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Spring, 2004

Instructor: Tom Trelogan
Office: Smith House (1007 20th St.)
Office Hours: 10:30-11:30 MWF, and by appointment
Office Phone: 351-1561
Home Phone: 353-8253
E-mail: tom.trelogan@unco.edu

Course Objectives

The aim of this course—the second course in the department’s two-semester sequence in formal logic—is to (1) help you to become still better at working with logistic systems: better at doing translations, constructing proofs, and discovering logically illuminating models of sentences and sets of sentences, (2) show you how such systems can be studied from a metatheoretical point of view, (3) establish a number of metatheorems concerning Mates’s own system, (4) examine two extensions of L—LI and L´—suitable for the study of the logic of identity and terms, (5) show you how various parts of elementary logic can be axiomatized, (6) show you how L, LI, and L´ can be used to formalize a variety of theories, and (7) take a brief look at the history of logic.

Texts

Mates’s Elementary Logic will continue to serve as our basic text. Extracts from Volume II of Basic Symbolic Skills—still in preparation—will serve as companion pieces thereto.

Assignments

Again, there will be regular homework assignments, unannounced quizzes, two midterm examinations (on Feb. 6 and Mar. 12), and a final examination (on May 3).

Your grade for the course will again be determined by your performance on the homework, on the quizzes, and on the three examinations. Your performance on the homework will be worth 30% of your final grade, your performance on the quizzes will be worth 10%, and your performance on each of the examinations will be worth 20% of your final grade. Again, the scale used to determine letter grades is this: 90-100 = A; 80-89 = B; 70-79 = C; 60-69 = D; 0-59 = F. As was the policy last semester, you must complete all work assigned to receive credit for the course (except for quizzes; once again, missed quizzes will be recorded as zeros, and so once again, the moral is that you should come to class every day). Also the penalty for late submission of homework will again be a recorded grade of zero for each late assignment—which you will still have to complete in any case in order to receive credit for the course. Extensions will be given on homework assignments only in the most extraordinary of circumstances. The penalty for plagiarism on the homework assignments or for cheating on the quizzes or examinations will be denial of credit for the entire course.

Availability of Help

Formal Logic II is like Formal Logic I in being a course in which you cannot afford to fall behind. If anything, making sure you keep up with the assignments will be even more important this term than it was in the fall. As ever, I am more than willing to help you master all the things you’ll need to learn, so as soon as you think you need any help with anything, let me know.

Computerized Practice Opportunities

New this term: Logic Stacks modules designed to help you learn to operate comfortably with System W* and Mates’s L. Many of the exercises from Chapters 5, 6, and 7 of Mates’s Elementary Logic have been installed so you can benefit from the computer’s ability to check your work as you do it. Also new this term: Tarski’s World—a program designed to give you a feel for the meaning of the quantifiers in relation to n-place predicates and identity. Both programs will be available on the computers in the logic lab in the basement of Smith House.

Course Outline

The following outline is tentative and subject to revision.

Jan.	M	12	Overview of the course.
	W	14	Review: Mates, Elementary Logic, Chapters 1-5.
	F	16	Mates’s Sentential Calculus. Basic Rules and a Short-Cut Rule: The Theorem Rule. EL, Ch. 6, §6.
	M	19	No class — Martin Luther King Day
	W	21	More on the Basic Rules and the Theorem Rule.
	F	23	Another Short-Cut Rule: The Replacement Rule.
	M	26	Proof Strategies Using the SC Rules.
	W	28	Truth-Functions and the Method of Truth-Tables Revisited. EL, Chapter 6, §§1-5.
	F	30	A Deductive Apparatus for the Whole of L. Basic Rules and Short-Cut Rules. EL, Chapter 7.
Feb.	M	2	Proof Strategies Using the Rules of the Predicate Calculus.
	W	4	Mates’s Predicate Calculus vs. System WHY? (W*): A Comparison.
	F	6	Test. First Midterm
	M	9	Metatheoretical Investigations—Their Nature, Interest, and Utility.
	W	11	Syntactical Metatheorems. Proof Strategies Using Mathematical Induction.
	F	13	Semantical Metatheorems. More on Proof Strategies.
	M	16	Metatheorems concerning L. Preliminaries. EL, Chapter 7.
	W	18	Metatheorems about Substitution Instances and Closures of Formulas That Are Theorems of Logic.
	F	20	More Metatheorems concerning the Theorems of Logic.
	M	23	Replacement and Rewriting Bound Variables.
	W	25	The Negation Theorem.
	F	27	Prenex Normal Form; Duality.
Mar.	M	1	The Soundness and Consistency of the Rules.
	W	3	The Completeness of the Rules. Preliminaries: d-Consistent Sets and Maximal d-Consistent Sets.
	F	5	More Preliminaries: w-Complete Sets. Statement of the Principle Lemma. Strategy of the Proof. — Withdrawal Deadline: noon, Mar. 7
	M	8	Proof of Lemma II.
	W	10	Proof of Lemma III. The Löwenheim-Skolem Theorem. A Proof Procedure for L.
	F	12	Test. Second Midterm.
— Spring Break (Mar. 15-19) —
	M	22	Identity Revisited. The Language LI. EL, Chapter 9.
Nov.	W	24	A Deductive Apparatus for LI.
	F	26	Terms and Operation Symbols. The Language L´ and an Appropriate Deductive Apparatus.
	M	29	An Axiomatic Sentential Calculus: System W´.
	W	31	Justification of Conditionalization and Replacement in W´.
Apr.	F	2	An Axiomatization of L. EL, Chapter 10.
	M	5	The Formalization of Theories in First Order Predicate Calculi. EL, Chapter 11.
	W	7	Example I: Aristotelian Syllogistic.
	F	9	Example II: The Theory of Betweenness.
	M	12	Example III: Boolean Algebras.
	W	14	The Role of Definitions in Formalized Theories.
	F	16	More on Definitions.
	M	19	Overview of the History of Logic. EL, Chapter 12.
	W	21	Ancient Logic.
	F	23	Medieval Logic.
	M	26	Modern Logic.
	W	28	Review.
	F	30	Review.
May	M	3	Final Exam: 1:30-4:00 p.m.

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