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. Contact me for a link to the Dropbox folder in which you can find both the text and the solutions manual.
Other readings, important for your paper, are available here.
Class notes and slides, when they supplement the text, are here.
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, and the final five problem sets, those which are due after the fifth exam. Between Test #1 and Tet #5, 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 (except Test #5), 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 need not be written out fully, but solutions must be.
Sample solutions to all homework problems are in the solutions manual, available in our shared Dropbox folder. Complete your homework and check your solutions against the sample solutions before the beginning of class. Acceptable solutions to most problems vary. Come to class prepared to ask questions which remain unanswered after looking at the solutions manual. We will begin most classes with time to review a few homework exercises. Mark any changes you make to your original solutions in a different-colored writing utensil. Feel free to write questions or comments on the homework you submit.
Homework will be checked by me or our course assistant, Spencer Livingstone. In checking the homework, we are looking for questions you have raised or recurring problems. We will not be grading your homework, but monitoring your progress and looking for ways to help you.
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 very difficult in the end.
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 Chapters 4 and 5 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 Friday, December 5, 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.
Accessibility: We learn in different ways and the organization of any course will accommodate each student differently. Some people process information best by speaking and listening, others by reading. Some folks learn best in groups; others focus best in solitude. Your success in this class is important to me, so please talk to me as soon as you can about your individual learning needs and how this course can best accommodate them. If there are circumstances that adversely affect your performance in this class, please let me know as soon as possible so that we can work together to develop strategies for adapting assignments to meet your needs and the course requirements. Hamilton College and I will make reasonable accommodations for students with properly documented disabilities. If you are eligible to receive an accommodation and would like to make a request for this course, please discuss it with me during the first two weeks of class and provide Allen Harrison, Associate Dean of Students (Elihu Root House; 315-859-4021) with appropriate documentation.
The Hamilton College Honor Code will be strictly enforced.
Office Hours
My office hours for the Fall 2015, term are 11am - noon, Monday through Friday. My office is 202 College Hill Road, Room 210.
Schedule:
Class | Date | Topic Name | Homework to do prepare for class |
1 | Friday August 28 |
Arguments Validity and Soundness |
Read §5.1: Deduction and Induction |
2 | Monday August 31 |
Translation using
Propositional Logic
Wffs |
Problem Set #1 |
3 | Wednesday September 2 |
Truth Functions | Problem Set #2 |
4 | Friday September 4 |
Philosophy Friday #1: Conditionals | Read §4.3: Conditionals |
5 | Monday September 7 |
Truth Tables for Propositions | Problem Set #3 Read §4.1: Laws of Logic and Their Bearers |
6 | Wednesday
September 9 |
Truth Tables for Arguments | Problem Set #4 Read §4.2: Notes on Translation with PL |
7 | Friday
September 11 |
Philosophy Friday #2: Religion and Argumentation | Read §5.5: Logic and the Philosophy of Religion |
8 | Monday September 14 |
Invalidity and
Inconsistency:
Indirect Truth Tables |
Problem Set #5 |
9 | Wednesday September 16 |
Rules of Inference I | Problem Set #6 |
10 | Friday September 18 | Test #1: Chapter 1 | Prepare for Test #1 |
11 | Monday
