Syllabus
Course Description and Overview:
Philosophy has one technical tool: logic. Logic is the study of inferences. Formal logic, the subject of this course, is the study of inferences in artificial languages designed to maximize precision. Philosophy 240 is a standard introduction to elementary formal logic, covering propositional logic and predicate logic, including identity theory, functions, and second-order quantification. The central goal of this course is to provide you with technical methods for deciding what follows from what.
The two main techniques we will study are translation and derivation. We will establish a formal definition of valid inference using logical operators and truth functions. We will translate sentences of English into the formal languages of propositional and predicate logic and back. We will use a proof system to infer new claims from given ones, following prescribed rules of inference and proof strategies.
Thirty of the forty-two class meetings will be devoted to learning logical techniques. There will be seven Philosophy Fridays during which we will examine some philosophical questions about logic. Some of these questions concern the status of logic and its relation to the rest of our knowledge. Some of these questions concern how best to construct logical systems. The remaining five classes, and the final exam period, will be used for tests. You will be asked to write one essay on philosophical issues concerning logic.
Texts
The draft of my logic book, What Follows, is the main text of the course.
Other readings, important for your paper, are available here.
Class notes and slides, when they supplement the text, are here.
Other recommended sources are listed in the Course Bibliography.
Course Requirements
Your responsibilities in this course include the following, with their contributions to your grade calculation in parentheses:
Attendance
Homework (8%)
Six Tests (72%, 12% each)
One four-to-six page paper (20%)
Attendance: Classes are for your edification. It will be useful for you to attend class. There is no direct penalty for missing class. Some students pick up on the technical material quickly. If you do miss a class, you should arrange to drop off your homework, if you have homework due.
Homework: Homework assignments and their due dates are listed on the schedule below. Most homework assignments are problem sets from Chapters 1-3. Other homework assignments are readings from Chapter 4, mainly in preparation for Philosophy Fridays.
All students will be expected to hand in the first six problem sets, those which are due before the first exam. If you receive less than an 85% on any exam, you must hand in all problem sets which are due before the next exam. If you receive an 85% or higher on the most recent exam, you may hand in your homework, if you wish, but it will not be required. When handing in homework, make it neat and presentable. There should be no ripped or crumpled pages. Problems should be clearly delimited. Questions may not need to be written out fully, but solutions must be.
Sample solutions to all homework problems are in the solutions manual, available on line. Acceptable solutions to most problems vary. You are expected to have completed the homework and looked at the sample solutions before the beginning of class. We will begin most classes with time to review a few homework questions. Mark any changes you make to your original solutions in a different-colored writing utensil so I can see where you may need help. Come to class prepared to ask questions which remain unanswered.
The homework assignments on the schedule are minimal. If you are still struggling with the material, you should do more problems.
Tests: All six tests are mandatory. Dates for the tests are given on the schedule below. No make-ups will be allowed for missed tests. If you are unable to take a test, you must request an arrangement from me in advance. The final exam will be of the same type as each of the first five tests. Be prepared: the work gets progressively harder and the final exam will be longer than the rest and cover the most difficult material in the course.
You will have an opportunity, at the time of the final, to take a compensatory version of up to two of the first five tests. I will average the grade on the compensatory exam with your original grade. If you miss a test during the term, the compensatory exam will be averaged with a 0. Practice problems for each test will be available on the course website.
Paper: Each student will write a short paper on a topic in logic, philosophy of logic, or the application of logic to philosophy. Seven class meetings, Philosophy Fridays, will be devoted to such topics. Readings for Philosophy Fridays come from Chapter 4 of What Follows. I expect you to do further research for your papers; suggestions are included in the text. Papers may be mainly expository, especially those covering technical topics. The best papers will philosophical, and will defend a thesis. I will suggest topics and readings through the term. Papers are due on December 6, though they may be submitted at any time during the course. More details about the papers will be distributed in class.
