Philosophy 2500
Logic
INTRODUCTION TO SYMBOLIC LOGIC
This course is intended to be a systematic introduction to the nature and norms
governing good deductive reasoning. Our aim is to identify and systematically
articulate principles that serve as the ultimate foundation for such reasoning.
Our methodology will be formal: the basic concepts and techniques of formal or
symbolic logic will be introduced. We will concentrate on developing and
understanding the rules of syntax and semantics for both sentential logic
(sometimes also called truth-functional logic) and first-order predicate logic
(sometimes also called first-order quantificational logic) with identity. We will
also introduce natural deduction systems for both sentential and predicate logic.
GE CATEGORY AND EXPECTED LEARNING OUTCOMES: Philosophy 2500
satisfies the Math or Logical Analysis subcategory of the Arts and Humanities
Quantitative Reasoning GE requirement. The expected learning objectives for this
subcategory are as follows: Students comprehend mathematical concepts and methods
adequate to construct valid arguments, understand inductive and deductive reasoning,
and increase their problem solving skills.
READING: The only text for the class is The Logic Book (6th edition), by Bergmann,
Moor, and Nelson. Solutions to selected exercises should be available on line. More
specifically, we will cover chapters 1-3, 5 (omitting section 5.4), 7-8 (omitting section 8.5),
and 10 (omitting sections 10.3 and 10.4). Copies should be available in the usual
bookstores, and you should be able to get used copies on line. Occasionally, there will
also be “handouts”, which I will not actually hand out but will post on the Carmen
website for this course, and whose availability I will announce in class.
ASSIGNMENTS: There will be homework, two “midterm” exams and a
comprehensive final exam. For purposes of evaluation, the homework will count for
one fifth of your course work; each midterm will count as one fifth; and the final exam
will count as two fifths. There will be a total of 5 homework assignments. No late
homework will be accepted, so make sure you get your homework done on time.
Homework assignments will be posted on the Carmen website for this course. Their
availability will be announced in class or via e-mail.
OFFICE HOURS: The GTA for this course is Matt Souba. He will announce his office
hours to you in section, which meets on Fridays. His e-mail address is
[email protected].
My office hours are Mondays 2:00-3:00 and by appointment. My office is 314G
University Hall; you need to go through the Gluck Library (UH 314) to get to it. My email address is [email protected].
STUDENTS WITH DISABILITIES that have been certified by the Office of Disability
Services will be appropriately accommodated. They should inform me as soon as
possible of their needs. The Office of Disability Services is located in 150 Pomerene Hall,
1760 Neil Avenue; telephone 292-3307; TDD 292-0901; http://www.ods.ohio-state.edu/
***
TARGET SYLLABUS
What follows is a target syllabus. All mention of “Chapters” refers to The Logic Book. I will try to
keep us as close to this schedule as possible. But we may find ourselves wanting to spend more
[or less] time on some of the topics, in which case the scheduling of what follows (including
exams) will need to be adjusted. Students are responsible for keeping track of any adjustments.
Homework assignments and all handouts will be posted on the Carmen website for this course.
Postings will be announced in class.
WEEK I Wednesday, August 27: INTRODUCING THE BASIC NOTIONS OF
DEDUCTIVE LOGIC.
READING: Chapter 1
WEEK II September 3 (no class on Monday/Labor Day): SENTENTIAL
LOGIC (SYNTAX): INTRODUCING THE TRUTH FUNCTIONAL CONNECTIVES AND
THEIR CHARACTERISTIC TRUTH TABLES.
READING: Chapters 1, 2
WEEK III September 8, 10: SENTENTIAL LOGIC (SYNTAX): (A) SYMBOLIZING
ENGLISH SENTENCES IN THE LANGUAGE OF SENTENTIAL LOGIC SL; (B) THE
FORMAL SYNTAX OF SL.
READING: Chapters 2
WEEK IV September 15, 17: SENTENTIAL LOGIC (SEMANTICS):
INTRODUCING TRUTH TABLES AND DEFINING SEMANTIC NOTIONS OF
SENTENTIAL LOGIC.
READING: Chapter 3
WEEK V September 22, 24: THE FORMAL SEMANTICS OF SL [First Midterm]
READING: Chapter 3
WEEK VI September 29, October 1: SENTENTIAL LOGIC (DERIVATIONS):
INTRODUCING THE NATURAL DEDUCTION SYSTEM FOR SENTENTIAL LOGIC, SD;
INTRODUCTION AND ELEMINATION RULES FOR THE TRUTH FUNCTIONAL
CONNECTIVES OF SL.