September 21 |
Rules of Inference II | Problem Set #7 |
12 | Wednesday
September 23 |
Rules of Equivalence I | Problem Set #8 |
13 | Friday
September 25 |
Philosophy Friday #3: Modal Logic | Read §4.8: Modal Logics |
14 | Monday September 28 |
Rules of Equivalence II | Problem Set #9 |
15 | Wednesday
September 30 |
The Biconditional Practice with Proofs |
Problem Set #10 |
16 | Friday
October 2 |
Test #2: Derivations | Prepare for Test #2 |
17 | Monday
October 5 |
Conditional Proof Logical Truths |
Problem Set #11 Read §4.6: Logical Truth, Analyticity, and Modality |
18 | Wednesday October 7 |
Indirect Proof | Problem Set #12 |
19 | Friday
October 9 |
Philosophy Friday #4: Logic and Science | Read §5.4: Scientific Explanation and Confirmation |
20 | Monday
October 12 |
More on Proofs | Problem Set #13 Read §4.11: Axiom Systems |
21 | Wednesday
October 14 |
Test #3: Conditional and Indirect Methods | Prepare for Test #3 |
October 16 | Fall Break | ||
22 | Monday October 19 |
Predicate Logic, Translation I | |
23 | Wednesday
October 21 |
Predicate Logic, Translation II | Problem Set #14 |
24 | Friday
October 23 |
Philosophy Friday #5: Infinity | Read §5.6: Infinity |
25 | Monday October 26 |
Derivations in Predicate Logic | Problem Set #15 |
26 | Wednesday
October 28 |
Quantifier Exchange | Problem Set #16 |
27 | Friday
October 30 |
Philosophy Friday #6: Truth | Problem Set #17 Read §5.9: Truth and Liars |
28 | Monday November 2 |
Conditional and Indirect Proof, Predicate Versions | Problem Set #18 |
29 | Wednesday November 4 |
Semantics for Predicate Logic | Problem Set #19 Read §4.9: Notes on Translation with M |
30 | Friday November 6 |
Test #4: Translation and Inference in M | Prepare for Test #4 |
31 | Monday November 9 |
Invalidity in Predicate Logic | Problem Set #20 |
32 | Wednesday
November 11 |
Translation Using Relational Predicates | Problem Set #21 |
33 | Friday
November 13 |
Philosophy Friday #7: Quantification and Ontological Commitment | Read §5.8: Quantification and Ontological Commitment |
34 | Monday November 16 |
Semantics for F Derivations Using Relational Predicates Paper proposal is due. |
Problem Set #22 |
35 | Wednesday
November 18 |
More Derivations with F | Problem Set #23 |
36 | Friday
November 20 |
Test #5: Validity and Invalidity in F | Prepare for Test #5 |
Thanksgiving | Break | ||
37 | Monday November 30 |
Translation Using Identity I | |
38 | Wednesday
December 2 |
Translation Using Identity II | Problem Set #24 Read §5.10: Names and Definite Descriptions |
39 | Friday
December 4 |
Derivations Using Identity Papers are due. |
Problem Set #25 Finish Paper |
40 | Monday December 7 |
Functions | Problem Set #26 |
41 | Wednesday
December 9 |
Second-Order Logic | Problem Set #27 Read §5.12: Second-Order Logic and Set Theory |
42 | Friday December 11 |
Catch-Up | Problem Set #28 |
Monday
December 14 7pm - 10pm |
Test #6 (Final): Relations, Identity Theory, Functions, and Second-Order Logic | Plus, Compensatory Material |
Problem Sets:
Set Number |
Due |
Exercises |
1 |
M |
§1.1: 1, 3, 22, 27, 33, 35, 39 |
2 |
W |
§1.3a: 11–20 |
3 |
M |
§1.3b: 61–65 |
4 |
W |
§1.6a: 8, 13, 22, 35, 41, 48 |
5 |
M |
§1.8: 3, 4, 6, 22, 28 |
6 |
W |
§1.9a: 3–5, 12–15, 20–23 |
7 |
M |
§2.1a: 4–6, 21–23, 32–34, 47 |
8 |
W |
§2.2a: 1–20 |
9 |
M |
§2.3a: 1–4, 7, 10–12, 16, 19, 24, 25 |
10 |
W |
§2.4a: 1–30 |
11 |
M |
§2.5a: 1–5, 30–33 |
12 |
W |
§2.7a: 1–4, 14, 15, 17, 19 |
13 |
M |
§2.9a: 1–3, 5, 7, 16, 17 |
14 |
W |
§3.1a: 5, 6, 9, 10 |
15 |
F |
§3.1c: 17–20, 26–30, 48, 51, 52, 67–70 |
16 |
W |
§3.3a 3, 4, 6, 8, 13, 18, 19, 23, 24, 31 |
17 |
F |
§3.3a 9, 16, 17, 22, 25 |
18 |
M |
§3.4: 1, 2, 4, 8, 10, 13, 17, 22, 24 |
19 |
W |
§3.3a 38, 39, 42 |
20 |
M |
§3.6a: 1, 2, 3 |
21 |
W |
§3.7: 2–4, 8, 12, 15, 19, 20, 21, 33 |
22 |
M |
§3.8b: 1–15, 21–23, 32–37 |
23 |
W |
§3.10a: 3, 5, 8, 9, 11, 13, 20, 24 |
24 |
W |
§3.11: 8–13, 22–26, 34–38 |
25 |
F |
§3.11: 4, 7, 14, 15, 27–31, 39–41, 43–45, 47 |
26 |
M |
§3.12a: 3, 4, 8, 10, 11, 15, 19 |
27 |
W |
§3.13a: 9–16 |
28 |
F |
§3.14: 1–10, 12–14, 16, 18 |