the course, you should be competent with the formal methods introduced from Chapter 1 through to Chapter 6, section 2 of the textbook. If you have mastered these concepts you will be well-positioned to appreciate the significance of formal logic as a benchmark for argumentative rigor in fields as diverse as philosophy, law, mathematics, and science. You will also be in a position to understand the foundational role of logic for technological developments in computing hardware and software design.
Textbook and Website
The textbook for the course is Logic Primer, 3rd Edition by Colin Allen and Michael Hand. PDFs of each chapter are provided to you for your personal use via Canvas. Printed copies of the book are available from various online book vendors including the publisher MIT Press. The current printing of the 3rd edition contains some typographical errors. A webpage with the list of errata and PDFs of fixed pages is available at https://logic.tamu.edu/errata3.html . The PDF version in Canvas has all these fixed, but let your instructor know if you find others.
There is also a website where you may practice the techniques and test yourself with exercises from the book. It is freely available at https://logic.tamu.edu/. Using this website for your homework practice will greatly improve your chance of success in the course. A second website JustInfer written by UCSB graduate student Morgan Davies also supports the system of logic we will be using. Go to Settings and choose one of the Logic Primer options
Grading Basis
Grades will be assigned on the basis of two midterms (during regular class each), final exam, and in-class quizzes. The quizzes are for extra credit and unless otherwise stated at the top of the quiz sheet, your response to the quiz questions must be perfect to receive credit (i.e., there will be no partial credit on quizzes). Quiz answers can be turned in immediately for double credit or taken home and turned in at the beginning of the next class meeting for regular credit. Full regular credit will convert to a 4% boost for the course. Double credit can therefore be as high 8%, or nearly a full letter grade.
Your overall score will be computed using three methods and you will be assigned a grade based on the best of these methods.
Your best score out of 400 will be converted to a percentage and then a letter grade for the course according to the following scale: [100+:A+] [95-99:A] [90-94:A-] [87-89:B+] [84-86:B] [80-83:B-] [77-79:C+] [74-76:C] [70-73:C-] [65-79:D+] [60-64:D] [0-59:F]
Implications of this grading scheme: If you are satisfied with your grade after midterms you won't need to take the final. If you have done poorly on earlier exams, you can still pull everything out on the comprehensive final exam.
Bring your own paper for quizzes and exams. (Blue books not required.) Midterms and finals will be open book and notes--but not open neighbor! Midterm dates will be confirmed with 7 days notice. Numerical scores on midterms and finals will not be curved. Make up tests will be provided only in cases of authorized absence. See below for policy on in-class quizzes.
Course Format, Assessments, and Attendance
Attendance will not be formally monitored but quiz credit is available only for those attending class. Because all quizzes are for extra credit, no make-ups will be provided, although if you miss class you may obtain the quiz from a classmate and turn it in at the beginning of the next meeting (usually the discussion section).
Homework and Schedule of Readings and Exams
The schedule shown is tentative. It is a good idea to read a section or two ahead of wherever we are in the class at that moment. The pace is high and it will be important for you to stay on track with the homework (ungraded) and quizzes (graded). Homework consists of all the exercises in the book. The "Quizmaster" section of the website at logic.tamu.edu contains the book's exercises as well as additional practice exercises.
| Date | Topic | Readings / Assignments |
|---|---|---|
| Week 1 | ||
| Mon Mar 31 | Introduction to the Course/Arguments, Validity, Soundness, and a Language for Sentential Logic | 1.1-1.3 |
| Wed Apr 1 | Wffs and Translations | 1.4 |
| Week 2 | ||
| Mon Apr 7 | Translations & Primitive Rules of Proof | 1.4, 2.1 |
| Wed Apr 9 | Primitive Rules of Proof (and Strategies) | 2.1, Strategy Sheet |
| Week 3 | ||
| Mon Apr 14 | Proof Strategies, More Rules, and Theorems | Strategy Sheet, 2.2, 2.3 |
| Wed Apr 16 | Truth Tables for Sentences and Sequents | 3.1-3.3 |
| Week 4 | ||
| Mon Apr 21 | Direct and Indirect Truth Tables for Sequents | 3.3, 3.4 (optional 3.5) |
| Wed Apr 23 | Review Chapters 1-3 | 1.1-3.4 |
| Week 5 | ||
| Mon Apr 28 | First Midterm | |
| Wed Apr 30 | The Language of Predicate Logic | 4.1, 4.2 |
| Week 6 | ||
| Mon May 5 | Translations | 4.2 |
| Wed May 7 | Translations and Primitive Rules of Proofs | 4.2, 5.1 |
| Week 7 | ||
| Mon May 12 | More Rules of Proof | 5.2 |
| Wed May 14 | Finite Interpretations and Countermodels for One-Place Predicates | 6.1, 6.2 |
| Week 8 | ||
| Mon May 19 | Finite Countermodels for Multi-Place Predicates | 6.3 |
| Wed May 21 | Review | Chapters 3-6 |
| Week 9 | ||
| Mon May 26 | Memorial Day | no class |
| Wed May 28 | Second Midterm | |
| Week 10 | ||
| Mon Jun 2 | Review | All chapters |
| Wed Jun 4 | Review | All chapters |
| Finals Week | ||
| Mon Jun 09 | Comprehensive Final Exam 4-7 p.m. | Note time! 4-7 p.m. |
Still Relatively New to Philosophy Courses?
Except in Logic (PHIL 183), you may find my concise guides to reading philosophy and writing philosophy helpful. You may find them useful even if you are not so new to philosophy.
Missed Assignments
Statement about Academic Misconduct
Students in this course are obliged to comply with UCSB's Academic Integrity Policies. Any student suspected of violating this obligation for any reason during the quarter will be referred via the Academic Integrity procedures detailed at the above link. When you submit assignments with your name on them in this course, you are signifying that the work contained therein is all yours, unless otherwise cited or referenced. Any ideas or materials taken from another source for either written or oral use must be fully acknowledged. If you are unsure about the expectations for completing an assignment or taking a test or exam, be sure to seek clarification beforehand. Use of ChatGPT or similar generative AI products will be discussed in prior to any writing assigments, and may not be used unless you are explicitly given permission to do so, and never without explicit acknowledgment of its use.
Diversity and Inclusion
The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and UCSB's Disabled Students Program for information about accomodations and services.
The University of California, in accordance with applicable federal and state laws and University policy, prohibits discrimination against or harassment of any person at the University on the basis of race, color, national origin, religion, sex, gender identity, pregnancy, physical or mental disability, medical condition (cancer-related or genetic characteristics), ancestry, marital status, sexual orientation, citizenship, or age. For more information see https://eodp.ucsb.edu/resources/policies.
I ask that everyone in the class strive to help ensure that other members of this class can learn in a supportive and respectful environment. If there are instances of the aforementioned issues, you may contact the Title IX Office, by calling 805-893-2701 or visiting https://titleix.ucsb.edu/. You may also choose to report this to a faculty/staff member; they may also be required to communicate about such issues to the University’s Office of Diversity and Incusion. If you wish to maintain complete confidentiality, you may also contact University Counseling & Psychological Services .
Statement on Classroom Recording
To ensure the free and open discussion of ideas, students may not record classroom lectures, discussion and/or activities without the advance written permission of the instructor, and any such recording properly approved in advance can be used solely for the student’s own private use.
Materials provided for the course may be protected by copyright. United States copyright law, 17 USC section 101, et seq., in addition to University policy and procedures, prohibit unauthorized duplication or retransmission of course materials. See Library of Congress Copyright Office and the University Copyright Policy.