On Grades: Grades on assignments will be posted on Blackboard, along with a running total, which I call your grade calculation. Your grade calculation is a guide for me to use in assigning you a final grade. There are no rules binding how I translate your grade calculation, which will appear in Blackboard as a percentage, into a letter grade. In particular, the Hamilton College key for translating your letter grades into percentages, used for graduate school admissions, is not a tool for calculating your final grade. I welcome further discussion of the purposes and methods of grading, as well as my own grading policies.
The Hamilton College Honor Code will be strictly enforced.
Office Hours
My office hours for the Fall 2013, term are 11am - noon, Monday through Friday. My office is 202 College Hill Road, Room 210.
Schedule:
| Class | Date | Topic Name | Homework to do before the next class meets |
| 1 | Friday August 30 |
Arguments Validity and Soundness |
§1.1: 1, 3, 8, 20, 22, 27, 33, 35, 39
§1.2: 2-5, 13-18 |
| 2 | Monday September 2 |
Translation using
Propositional Logic
Wffs |
§1.3a: 11-20
§1.3b: 6-10 §1.4a: 1-5, 10-13 §1.4b: 1-5, 13, 14, 16 |
| 3 | Wednesday September 4 |
Truth Functions | Read §4.3: Conditionals |
| 4 | Friday September 6 |
Philosophy Friday #1: Conditionals | §1.4b: 12, 17-20
§1.5a: 1-4, 9-13, 17, 18 §1.5b: 1-5, 11, 12, 16 §1.5c: 4, 5, 7, 10 |
| 5 | Monday September 9 |
Truth Tables for Propositions | Read §4.2: Disjunction, Unless, and the Sixteen
Truth Tables
§1.6a: 3, 8, 10, 19, 26 §1.6b: 6, 12, 15, 26 §1.6c: 3, 4, 6, 7, 26, 33 |
| 6 | Wednesday
September 11 |
Truth Tables for Arguments | Read §4.5: Adequacy |
| 7 | Friday
September 13 |
Philosophy Friday #2: Adequate Sets of Connectives | §1.7: 1, 3, 4, 6, 8, 12, 13, 16, 19 |
| 8 | Monday September 16 |
Invalidity and
Inconsistency:
Indirect Truth Tables |
§1.8a: 3-5, 12-15, 20-23 §1.8b: 1, 3, 5, 17-19 |
| 9 | Wednesday September 18 |
Rules of Inference I | Prepare for Test #1 |
| 10 | Friday
September 20 |
Test #1: Chapter 1 | §2.1a: 1-3, 6-8, 16-18, 24
§2.1b: 4, 5, 8, 10 |
| 11 | Monday
September 23 |
Rules of Inference II | §2.2a: 1-12 §2.2b: 1-3, 10-15, 22, 24 §2.2c: 5, 7, 8 |
| 12 | Wednesday
September 25 |
Rules of Equivalence I | Read §4.4: Syntax, Semantics, and the Chinese Room |
| 13 | Friday
September 27 |
Philosophy Friday #3: Syntax and Semantics | §2.3a: 1-4, 7, 10-12, 16, 19, 24, 25
§2.3b: 4, 7, 8, 10 |
| 14 | Monday September 30 |
Rules of Equivalence II | §2.4a: 2, 4-8, 12-14, 20, 25, 26
§2.4b: 2, 3, 8 |
| 15 | Wednesday
October 2 |
The Biconditional Practice with Proofs |
§2.5a: 1-5 |
| 16 | Friday
October 4 |
Test #2: Derivations | Read §4.1: The Laws of Logic and Their Bearers |
| 17 | Monday
October 7 |
Conditional Proof | §2.6a: 1-4, 14, 15, 17, 19
§2.6b: 4-7 §2.7a: 1, 4, 8, 10 §2.7b: 2, 6, 7 |
