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(ud999e(,999999999 0: Formal Reasoning
Philosophy 330
Spring 2009
T & TH: 10:20 - 12:10p
Berkey Hall, Rm. 100
Instructor Information
Matthew McKeon
Office: 509 South Kedzie Hall
Office hours: Tuesday, 12:30-1:45pm; and by appt.
Telephone: Office355-4215, main-355-4490
E-mail: HYPERLINK mailto:mckeonm@msu.edu mckeonm@msu.edu
Required Text
Courseware Package (Text plus CD software): Jon Barwise and John Etchemendy. Language, Proof and Logic. Stanford, CA: CLSI Publications, 2008.
The courseware package includes several software tools that students will use to complete homework assignments and the self-diagnostic exercises from the text. DO NOT BUY USED BOOKS, BECAUSE THEY LACK THE CD THAT CONTAINS THE NEEDED SOFTWARE. The software, easy to learn and use, makes some of the more technical aspects of symbolic logic accessible to introductory students. Also, it is fun to use. However, since students cannot use a computer to complete the two in-class exams, the software should be used as a learning aid and not as a crutch.
Course Objectives
Introduce you to the concept of logical consequence, and other notions central to logic such as argument, consistency, and logical truth.
Introduce you to the basic methods of proof (both formal and informal), and teach you how to use them.
Introduce you to the formal structure of the language or languages that we use daily in order to deepen your understanding of the meaning of words and of the nature of truth.
Provide those of you who will encounter formal logic outside of this course with a firm foundation in symbolic logic. (This includes students of philosophy, especially analytic philosophy, as well as students of mathematics, computer science, and other technical disciplines.)
To give you a sense of what a logician does for a living and to jumpstart your thinking about an answer to the historically significant and philosophically important question: What is logic?
Please let me know at any point if you think we arent making sufficient progress toward these goals, or if there are goals that you think we should have. The following course requirements measure the extent to which these goals are attained.
Course Requirements
Six homework assignments. Your average grade will make up 30% of your final course grade. Each assignment consists of problems from text exercise sets. An assignment not turned in by the end of class counts as late. Late homework will be excused only in the event of hospitalization (yours not someone elses) with the proper documentation. A visit to the clinic or a doctors appointment does not count as hospitalization. There will be no make-up for late homework.
Six to eight class assignments. The lowest assignment grade will be dropped. Your average grade will make up 20% of your final grade. From time to time the class will break up into groups, and work on exercises which must be turned in by the conclusion of class. The exercises may be composed of T/F questions, multiple choice questions, and problems similar to text exercises. Assignments will be unannounced, and there are no makeups.
A mid-term and a final examination. Each exam may consist of some combination of the following: problems similar in kind to those encountered in the text, T/F questions, short-essay questions, and problems that require you to extrapolate from what you have learned in class and from the text. Your average exam grade will comprise 50% of your final grade. The first exam will be given in class on Tuesday, March 3rd. Note well: this exam will not be rescheduled unless a student is hospitalized (again, going to the clinic or visiting a doctor does not count as hospitalization), and makes available the required documentation or if an MSU athlete has a scheduled event. Documentation will be required in either case. The final exam is scheduled for Tuesday, May 5th from 10:00am-12:00pm in our classroom. The exam is not cumulative; it will cover material after the midterm. This exam will be rescheduled if the student is hospitalized during the exam time, or there is a confirmed conflict with another final exam.
Course Overview
This course is a rigorous introduction to logical consequence, the central concept of logic. The primary aim of logic is to tell us what follows logically from what. We shall take logical consequence to be a relation between a given set of sentences and the sentences that logically follow from that set. A central question of the course is: what conditions must be met in order for a sentence to be a logical consequence of others?
We shall develop an account of logical consequence for a symbolic language (specifically, the language of first-order predicate logic or FOL). This will allow us to investigate rigorous methods for determining when one FOL sentence follows from others, and will help us develop a method for showing that an FOL sentence is not a consequence of others. In addition to FOL, these two methods, the method of proof and the method of counterexample, will be the principle subject matter of the course. In order to give you a glimpse of what lies ahead, I say a bit more about the notion of proof, a notion central to mathematics, logic and other deductive disciplines.
A proof is a step by step demonstration showing that the conclusion of an argument is a logical consequence of the set of the arguments premises. Another way of relating logical consequence to proof is to say that each step in a proof is a logical consequence of previous steps and/or the set of the arguments premises. Hence, in order to build a proof one must be able to determine whether or not the relation of logical consequence holds between sentences. Typically, informal proofs leave out steps (perhaps because they are too obvious) and do not justify each and every step made in moving towards the conclusion (again, obviousness begets brevity). Proofs are not only epistemologically significant as tools for slaying Descartes evil demon and securing knowledge. The formal derivations that make up a proof serve as models of the informal reasoning that we perform in our native languages. This is of importance in, among other areas, computer science and artificial intelligence. Furthermore, the study of proofs allows us to follow Socrates and better know ourselves as reasoners. After all, like Molires M. Jourdain, who spoke prose all his life without knowing it, we reason all the time without being aware of the principles underlying what we are doing.