READING: Chapter 5 [omit section 5.4]
WEEK VII October 6, 8: SENTENTIAL LOGIC (DERIVATIONS): DEFINING THE
SYNTACTIC SD CORRELATES TO THE SEMANTIC NOTIONS OF SL; PREDICATE
LOGIC (SYNTAX): REFLECTING ON THE LIMITATIONS OF SENTENTIAL LOGIC.
READING: Chapters 5, 7
WEEK VIII October 13, 15: PREDICATE LOGIC (SYNTAX): INTRODUCING THE
QUANTIFIERS AND THEIR INFORMAL SEMANTICS; SYMBOLIZING ENGLISH
SENTENCES IN THE LANGUAGE OF PREDICATE LOGIC PL.
READING: Chapter 7
WEEK IX October 20, 22: PREDICATE LOGIC (SYNTAX): COMPLEX
SYMBOLIZATION INVOLVING MULTIPLE QUANTIFIERS; THE FORMAL SYNTAX OF
PL.
READING: Chapter 7, 8 [omit section 8.5]
WEEK X October 27, 29 : PREDICATE LOGIC (SEMANTICS): DEFINING THE
SEMANTIC NOTIONS OF PREDICATE LOGIC.
READING: Chapter 8
WEEK XI November 3, 5: PREDICATE LOGIC: (SEMANTICS): CONSTRUCTING
MODELS AND COUNTER-MODELS; THE FORMAL SEMANTICS OF PL. [Second
Midterm]
READING: Chapter 8
WEEK XII November 10, 12: PEDICATE LOGIC (DERIVATIONS):
INTRODUCING THE NATURAL DEDUCTION SYSTEM PREDICATE LOGIC; THE
INTRODUCTION AND ELIMINATION RULES FOR THE UNIVERSAL AND EXISTENTIAL
QUANTIFIERS.
READING: Chapter 10 [omit sections 10.3 and 10.4]
WEEK XIII November 17, 19: PREDICATE LOGIC (DERIVATIONS):
DERIVATION STRATEGIES.
READING: Chapter 10
WEEK XIV November 24, 26: PREDICATE LOGIC (DERIVATIONS): DEFINING
THE PD CORRELATES FOR THE SEMANTIC NOTIONS OF PL.
READING: Chapter 10 cont.
WEEK XV December 1, 3: PREDICATE LOGIC (DERIVATIONS): MORE ON
DERIVATION STRATEGIES; SOME METALOGICAL ISSUES.
READING: Chapter 10 cont.
Week XVI December 8 [Review for Final Exam]
NB: As best as I can currently tell, our final exam is scheduled for the same room on Wednesday,
December 17th from 12:00 to 1:45.
ACADEMIC INTEGRITY (ACADEMIC MISCONDUCT): Academic integrity is essential to
maintaining an environment that fosters excellence in teaching, research, and other educational and
scholarly activities. Thus, The Ohio State University and the Committee on Academic Misconduct
(COAM) expect that all students have read and understand the University’s Code of Student Conduct, and
that all students will complete all academic and scholarly assignments with fairness and honesty. Students
must recognize that failure to follow the rules and guidelines established in the University’s Code of
Student Conduct and this syllabus may constitute “Academic Misconduct.”
The Ohio State University’s Code of Student Conduct (Section 3335-23-04) defines academic misconduct
as: “Any activity that tends to compromise the academic integrity of the University, or subvert the
educational process.” Examples of academic misconduct include (but are not limited to) plagiarism,
collusion (unauthorized collaboration), copying the work of another student, and possession of
unauthorized materials during an examination. Ignorance of the University’s Code of Student Conduct is
never considered an “excuse” for academic misconduct, so I recommend that you review the Code of
Student Conduct and, specifically, the sections dealing with academic misconduct.
If I suspect that a student has committed academic misconduct in this course, I am obligated by University
Rules to report my suspicions to the Committee on Academic Misconduct. If COAM determines that you
have violated the University’s Code of Student Conduct (i.e., committed academic misconduct), the
sanctions for the misconduct could include a failing grade in this course and suspension or dismissal from
the University.
If you have any questions about the above policy or what constitutes academic misconduct in this course,
please contact me.
Other sources of information on academic misconduct (integrity) to which you can refer include:
• The Committee on Academic Misconduct web pages (COAM Home)
• Ten Suggestions for Preserving Academic Integrity (Ten Suggestions)
• Eight Cardinal Rules of Academic Integrity (www.northwestern.edu/uacc/8cards.html)