Class Information

Course Title Math 218M2: Non-binary thinking in mathematics

Instructor Julia Kameryn Williams

Website http://kamerynjw.net/teaching/2024/math218m/

Email kwilliams [at] simons-rock (dot) edu

Primary out of class contact course website or email me

Class Hours and Room

• MWF 12:31–1:25

• CL1-01

Office Hours M 3:45–4:45, WF 2:35–3:35

Office 2T Hall College Center

Textbook Audrey Yap and Richard Zach, What If? An Open Introduction to Non-Classical Logics (2021). [PDF] )

Course Description Popular perception has it that mathematics is a domain of rigid, binary thinking. This is not the case. This class is a survey of some formal systems in mathematics which provide tools to study phenomena which don’t cohere to a binary. We will learn about a variety of propositional logical systems which don’t adhere to the true-false binary, including multi-valued, intuitionistic, and paraconsistent systems. We will look at these systems from both a mathematical and a philosophical perspective. We will investigate the use of these tools to understand topics outside of mathematics, especially gender and sexuality.

Prerequisite Prerequisites: Math 107M, Math 113, or instructor permission.

Learning Outcomes

This class is an introduction to a scholarly conversation that has been ongoing for several decades. Namely, do the lessons of radical social movements such as feminism or the queer movement affect which laws of logic we accept, much as they did for other deeply held beliefs? To understand this question we will study the philosophy of logic, investigate the properties of formal systems of logic, and consider their applications to human phenomena which do not fit into a dualistic binary. Upon completion of this course, the successful student will have begun to compute with different formal systems and philosophically analyze the use of logic.

Grading Policy

Grading for this class is done a specifications model. What this means is, rather than averaging together numerical scores to determine your overall grade, your grade is determined based on meeting specifications in multiple categories. There are three categories: Technical Problems, Discussion and Reading, and Term Paper. Each is graded on on a high pass/pass/fail scale.

Here’s the specifications to earn each grade:

• A: High pass in all three categories.

• B: Not meet the requirements for an A, one high pass, and two passes.

• C: Not meet the requirements for a B, and three passes.

• D: Not meet the requirements for a C, and pass in Technical Problems and Discussion and Reading.

• F: Not meet the requirements for a D.

I reserve the right to use +’s or -‘s for borderline cases.

Here’s the overview of how each category is graded. Details about the categories are later in the syllabus.

• Technical Problems. I will assign you problems to demonstrate your understanding of the logics we will study. These will be graded on a numerical scale.

  • High Pass. Achieve at least $85\%$.

  • Pass. Not meet a High Pass, and achieve at least $65\%$.

  • Fail. Don’t meet the requirements for a Pass.

• Discussion and Readings. I will assign you core readings. You will respond to some short prompts about the reading, and we will discuss the reading together in class.

  • High Pass. Submit all short prompts and participate in all class discussions.

  • Pass. Not meet a High Pass, submit all but one short prompt, and miss at most one class discussion.

  • Fail. Not meet the requirements for a Pass.

• Term Paper. You will write a paper further delving into the ideas from one core reading and how they relate to one extended reading.

  • High Pass. Participate in the term paper discussion, submit the first draft on time, and submit an adequate final draft.

  • Pass. Not meet a High Pass, and submit a mostly adequate final draft.

  • Fail. Don’t meet the requirements for a pass.

I reserve the right to modify the grading requirements for an individual student based on special circumstance. For example, if you have an emergency and have to miss a discussion session that should not count against you. But you have to communicate with me. If anything comes up that seriously impairs your ability to engage in the class please let me know as soon as possible.

Technical Problems

Problem sets are assigned weekly for weeks 2 through 6, due on the Friday of each week. These problems will ask you to do computations with a formal logical system, or make a mathematical argument. Handwritten solutions are preferred.

You are encouraged to work together on homework, but the work you turn in is expected to be your own. If you do collaborate with classmates, please say so and give their names with your submitted work.

If you will not be able to submit your completed homework on Friday, send me an email to let me know and you can turn it in on the following Monday. Late work is not penalized, but because this is a half-semester course I cannot offer long extensions.

If exceptional circumstances make it impossible to get work done, please talk to me so we can figure out the best solution for what to do.

Discussion and Readings

Readings will be assigned weekly, except for weeks 5 and 7. For each reading I will assign a few small prompts for you to write a response to. You will submit your responses of the Monday of the following week, and we will use that class period to discussion the reading together.

For each reading you will be assigned a selection of pages. These pages are where the author(s) develop the ideas which will be the focus of the short prompts and the discussion. But you are strongly encouraged to read beyond those pages. This is especially important for your term paper.

In addition to the core readings which we will discuss in class, there is a list of extended readings. These are further texts which explore the ideas we will see during class time, but sadly we don’t have the time to read everything. Instead you will pick one of the extended readings to read on your own to then make up part of your term paper.

The readings can be found on the class google drive, which I will share with you via email.

Core readings

• Helen L. Daly, “Modelling sex/gender” (2017).

• Susan Haack, “Chapter 5: Intuitionism”, in Deviant Logic: Some Philosophical Issues (1974).

