Critical Reasoning and Logic

Formal Logic PHI-108-1, Fall 2016

Contact Information Instructor: Dr. David Vander Laan Office: Porter Center 4 E-mail: [email protected] Phone: x7041 Office Hours: MW, 2:00-3:30, and by appointment

Text Howard-Snyder, Howard-Snyder, and Wasserman, The Power of Logic, 4th ed. Papineau, Philosophical Devices Konyndyk, Introduction to Modal Logic course reader

Website Online Learning Center at www.mhhe.com/howardsnyder4e

Course Goals The primary goal of the course is to enable the student to develop facility with a variety of the technical methods commonly used by contemporary philosophers. Our focus will be formal proof methods in what is known as first-order logic. We will also learn the basics of modal logic and explore some of the issues that motivate non-classical (or “deviant”) logics.

A second goal of the course is to appreciate both the power and the limitations of formal systems in our reasoning. Some of the results of metatheory (i.e., mathematical results about the formal systems that we will study) will give a deeper understanding of what they can do, what they cannot do, and what similar systems might do in the future.

We will also aim to understand the philosophical implications of various systems, especially in metaphysics and epistemology.

Course Learning Outcomes By semester’s end, students will be able to:  construct advanced formal proofs, and  explain the utility and the limitations of formal systems in philosophical reasoning. What This Course Will Require of You

As in any mathematics course, the material is cumulative. Thus it is important that you understand new material as it is introduced. Much of our class time will be devoted to practice with argument analysis and proofs. It is absolutely crucial that you do the exercises in the text. Logic is learned almost entirely by practice. The starred exercises in the text will be the assigned problems. You will occasionally be asked to present your answers to the class.

There will be frequent tests (all of them together, save one, 65% of final grade) and a cumulative final examination (8 am, Thursday, May 2, 20% of final grade).

The biweekly tests will be designed to encourage very regular practice and careful reading of the texts. Naturally, you should expect questions you have not seen before. Mastery of the material will give you the freedom to think creatively about the test questions.

There will be three application assignments (15% of final grade). These will help you practice your logical skills on arguments in their natural habitat. The assignments will involve argument formalization (due Feb. 15), fallacy identification (due March 21), and constructive criticism (due April 18). Detailed assignment descriptions are given below.

Some of you will have required visits to my office hours, though everyone is encouraged to come. Individual attention is the best kind of help. If the regular hours are not convenient, we will find another time.

I would love to get to know you better. Feel free to invite me to lunch in the DC. After chapel is the best time. I’ll be glad for conversation over lunch. I also take all comers in short games of chess, Scrabble, and the like. If you and a friend would like to try a game of my own design, let me know.

To help you learn most effectively, use of computers, tablet devices, and the like will not be permitted unless the instructor specifically requests it. Cell phones must be turned off and stored out of sight.

You are expected to be considerate of each other and of the professor by arriving to class on time and turning off your cell phones. You are expected to know and abide by the standards for academic integrity as stated in the Student Handbook and the Academic Policies and Procedures.

Grades will be calculated as percentages and assigned letters according to the chart below. 95 ≤ x A 73.33 ≤ x < 76.66C 90 ≤ x < 95 A- 70 ≤ x < 73.33 C- 86.66 ≤ x < 90 B+ 66.66 ≤ x < 70 D+ 83.33 ≤ x < 86.66B 63.33 ≤ x < 66.66D 80 ≤ x < 83.33 B- 60 ≤ x < 63.33 D- 76.66 ≤ x < 80 C+ x < 60 F

Academic Accommodations Students who have been diagnosed with a disability (learning, physical/medical, or psychological) are strongly encouraged to contact the Disability Services office as early as possible to discuss appropriate accommodations for this course. Formal accommodations will only be granted for students whose disabilities have been verified by the Disability Services office. These accommodations may be necessary to ensure your full participation and the successful completion of this course. For more information, contact Sheri Noble, Director of Disability Services (565-6186, [email protected]) or visit the website http://www.westmont.edu/_offices/disabilitySchedule Below is a provisional list of reading assignments and class topics.

Statement Logic Jan. 9 The Power of Logic, 7.1, Symbolizing English Arguments The Power of Logic, 7.2, Truth Tables

Jan. 11 The Power of Logic, 7.3, Using Truth Tables to Evaluate Arguments

Jan. 14 The Power of Logic, 7.4, Abbreviated Truth Tables The Power of Logic, 7.5, Tautology, Contradiction, Contingency, and Logical Equivalence

Jan. 16 Test #1

Jan. 18 The Power of Logic, 8.1, Implicational Rules of Inference

Jan. 22 The Power of Logic, 8.2, Five Equivalence Rules

Jan. 23 The Power of Logic, 8.3, Five More Equivalence Rules

Jan. 25 Proof strategies in statement logic

Jan. 28 The Power of Logic, 8.4, Conditional Proof

Jan. 30 The Power of Logic, 8.5, Reductio ad Absurdum The Power of Logic, 8.6, Proving Theorems

Feb. 1 Test #2

Predicate Logic Feb. 4 The Power of Logic, 9.1, Predicates and Quantifiers Categorical logic Translation strategies in predicate logic

Feb. 6 The Power of Logic, 9.2, Demonstrating Invalidity

Feb. 8 The Power of Logic, 9.3, Constructing Proofs

Feb. 11 Proof strategies in predicate logic

Feb. 13 The Power of Logic, 9.4, Quantifier Negation, RAA, and CP Application assignment #1 due

Feb. 15 Test #3

Feb. 18-9 Presidents’ Holiday (no class) Feb. 20 The Power of Logic, 9.5, The Logic of Relations: Symbolizations

Feb. 22 The Power of Logic, 9.6, The Logic of Relations: Proofs

Feb. 25 The Power of Logic, 9.7, Identity: Symbolizations

Feb. 27 The Power of Logic, 9.8, Identity: Proofs van Inwagen, “A Formal Approach to the Problem of Free Will and Determinism” (course reader)

Mar. 1 Test #4

Metatheory Mar. 4 Philosophical Devices, Ch. 10, Syntax and Semantics Consistency

Mar. 6 Philosophical Devices, Ch. 11, Soundness and Completeness Decidability

Mar. 8 Decidability of First-Order Logic Undecidability of Predicate Logic Other Results of Metatheory

Mar. 11-15 Spring Recess (no class)

Mar. 18 Philosophical Devices, Ch. 12, Theories and Godel’s Theorem

Mar. 20 Godel’s Incompleteness Theorems and the Nature of the Mind

Mar. 22 Test #5

Modal Logic Mar. 25 Introductory Modal Logic 2.3, “The System T” Introductory Modal Logic 2.4, “The System S4” Introductory Modal Logic 2.5, “The System S5”

Mar. 27 Introductory Modal Logic 2.6, “Philosophical Matters”

Mar. 29 Easter Recess (no class)

Apr. 1 Easter Recess (no class)

Apr. 3 The Barcan Formulas Introductory Modal Logic 4.8, “A Kripke System” Introductory Modal Logic 4.9, “Objections to This System” Apr. 5 Williamson on Modal Logic as Metaphysics

Apr. 8 Counterfactuals Lewis, excerpts from Counterfactuals (reader)

Apr. 10 Metaphysics of Modality

Apr. 12 Test #6

Philosophical Issues Apr. 15 Paradoxes of Implication

Apr. 17 The Liar Paradox

Apr. 19 Bivalence vs. Multi-valued Logics

Apr. 22 Vagueness and Supervaluationism

Apr. 24 Intuitionism

Apr. 26 Study Day

May 2 Final exam (8 am)