Have a Question? Contact the Humanities Office or an Academic Unit

PHILOS 4XX3 IntermediateLogic

Academic Year: Winter 2017

Term: Winter

Day/Evening: D

Instructor: Dr. Richard Arthur

Email: rarthur@mcmaster.ca

Office: University Hall 305

Phone: 905-525-9140 x 23470


Office Hours: TBA

Course Objectives:

Course Description

Although this course presupposes a high level of competence in logic, it develops into something very different from Phil 2B03. Thus on the one side, various alternative logics have been developed that build on those foundations. But on the other, investigations of those foundations have raised some profound and fascinating questions. The following quotation from Nietzsche puts it well: “When the enquirer, having pushed to the [periphery of science], realizes how logic in that place curls about itself and bites its own tail, he is struck with a new type of perception: a tragic perception which requires, to make it tolerable, the remedy of art.” This could serve as the motif for this course: logic biting its own tail. It is implicit in paradoxes such as Zeno’s paradoxes of motion and plurality, which Lewis Carroll extends to modus ponens. But the theme of logic curling about itself is unfolded with a vengeance in developments in modern mathematical logic , particularly with the theory of recursive functions, and the discoveries of Gödel’s Theorem and Skolem’s Paradox. These have profound implications for subjects as diverse as the theory of knowledge and the nature of artificial intelligence, and are imaginatively and artistically explored in Hofstadter’s Gödel, Escher, Bach—as are their implications for artificial intelligence, their connections with Escher's woodcuts, Bach's fugues, molecular genetics, Zen Buddhism and a million other fascinating subjects. Meanwhile Logical Options will serve as our guide for alternative systems of logic.

Textbooks, Materials & Fees:

  1. Gödel, Escher, Bach:, Douglas R. Hofstadter, Vintage Books, N.Y., 1979.

  2. Logical Options: An Introduction to Classical and Alternative Logics, John L. Bell, David DeVidi and Graham Solomon., Broadview Press, 2001.

  3. I will be using Avenue to Learn (http://avenue.mcmaster.ca/) and a dedicated website (http://www.humanities.mcmaster.ca/~rarthur/4XX3/) to post regular announcements and information about the course, lists of supplementary readings, additional resources, and information and advice about assessment (including essay questions). You are expected to check in every couple of days.

Method of Assessment:

Course Requirements

Homework. During the course, you will be assigned a number of homework problems, solutions to be handed in at the beginning of class                                                                       (30%)

Midterm Exam. This will test you on your understanding of first- and second-order logic etc. (part 1-3 of Bell, DeVidi and Solomon)                                                                                   (30%)

Final Paper. This paper will either be on an alternative logic of your own choosing (e.g. Contextual Logic, Modal Logic, 3-valued Logic, Intuitionistic Logic, Fuzzy Logic, Quantum Logic, Free Logics), or on one of the topics that I will be assigning on matters discussed in the Hofstadter readings.         (40%)

Policy on Missed Work, Extensions, and Late Penalties:


Please Note the Following Policies and Statements:

Academic Dishonesty

You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.

Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g. the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: "Grade of F assigned for academic dishonesty"), and/or suspension or expulsion from the university.

It is your responsibility to understand what constitutes academic dishonesty. For information on the various types of academic dishonesty please refer to the Academic Integrity Policy, located at www.mcmaster.ca/academicintegrity

The following illustrates only three forms of academic dishonesty:

  1. Plagiarism, e.g. the submission of work that is not one’s own or for which other credit has been obtained.
  2. Improper collaboration in group work.
  3. Copying or using unauthorized aids in tests and examinations.

Email correspondence policy

It is the policy of the Faculty of Humanities that all email communication sent from students to instructors (including TAs), and from students to staff, must originate from each student’s own McMaster University email account. This policy protects confidentiality and confirms the identity of the student.  Instructors will delete emails that do not originate from a McMaster email account.

Modification of course outlines

The University reserves the right to change dates and/or deadlines etc. for any or all courses in the case of an emergency situation or labour disruption or civil unrest/disobedience, etc. If a modification becomes necessary, reasonable notice and communication with the students will be given with an explanation and the opportunity to comment on changes. Any significant changes should be made in consultation with the Department Chair.