We shall learn a natural-style deduction system derived from the work of the mathematician Gerhard Gentzen and the logician Fredrick Fitch. Our natural-style deduction system, called Fitch, is basically a collection of inference rules that license steps in deductive chains of reasoning. Natural deduction systems are distinguished from other types of deduction systems by their usefulness in modeling ordinary, informal deductive inferential practices. Accordingly, we shall introduce and motivate the inference rules of Fitch by uncovering their correlates at work in informal proofs. In logic, we like to reveal the meat and bones of a proof, making each step and justification explicit. We shall do this by first translating the premise(s) and conclusion of the argument at hand into formal (i.e., FOL) sentences, and then building a proof that appeals exclusively to the inference rules of Fitch. We shall call the result a formal proof. Although frequently we shall work on arguments already composed of FOL sentences, we shall spend time on translating from English to FOL and back again. As youll come to see, learning how to construct formal proofs using Fitch hones skills at constructing and evaluating informal proofs.
Class Time
Class time will primarily be spent going over text exercises, and reviewing or expanding on key points from the reading. It is imperative that students keep up with the rigorous pace of the course by doing the assigned readings in a timely manner, and by doing enough of the relevant practice exercises to get a feel for ones level of understanding BEFORE coming to class. Class time is your opportunity to clear up those things that you find mysterious or troublesome. So, coming to class unaware of what you don't know is not the best way to use class time. Frequently, well break up, work on exercises, and then reconvene to compare answers and to discuss matters that arise. Class materials (e.g., lecture notes, practice problems, homework and class assignments) will be made available on ANGEL.
Attendance
I do not take attendance. However, as Woody Allen says, 80% of success is just showing up. Regular class attendance is critical to being successful in this course. In general, it is my experience that the majority of those who frequently miss class are less successful in the course than those who attend regularly. I consider any more than two absences excessive. Students that are absent from class are responsible for missed announcements and for getting class notes.
Work Level
In order to be successful on the exams and homework that come later in the semester, one must understand the earlier material upon which this required work is based. Since later coursework is based on and incorporates earlier work, (again) it is imperative that you keep up with the pace of the course. Furthermore, while the course material is not especially difficult, it does demand quality thinking. Hence, it is vital that throughout the semester you reserve quality time for coursework (doing logic problems when you are rushed or exhausted tends to increase the difficulty of the problems), and that you work diligently and consistently on understanding class material (missing lots of classes and doing the reading for an assignment the night before that assignment is due is a recipe for disaster).
Grading
Grades on homework, class assignments, and tests will be on a 100-pt. scale. Your final grade will be first determined on a 100-pt. scale, and then converted to a 4.0 scale according to the below tabulations. For example, a final grade of an 83% corresponds to a 3.0 and a 77% corresponds to a 2.5.
Final Grades
4.0=90% and above
3.5=85--89%
3.0=80--84%
2.5=75--79%
2.0=70--74%
1.5=65--69%
1.0=60--64%
Tentative Schedule
1/13 Introduction
Part I--Propositional Logic
1/15 & 1/20 Introductionpages 1-10 & 15
Chapter 1, Atomic Sentences
Chapter 2, The Logic of Atomic Sentencesexcluding 2.6
1/22 Chapter 3, The Boolean Connectives--excluding 3.8
1/27 Chapter 4, The Logic of Boolean Connectives
1/29 - 2/10 Chapter 5, Methods of Proof for Boolean Logic
Chapter 6, Formal Proofs and Boolean Logic
2/12 - 2/26 Chapter 7, Conditionalsexcluding 7.4 & 7.5
Chapter 8, The Logic of Conditionals--excluding 8.3
3/3 Midterm exam (Chapters 1-8)
Part IIQuantifiers
3/5 Chapter 9, Introduction to Quantification--excluding 9.8
3/9 - 3/13 Spring break
3/17 & 3/19 Chapter 9, Introduction to Quantification--excluding 9.8
Chapter 10, The Logic of Quantifiers
3/24 & 3/26 Chapter 11, Multiple Quantifiers
3/31 - 4/14 Chapter 12, Methods of Proof for Quantifiersexcluding 12.5
Chapter 13, Formal Proofs and Quantifiers
4/16 - 4/28 Chapter 13, Formal Proofs and Quantifiers
Chapter 14, More On Quantification
4/30 Conclusion and Review
Homework Schedule
Due by the end of class Chapter(s) covered
#1 1/29 Chapters 1-3
#2 2/17 Chapters 4-6
#3 2/26 Chapters 7 & 8
#4 3/24 Chapters 9 & 10
#5 4/14 Chapters 11 & 12
#6 4/28 Chapter 13 & 14
The philosophy department offers twice a week free tutoring sessions for students. Please stop by if you need help with logic.
Date and time: Tuesdays and Wednesdays, 5-7pm
Place: 523 South Kedzie
PAGE
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