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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
The aim of this course -- the second course in the department's two semester sequence in formal logic -- is to round out your introduction to first order logic by (1) helping you to consolidate your understanding of Mates's language L and of the types of deductive apparatus that can be used to turn it into a logistic system and then (2) showing you how one can establish a number of metatheorems concerning at least one logistic system of which that language can be a part. We shall also study System W in greater depth and further explore the two related systems W´ and W´´.
Mates's Elementary Logic will continue to serve as our basic text. Parts of Volume II of Basic Symbolic Skills -- still in preparation -- will serve as a companion piece thereto.
Again, there will be regular homework assignments, unannounced quizzes, two midterm examinations (on Feb. 23 and Mar. 30), and a final examination (on May 11).
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.
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, Kyle and I are 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 us know.
New this term: a Logic Stacks module designed to help you learn to operate comfortably within the language 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: 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, and the Logic Stacks will be available in CHE as well.
The Logic Stacks will be available in the logic lab in the basement of Smith House.
The following outline is tentative and subject to revision.
| Jan. | W | 17 | Overview of the course. |
| F | 19 | Review: Basics. Mates, Elementary Logic, Chapters 1-3. | |
| M | 22 | More Review: Basics. Mates, Elementary Logic, Chapter 4. | |
| W | 24 | Yet More Review: Translation. EL, Chapter 5. | |
| F | 26 | Tips on Reading the Connectives and Quantifiers. | |
| M | 29 | Identity, Numbers, Definite Descriptions. -- Drop/Add Deadline: Mon., Jan. 29. | |
| W | 31 | Translation and Logical Analysis. | |
| Feb. | F | 2 | The Limits of L. |
| M | 5 | A New Deductive Apparatus for Propositional Logic: Mates's Sentential Calculus. EL, Chapter 6. | |
| W | 7 | Truth-Functions and the Method of Truth-Tables. Mates's Derivation Rules. | |
| F | 9 | Yet Another Sentential Calculus: System W´. | |
| M | 12 | Justification of Conditionalization in W´. | |
| W | 14 | Justification of Replacement of Logically Equivalent Expressions in W´. | |
| F | 16 | A Deductive Apparatus Adequate for the Whole of L. EL, Chapter 7. | |
| M | 19 | Mates's Quantifier Rules and the Tautological Consequence Rule. System W´´. | |
| W | 21 | Comparison of These New Rules with the Quantifier Rules in System I. | |
| F | 23 | Test. First Midterm | |
| M | 26 | Metatheoretical Investigations -- Their Nature, Interest, and Utility. | |
| W | 28 | Syntactical Metatheorems. Proof Strategies Using Mathematical Induction. | |
| Mar. | F | 2 | Semantical Metatheorems. More on Proof Strategies. |
| M | 5 | Metatheorems concerning L. EL, Chapter 8. | |
| W | 7 | Preliminaries. | |
| F | 9 | Replacement. | |
| M | 12 | The Negation Theorem. -- Withdrawal Deadline: noon, Mar. 12 | |
| W | 14 | Prenex Normal Form; Duality. | |
| F | 16 | The Soundness and Consistency of the Rules for L. | |
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-- Spring Break (Mar. 19-23) -- |
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| M | 26 | The Completeness of the Rules for L. | |
| Nov. | W | 28 | More on Completeness. |
| F | 30 | Test. Second Midterm | |
| Apr. | M | 2 | Identity Revisited. The Language LI. EL, Chapter 9. |
| W | 4 | A Deductive Apparatus for LI. | |
| F | 6 | Terms and Operation Symbols. The Language L´ and an Appropriate Deductive Apparatus. | |
| M | 9 | An Axiomatization of LI. EL, Chapter 10. | |
| W | 11 | The Method of Characterizing the Theorems of a System by Means of a Series of Metatheorems. | |
| F | 13 | The Use of This Method to Develop a First Order Predicate Calculus with Identity. | |
| M | 16 | The Formalization of Theories in First Order Predicate Calculi. EL, Chapter 11. | |
| W | 18 | Examples: Aristotelian Syllogistic; The Theory of Betweenness; Groups; Boolean Algebras. | |
| F | 20 | The Role of Definitions in Formalized Theories. | |
| M | 23 | Overview of the History of Logic. EL, Chapter 12. | |
| W | 25 | Ancient Logic. | |
| F | 27 | Medieval Logic. | |
| M | 30 | Modern Logic. | |
| May | W | 2 | Review. |
| F | 4 | Review. | |
| F | 11 | Final Exam Period: 1:30-4:00 Final Examination | |