| 18 | Wednesday October 9 |
Indirect Proof | Read §4.6: Three-Valued Logics |
| 19 | Friday
October 11 |
Philosophy Friday #4: Three-Valued Logics | §2.8a: 1-3, 5, 7, 16, 17 §2.8b: 4, 6-10 §2.8c: 1, 4-6 |
| 20 | Monday
October 14 |
More on Proofs | Prepare for Test #3 |
| 21 | Wednesday
October 16 |
Test #3: Conditional and Indirect Methods | |
| October 18 | Fall Break | ||
| 22 | Monday October 21 |
Predicate Logic, Translation I | §3.1a: 5-10 §3.1b: 2-4, 12, 13, 16-20 §3.1c: 1-5, 8-10 |
| 23 | Wednesday
October 23 |
Predicate Logic, Translation II | §3.1c: 17-20, 26-30, 39-43, 46, 48, 51, 52 §3.2: 2, 9, 12 |
| 24 | Friday
October 25 |
Derivations in Predicate Logic | Prepare for Test #4 |
| 25 | Monday October 28 |
Test #4: Predicate Logic Translation | §3.3: 3, 4, 6, 8, 13, 18, 19, 23, 24, 31 |
| 26 | Wednesday
October 30 |
More Derivations and Changing Quantifiers | Read §4.7: Truth and Liars §3.3: 9, 16, 17, 22, 25 |
| 27 | Friday
November 1 |
Philosophy Friday #5: Truth and Liars | §3.4: 1, 2, 4, 8, 10, 13, 17, 22, 24 |
| 28 | Monday November 4 |
Conditional and Indirect Proof, Predicate Versions | §3.5: 1, 3, 5, 8, 11, 14, 19, 20, 22 |
| 29 | Wednesday
November 6 |
Semantics for Predicate Logic | Read §4.8: Quantification and Ontological Commitment |
| 30 | Friday
November 8 |
Philosophy Friday #6: Quantification and Ontological Commitment | §3.3: 38, 39, 42 §3.4: 9, 16, 18 §3.5: 10, 15 §3.6: 1, 2 |
| 31 | Monday November 11 |
Invalidity in Predicate Logic | §3.7: 2-4, 8, 12, 15, 19, 20, 21, 33 |
| 32 | Wednesday
November 13 |
Translation Using Relational Predicates | Prepare for Test #5 |
| 33 | Friday
November 15 |
Test #5: Predicate Logic Derivations and Invalidity | §3.8b: 1-15, 21-23, 32-37 §3.8d: 1-12 |
| 34 | Monday November 18 |
Rules of Passage | §3.8c: 5-9, 15-18, 21, 27-31 §3.9a: 1-6 §3.9b: 4-9 |
| 35 | Wednesday
November 20 |
Derivations Using Relational Predicates | Read §4.9: Color Incomaptibility |
| 36 | Friday
November 22 |
Philosophy Friday #7: Color Incompatibility | §3.10a: 3, 5, 8, 9, 11, 13, 20, 24 §3.10b: 3, 7, 10 §3.10c: 3, 5, 6 |
| Thanksgiving | Break | ||
| 37 | Monday December 2 |
Translation Using Identity I | §3.11: 8-13, 22-26, 34-38 |
| 38 | Wednesday
December 4 |
Translation Using Identity II | §3.11: 4, 7, 14, 15, 27-31, 39-41, 43-45, 47 Finish Paper |
| 39 | Friday
December 6 |
Derivations Using Identity Papers are due. |
§3.12a: 2-4, 7, 10, 11, 15, 19 §3.12b: 2, 6, 8, 10 |
| 40 | Monday December 9 |
Functions | §3.13a: 1-8 §3.13b: 2, 4, 5, 7, 8, 9 |
| 41 | Wednesday
December 11 |
Second-Order Logic | Read §4.10: Second-Order Logic and Set Theory §3.14: 1-10, 12-14, 16, 18 |
| 42 | Friday December 13 |
Catch-Up | Prepare for Test #6 |
| Wednesday
December 18 2pm - 5pm |
Test #6 (Final): Relations, Identity Theory, Functions, and Second-Order Logic | Plus, Compensatory Material |