McMaster Student Absence Form (MSAF)

In the event of an absence for medical or other reasons, students should review and follow the Academic Regulation in the Undergraduate Calendar Requests for Relief for Missed Academic Term Work. Please note these regulations have changed beginning Fall 2015. You can find information at mcmaster.ca/msaf/. If you have any questions about the MSAF, please contact your Associate Dean's office.

Academic Accommodation of Students with Disabilities

Students who require academic accommodation must contact Student Accessibility Services (SAS) to make arrangements with a Program Coordinator. Academic accommodations must be arranged for each term of study. Student Accessibility Services can be contacted by phone 905-525-9140 ext. 28652 or e-mail sas@mcmaster.ca. For further information, consult McMaster University's Policy for Academic Accommodation of Students with Disabilities.

Academic Accommodation for Religious, Indigenous and Spiritual Observances

Students requiring academic accommodation based on religion and spiritual observances should follow the procedures set out in the Course Calendar or by their respective Faculty. In most cases, the student should contact his or her professor or academic advisor as soon as possible to arrange accommodations for classes, assignments, tests and examinations that might be affected by a religious holiday or spiritual observance.

Topics and Readings:

Syllabus (provisional; updates on the course webpage)

Week 1    Jan 4       introduction

Reading:      [Read ahead if you have the syllabus!]                            

Week 2    Jan 11     Zeno and Carroll

Reading:      GEB, Intro, chs. 1-2 (pp. 3-60); BDS 1.1-1.22 (pp. 1-13)

Homework:   Solve the “MU puzzle” (GEB, p. 3-63);

Week 3   Jan 18      meaning, form and self-reference

Reading:      GEB, chs. 3-4 (pp. 61-102); BDS 1.23-1.25 (pp. 14-21); Homework: TBD

Week 4    Jan 25     consistency, completeness, recursion

Reading:      GEB, chs. 5-6 (pp. 103-176); BDS 1.3-1.4 (pp. 21-34); Homework: TBD

Homework:   Solve the “MU puzzle” (GEB, p. 3-63);

Week 5    Feb 1      the propositional calculus

Reading:      GEB, ch. 7 (pp. 177-197); BDS 1.5 (pp. 34-53); Homework: TBD

Week 6    Feb 8      predicate calculus and number theory

Reading:      GEB, ch. 8 (pp. 199-230); BDS 2.1-2.5 (pp. 54-87); Homework: TBD

Week 7    Feb 15    Gödel’s Incompleteness Theorem (1)

Reading:      GEB, ch. 9 (pp. 231-272); BDS 2.6-2.7 (pp. 87-101); Homework: TBD

————— Feb 20-25      Midterm Recess—————                         

Week 7     Mar 1    on levels, computers and brains

Reading:      GEB, chs. 10-11 (pp. 275-365); BDS 2.6-2.7 (pp. 87-101); Homework: TBD

Week 8     Mar 8    on minds, thoughts, and recursive functions

Reading:      GEB, chs. 12-13 (pp. 366-430); BDS 2.6-2.7 (pp. 87-101); Homework: TBD

Week 9     Mar 15   Gödel’s Incompleteness Theorem (2)

Reading:      GEB, chs. 14-15 (pp. 431-479); BDS 2.6-2.7 (pp. 87-101); Homework: TBD

Week 10   Mar 22   self-ref, DNA and  life

Reading:      GEB, ch. 16 (pp. 480-548); BDS 2.6-2.7 (pp. 87-101); Homework: TBD

Week 11   Mar 29  Church, Turing, Tarski etc.

Reading:      GEB, ch. 17 (pp. 549-585); BDS 2.6-2.7 (pp. 87-101); Homework: TBD

Week 12   Apr 5     strange loops

Reading:      GEB, ch. 20 (pp. 681-742); BDS 2.6-2.7 (pp. 87-101); Homework: TBD

—a more detailed syllabus with all the homework assignments will gradually unfold on the course website.


Other Course Information: