PHILOS 4XX3 IntermediateLogic
Academic Year: Winter 2017
Instructor: Dr. Richard Arthur
Office: University Hall 305
Phone: 905-525-9140 x 23470
Office Hours: TBA
- Course Objectives
- Textbooks, Materials & Fees
- Method of Assessment
- Policy on Missed Work, Extensions, and Late Penalties
- Additional Policies and Statements
- Topics and Readings
- Other Course Information
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:
Gödel, Escher, Bach:, Douglas R. Hofstadter, Vintage Books, N.Y., 1979.
Logical Options: An Introduction to Classical and Alternative Logics, John L. Bell, David DeVidi and Graham Solomon., Broadview Press, 2001.
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:
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:
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:
- Plagiarism, e.g. the submission of work that is not one’s own or for which other credit has been obtained.
- Improper collaboration in group work.
- 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 email@example.com. 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: