Student Workbook - Oxford University Press

Introduction to Logic
BY PAUL HERRICK (OXFORD UNIVERSITY PRESS, 2012)

STUDENT WORKBOOK


THIS DOCUMENT IS DIVIDED INTO TWO PARTS. PART ONE CONTAINS SUPPLEMENTARY
MATERIALS CREATED BY PAUL HERRICK AND MARK STOREY, UNDER A GRANT FROM THE
BILL AND MELINDA GATES FOUNDATION ADMINISTERED BY THE WASHINGTON STATE
BOARD FOR COMMUNITY AND TECHNICAL COLLEGES. THESE MATERIALS ACCOMPANY THE
STANDARD SYMBOLIC LOGIC CLASS AND COMPRISE THE OPEN COURSE LIBRARY SYMBOLIC
LOGIC COURSE, PHILOSOPHY 120. INCLUDED HERE ARE ONLINE LECTURES COVERING
CHAPTERS 1 - 35 OF THE TEXTBOOK, INTRODUCTION TO LOGIC (OXFORD UNIVERSITY
PRESS, 2012), AND URLS FOR ONLINE VIDEOS ON THE SAME MATERIAL.

PART TWO CONTAINS THE STUDENT MANUAL MATERIALS FOR THE TEXT, POSTED AT THE
STUDENT SUPPORT PAGE AT THE OXFORD UNIVERSITY PRESS WEBSITE. ALL MATERIALS
FROM THE STUDENT MANUAL AT THE OXFORD UNIVERSITY PRESS WEBSITE ARE
COPYRIGHT OXFORD UNIVERSITY PRESS AND MAY NOT BE REPRODUCED WITHOUT
PERMISSION. INCLUDED IN THIS SECTION IS A SUMMATION OF NEARLY ALL THE
DEFINITIONS AND RULES (TRUTH-TABLE RULES, INFERENCE RULES, REPLACEMENT
RULES, ETC.) USED IN THE TEXT. THIS SECTION ENDS WITH A LIST OF ERRATA FOR
THE TEXT AS OF JUNE 2013.

TABLE OF CONTENTS

PART ONE

LECTURES AND SUPPLEMENTS...........................................2
URLS FOR THE
VIDEOS......................................................233

PART TWO

STUDENT
MANUAL............................................................244
LIST OF DEFINITIONS AND RULES........................................366
ERRATA........................................................................
....391



PART ONE.
OPEN COURSE LIBRARY LECTURES ON LOGIC


UNIT ONE
ONLINE LECTURE 1

OVERVIEW

REMARKS ON UNIT ONE IN GENERAL

WELCOME TO LOGIC CLASS! YOU ARE ABOUT TO STUDY A SUBJECT THAT COLLEGE
STUDENTS HAVE BEEN STUDYING SINCE THE DAYS OF ANCIENT GREECE. LOGIC IS ONE
OF THE OLDEST OF ALL ACADEMIC SUBJECTS.

WHEN YOU BEGIN A JOURNEY SOMETIMES IT HELPS TO HAVE A ROADMAP OF WHERE YOU
ARE GOING AND WHY YOU ARE ON THE ROAD. UNIT ONE, WHICH COMPRISES CHAPTERS 1-
6 IN THE TEXTBOOK, PRESENTS AND CAREFULLY DEFINES ALL THE FUNDAMENTAL IDEAS
OF LOGICAL THEORY, FROM THE DEFINITION OF LOGIC ITSELF, TO THE NOTION OF AN
ARGUMENT, TO THE DEFINITION OF LOGICAL CONTINGENCY AT THE END OF CHAPTER 6.
IN THESE OPENING CHAPTERS, THE BASIC IDEAS OF LOGIC ARE ALL DEFINED IN
PLAIN ENGLISH, WITHOUT THE USE OF SPECIAL SYMBOLS OR MATHEMATICAL FORMULAS.
THIS IS A VERY IMPORTANT PART OF THE TEXTBOOK BECAUSE IT LAYS THE
FOUNDATION FOR THE REST OF THE COURSE. A CLEAR UNDERSTANDING OF THE BASIC
IDEAS OF LOGIC IN THE BEGINNING, IN ENGLISH, WITHOUT SYMBOLS AND FORMULAS,
WILL PREPARE YOU FOR EVERYTHING TO FOLLOW.

IN SHORT, UNIT ONE IS THE LAUNCHING PAD FOR THE REST OF THE COURSE. AFTER
UNIT ONE, EACH SUCCEEDING UNIT SYSTEMATICALLY DEEPENS AND SHARPENS ONE OR
MORE OF THE FUNDAMENTAL CONCEPTS TAUGHT IN UNIT ONE AND APPLIES IT TO A
PARTICULAR TYPE OF REASONING. THE FIRST UNIT IS THE CONCEPTUAL FOUNDATION
FOR THE COURSE; THE MATERIAL GETS MORE TECHNICAL AFTER UNIT ONE. THIS IS
WHY IT IS IMPORTANT THAT YOU STUDY THIS OPENING UNIT CAREFULLY.

WHEN YOU START THE TEXTBOOK, WE RECOMMEND THAT YOU READ THE "TO THE
STUDENT" GREETING BEFORE YOU START READING CHAPTER 1. THAT PAGE IN THE
TEXTBOOK CONTAINS IMPORTANT INFORMATION AS YOU START THE TEXT. ALSO, IT IS
IMPORTANT THAT YOU READ THE OVERVIEW OF UNIT ONE AS WELL, ON THE PAGE
BEFORE THE START OF CHAPTER 1. ALL OF THIS WILL HELP YOU GET PROPERLY
ORIENTED AT THE START OF THE COURSE.

THINGS TO WATCH FOR AS YOU STUDY UNIT ONE

THE CHAPTERS IN THE TEXT BUILD ON EACH OTHER. MAKE SURE THAT YOU UNDERSTAND
CHAPTER 2 BEFORE YOU STUDY CHAPTER 3, AND CHAPTER 3 BEFORE YOU UNDERSTAND
CHAPTER 4, AND SO ON. THE CONCEPTS INTRODUCED IN CHAPTERS 1 AND 2 ARE VERY
ELEMENTARY; THINGS DO NOT START TO BUILD UNTIL CHAPTER 3, WITH THE
DISTINCTION BETWEEN DEDUCTION AND INDUCTION. FOR A THOROUGH UNDERSTANDING
OF THIS VERY CRUCIAL DISTINCTION-THE DIFFERENCE BETWEEN DEDUCTIVE AND
INDUCTIVE ARGUMENTS--STUDY THE DEFINITIONS AND EXAMPLES CAREFULLY.

THE MOST DIFFICULT CONCEPT TO MASTER, IN ALL OF UNIT ONE, IS SURELY THE
CONCEPT OF DEDUCTIVE VALIDITY, INTRODUCED IN CHAPTER 4. WE RECOMMEND THAT
YOU PAY SPECIAL ATTENTION WHEN LEARNING THIS BASIC LOGICAL IDEA. THE
TEXTBOOK EXPLAINS THE CONCEPT VERY, VERY CAREFULLY, WITH MANY EXAMPLES.
SOMETIMES WHEN LEARNING A DIFFICULT CONCEPT, IT HELPS TO HEAR IT EXPLAINED
IN SEVERAL DIFFERENT WAYS. THIS IS WHY THE TEXT EXPLAINS THE CONCEPT OF
VALIDITY IN SEVERAL DIFFERENT WAYS. ONE WAY OF EXPLAINING THE BASIC IDEA
MAY MAKE BETTER SENSE TO ONE PERSON, ANOTHER WAY OF EXPLAINING IT MAY MAKE
BETTER SENSE TO SOMEONE ELSE, AND SO ON. THE EXPLANATIONS MAY BE A LITTLE
"WORDY" AT TIMES, BUT THEY ARE VERY EXACT. EXPLANATIONS IN TECHNICAL
SUBJECTS OFTEN TEND TO BE A LITTLE COMPLICATED AND WORDY.

IN ADDITION TO PAYING CLOSE ATTENTION TO THE EXPLANATIONS OF VALIDITY,
STUDY THE APPLICATIONS AND EXAMPLES CAREFULLY TO REALLY NAIL DOWN THE
CONCEPT. THE TEXT ALSO WARNS YOU AWAY FROM CERTAIN COMMON MISTAKES STUDENTS
OFTEN MAKE WHEN FIRST LEARNING THE DEFINITION OF VALIDITY AND WHEN FIRST
LEARNING TO DISTINGUISH VALID FROM INVALID ARGUMENTS. THESE WARNINGS ARE
MARKED WITH A BOLD "CAUTION!" HEADING. BE SURE TO NOTICE THEM!

SO, READ THE SECTION ON VALIDITY WITH EXTRA CARE, CONCENTRATING ON THE
DEFINITIONS AND THE EXAMPLES. MAKE SURE YOU REALLY UNDERSTAND THIS CRUCIAL
IDEA, ONE OF THE CENTRAL IDEAS IN ALL OF LOGICAL THEORY.

A WORD OF CAUTION

SOME STUDENTS TAKE THE FIRST QUIZ OR THE FIRST TEST, OVER THE FUNDAMENTAL
IDEAS OF LOGICAL THEORY, AND THEY ACE IT AND ARE VERY HAPPY. BUT MANY
STUDENTS TAKE THE VERY FIRST TEST OR QUIZ, EARN A LOW SCORE, AND ARE BOTH
SURPRISED AND DISCOURAGED. THEY STUDIED, AND THEY THOUGHT THEY UNDERSTOOD
THE MATERIAL. AND THEY ARE DISAPPOINTED. WHEN THIS HAPPENS, THEY SOMETIMES
EXPRESS THEIR DISAPPOINTMENT, TELLING US THAT THEY STUDIED AND REALLY
THOUGHT THEY KNEW THE MATERIAL. IN MOST CASES, WHAT HAPPENED WAS PROBABLY
THIS: THEY THOUGHT THEY UNDERSTOOD THE MATERIAL, BUT IN REALITY THEY DID
NOT UNDERSTAND IT VERY WELL AT ALL. THEY OVERESTIMATED HOW WELL THEY
UNDERSTOOD THE MATERIAL. SOMETIMES WE FOOL OURSELVES AND THINK WE
UNDERSTAND SOMETHING WHEN WE IN REALITY WE DON'T. SOMETIMES WE ONLY
DISCOVER THAT WE DO NOT UNDERSTAND SOMETHING WHEN WE TEST OUR KNOWLEDGE
AGAINST A MORE OBJECTIVE MEASURE. THIS IS TRUE IN LIFE AS WELL AS IN THE
CLASSROOM, ISN'T IT? THIS IS WHY THE SELF-TESTS-THE "PRACTICE PROBLEMS WITH
ANSWERS"-PROVIDED IN THE INDIVIDUAL LECTURES ON EACH CHAPTER IN THE TEXT,
ARE SO IMPORTANT. IF USED PROPERLY THE ONLINE LECTURES (IN COURSE
MATERIALS, ONLINE LECTURES TO ACCOMPANY THE TEXT) CAN GIVE YOU VALUABLE
FEEDBACK.

HOWEVER, IT IS ALSO TRUE THAT THE FUNDAMENTAL IDEAS OF LOGIC ARE NOT AS
EASY TO GRASP AS THE IDEAS TAUGHT IN WATER BOILING 101. ("PLACE PAN OF
WATER ON STOVE, TURN BURNER TO HIGH...") WE BELIEVE THAT ONE REASON THE
FUNDAMENTAL IDEAS OF LOGIC ARE MORE DIFFICULT (QUITE A BIT MORE DIFFICULT)
IS THAT (A) THEY ARE EXTREMELY ABSTRACT AND CONCEPTUAL, AND (B) FOR MOST OF
US, THE AUTHORS OF THIS COURSE INCLUDED, EXTRA MENTAL EFFORT IS REQUIRED
WHEN WE LEARN EXTREMELY ABSTRACT IDEAS. WHETHER THE SUBJECT IS CALCULUS,
PHYSICS, OR CHEMISTRY, ABSTRACT SUBJECTS ALL REQUIRE A LOT OF MENTAL
CONCENTRATION, THE POWER OF ABSTRACTION, SUSTAINED MENTAL ATTENTION AND
EFFORT, GOOD STUDY HABITS, AND EFFECTIVE NOTE-TAKING SKILLS. LOGIC IS NO
EXCEPTION.


AFTER UNIT ONE

HERE IS WHAT HAPPENS AFTER UNIT ONE. EACH UNIT AFTER THE FIRST UNIT WILL
ANALYZE AND SHARPEN CERTAIN OF THE FUNDAMENTAL IDEAS OF LOGIC, FORMING THEM
INTO A SYSTEM OF PRECISE THOUGHT WITH VERY EXACT RULES FOR THE EVALUATION
OF IMPORTANT KINDS OF REASONING. ONCE WE ENTER MODERN LOGIC, REASONING WILL
BE TRANSLATED INTO A SYMBOLIC LOGICAL LANGUAGE MUCH LIKE THE SYMBOLIC
LANGUAGES USED IN MATHEMATICS AND COMPUTER PROGRAMMING. COMBINED WITH EXACT
RULES, THESE LANGUAGES WILL ALLOW US TO SOLVE PROBLEMS WITH THE PRECISION
OF MATHEMATICS.

HERE IS ONE WAY TO PICTURE MODERN LOGIC: WE TRANSLATE REASONING FROM
ENGLISH INTO LOGICAL SYMBOLISM, SOMEWHAT THE WAY MATHEMATICIANS TRANSLATE A
"STORY PROBLEM" INTO MATHEMATICAL FORMULAS. AFTER THIS, EXACT RULES AND
PROCEDURES ARE APPLIED AND ANSWERS ARE FOUND WITH EXTREME PRECISION.

MAIN OBJECTIVES OF UNIT ONE

The student who successfully completes all six chapters of Unit One will be
expected to meet all of the following objectives.

1. Demonstrate your understanding of logic by accurately defining it in
your own words.



2. Demonstrate your understanding of reasoning by correctly defining it
in your own words.



3. Demonstrate your understanding of how logic (as an academic subject)
began by explaining its historical origin in your own words and by
correctly answering relevant questions, including true-false, multiple-
choice, and other types of short answer questions and essay questions.





4. Demonstrate your understanding of the basic concepts of logic
explained in Unit One by correctly distinguishing arguments from
nonarguments, by accurately identifying the parts of arguments, by
distinguishing deductive from inductive arguments, valid from invalid
arguments, and strong from weak arguments, by identifying the logical
properties of sentences (necessary truth and falsity and contingent
truth and falsity) and by correctly identifying the presence of
logical relations among groups of sentences (consistency,
inconsistency, implication, and equivalence