Syllabus
Course Description and Overview:
Philosophy has one technical tool: logic. Formal logic is the study of arguments and inferences, made in artificial languages designed to maximize precision. This course 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 a technical method of 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.
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 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 to be handed in.
Homework:Homework assignments and their due dates for approximately the first half of the term are listed on the schedule below. Assignments for Chapter 3 will be distributed later in the term. 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. We will begin most classes with time to review a few homework questions. You are expected to have completed the homework and looked at the sample solutions before the beginning of class. 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 final exam will 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 2, 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 2011, term are 10:30am - noon, Monday through Friday. My office is upstairs in 202 College Hill Road.
Schedule:
| Class | Date | Topic Name | Homework to do before the next class meets |
| 1 | Friday August 26 |
Arguments Validity and Soundness |
§1.1: 1, 3, 8, 20, 22, 27, 33, 35, 39
§1.2: 2-5, 13-18 |
| 2 | Monday August 29 |
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 August 31 |
Truth Functions | Read §4.3: Conditionals |
| 4 | Friday September 2 |
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 5 |
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 7 |
Truth Tables for Arguments | Read §4.5: Adequacy |
| 7 | Friday
September 9 |
Philosophy Friday #2: Adequate Sets of Connectives | §1.7: 1, 3, 4, 6, 8, 12, 13, 16, 19 |
| 8 | Monday September12 |
Invalidity and
Inconsistency:
Indirect Truth Tables |
§1.8a: 3-5, 12-15, 20-23 §1.8b: 1, 3, 5, 17-19 |
| 9 | Wednesday September 14 |
Rules of Implication I | Prepare for Test #1 |
| 10 | Friday
September 16 |
Test #1: Chapter 1 | §2.1a: 1-3, 6-8, 16-18, 24
§2.1b: 4, 5, 8, 10 |
| 11 | Monday
September 19 |
Rules of Implication II | §2.2a: 1-12 §2.2b: 1-3, 10-15, 22, 24 §2.2c: 5, 7, 8 |
| 12 | Wednesday
September 21 |
Rules of Equivalence I | Read §4.4: Syntax, Semantics, and the Chinese Room |
| 13 | Friday
September 23 |
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 26 |
Rules of Equivalence II | §2.4a: 2, 4-8, 12-14, 20, 25, 26
§2.4b: 2, 3, 8 |
| 15 | Wednesday
September 28 |
Practice with Proofs | Prepare for Test #2 |
| 16 | Friday
September 30 |
Test #2: Derivations | Read §4.1: The Laws of Logic and Their Bearers |
| 17 | Monday
October 3 |
Conditional Proof | §2.5a: 1-4, 14, 15, 17, 19
§2.5b: 4-7 §2.6a: 1, 4, 8, 10 §2.6b: 2, 6, 7 |
| 18 | Wednesday October 5 |
Indirect Proof | Read §4.6: Three-Valued Logics |
| 19 | Friday
October 7 |
Philosophy Friday #4: Three-Valued Logics | §2.7a: 1-3, 5-7, 16-18
§2.7b: 4, 6-10 |
| 20 | Monday
October 10 |
More on Proofs | Prepare for Test #3 |
| 21 | Wednesday
October 12 |
Test #3: Conditional and Indirect Methods | |
| October 14 | Fall Break | ||
| 22 | Monday October 17 |
Predicate Logic, Translation I | §3.1a: 5-10 §3.1b: 2-4, 12, 13, 16-10 §3.1c: 1-5, 8-10 |
| 23 | Wednesday
October 19 |
Predicate Logic, Translation II | §3.1c: 17-20, 26-30, 39-43, 46, 48, 51, 52 §3.2: 2, 9, 12 |
| 24 | Friday
October 21 |
Derivations in Predicate Logic | Prepare for Test #4 |
| 25 | Monday October 24 |
Test #4: Predicate Logic Translation | §3.3: 3, 4, 6, 8, 13, 18, 19, 23, 24, 31 |
| 26 | Wednesday
October 26 |
More Derivations and Changing Quantifiers | Read §4.7: Truth and Liars §3.3: 9, 16, 17, 22, 25 |
| 27 | Friday
October 28 |
Philosophy Friday #5: Truth and Liars | §3.4: 1, 2, 4, 8, 10, 13, 17, 22, 24 |
| 28 | Monday October 31 |
Conditional and Indirect Proof, Predicate Versions | §3.5: 1, 3, 5, 8, 11, 14, 19, 20, 22 |
| 29 | Wednesday
November 2 |
Semantics for Predicate Logic | Read §4.8: Quantification and Ontological Commitment |
| 30 | Friday
November 4 |
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 7 |
Invalidity in Predicate Logic | §3.7: 2-4, 8, 12, 15, 19, 20, 21, 33 |
| 32 | Wednesday
November 9 |
Translation Using Relational Predicates | Prepare for Test #5 |
| 33 | Friday
November 11 |
Test #5: Predicate Logic Derivations and Invalidity | §3.8:b: 1-15, 21-23, 32-37 §3.8c: 1-12 |
| 34 | Monday November 14 |
Rules of Passage | §3.9a: 1-6 §3.9b: 4-9 §3.9c: 5-9, 15-18, 21, 27-31 |
| 35 | Wednesday
November 16 |
Derivations Using Relational Predicates | Read §4.9: Color Incomaptibility |
| 36 | Friday
November 18 |
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 November 28 |
Translation Using Identity I | §3.11: 8-13, 22-26, 34-38 |
| 38 | Wednesday
November 30 |
Translation Using Identity II | §3.11: 4, 7, 14, 15, 27-31, 39-41, 43-45, 47 Finish Paper |
| 39 | Friday
December 2 |
Derivations Using Identity Papers are due. |
§3.12a: 2-4, 7, 10, 11, 15, 19 §3.12b: 2, 6, 8, 10 |
| 40 | Monday December 5 |
Functions | §3.13a: 1-8 §3.13b: 2, 4, 5, 7, 8, 9 |
| 41 | Wednesday
December 7 |
Second-Order Logic | Read §4.10: Second-Order Logic and Set Theory §3.14: 1-20 |
| 42 | Friday December 9 |
Catch-Up | Prepare for Test #6 |
| Thursday
December 15 7pm - 10pm |
Test #6 (Final): Relations, Identity Theory, Functions, and Second-Order Logic | Plus, Compensatory Material |