• Andrea Nye, “Conclusion: Words of power and the power of words”, in Words of Power: A Feminist Reading of the History of Logic (1990).

• Val Plumwood, “The politics of reason: towards a feminist logic” (1993).

Extended readings

• Maryann Ayim, “Passing through the needle’s eye: can a feminist teach logic?” (1995).

• Rory W. Collins, “Modeling gender as a multidimensional Sorites paradox” (2020).

• Robin Dembroff, “What is sexual orientation?” (2016).

• Maureen Eckert, “De-centering and genderqueering Val Plumwood’s feminist logic” (2024).

• Maureen Eckert and Charlie Donahue, “Towards a feminist logic: Val Plumwood’s legacy and beyond” (2020).

• Thomas Macaulay Ferguson, “From excluded middle to homogenization in Plumwood’s feminist critique of logic” (2023).

• Arend Heyting, “Chapter 1: Disputation” in Intuitionism: An Introduction (1956).

• Franci Mangraviti, “The liberation argument for inconsistent mathematics” (2023).

• Val Plumwood, “Some false laws of logic” (2023).

• Ivan Restović, “Feminist logic, literally” (2023).

• Catharine Saint-Croix and Roy T. Cook, “(What) is feminist logic? (What) do we want it to be?” (2024).

• Bonnie Shulman, “What if we change our axioms? A feminist inquiry into the foundations of mathematics” (1996).

• Anne Waters, “Language matters: nondiscrete nonbinary dualism” in American Indian Thought ed. Anne Waters (2004).

Term Paper

You will write a term paper comparing and contrasting the ideas in one core reading with the ideas in one core reading with the ideas in one extended reading. You will argue for a thesis statement about how the ideas in the two readings support the same point, conflict with each other, or how they inform a position not present in either text. Here are some sample topics to give you inspiration.

• Daly proposes a many strands model of gender while Collins uses a fuzzy logic model for gender. How do their models relate? Are they compatible with each other?

• Plumwood critques classical logic as a “logic of domination” and Eckert and Donahue further develop her critique. How do they build on it? Do their ideas contradict any of Plumwood’s?

• Both Daly and Eckert have, in part, the motivation that gender admits both ambiguity and vagueness. Can this same motivation be found in understanding the identities of multiracial people? In what ways do their models need to be modified to understand this different domain?

• Nye thinks that feminists should reject logic while Plumwood thinks feminists shoudl reform logic. What is the core of their disagreement? Is there a possibility for a reconciliation?

Format. Your paper should be 8 to 12 pages, double spaced and using a normal font size. You are required to cite your sources, including the readings. You may use your favorite citation style but be consistent.

Rubric. To be considered adequate your paper must meet each requirement, while mostly adequate relaxes the first three.

• Format. Your paper meets the page requirement (8 to 12 pages), is formatted according to the requirements, and you use a consistent citation style.

• Mechanics and Structure. You adhere to the normative grammar and style rules of academic writing. Your ideas flow, sentence to sentence and paragraph to paragraph.

• Clear Thesis. You clearly state the theis for which you are arguing near the beginning of your paper.

• Use of Readings. To support your thesis you refer to ideas from the readings. You display a cogent understanding of the readings.

• Analysis. Your reasoning and argumentation is sound.

Schedule.

• By Monday 11/18. Decide which readings you want to compare. Start writing.

• Monday 12/2. Term paper discussion.

• Friday 12/6, or at least by the end of the weekend. Submit first draft.

• By Monday 12/16. Submit final draft.

Textbook Information

As a reference for the technical material we will use Audrey Yap and Richard Zach, What If? An Open Introduction to Non-Classical Logics (2021). A pdf of this book is freely available under a Creative Commons Attribution-Noncommercial-ShareAlike 4.0 International Licensce: [hosted on my website] or [see their webpage].

Attendance Policy and Class Participation Guidelines

You are expected to attend class sessions, as per the college attendance policy, and to satisfy the Discussion and Reading category for your grade.

You are expected to participate in all parts of class sessions. Mondays will be used for discussion sessions, while Wednesdays and Fridays will be used to study technical material. For lecture you should be actively listening, taking notes, and asking questions as appropriate. For group discussions you should actively engage, sharing ideas and critiques with your classmates. Outside of class you should keeep up withb the reading assignments.

Mathematics has a reputation for being removed from social concerns and identities. Whether or not this is true for the content of mathematics, it is certainly false for the process of learning mathematics. Our classroom is to be a welcoming one, where everyone feels able to participate and learn regardless of their background or identity. As learners it is your obligation to treat others with respect and generosity, and be willing to exchange ideas with others.

If you miss a class, it is your responsibility to ensure you make up the missed lesson. Any handouts will be posted on the course website. If you know in advance you will have to miss a class, please email me.

If exceptional circumstances make it so you must miss multiple classes, please talk to me so we can figure out the best solution for what to do.

Communication Policy and Office Hours

Announcements, homework, and readings will be posted to the course website.

The best way to contact me outside of class is by email. Please put “math 218” in the subject line of your email.

Office hours are held multiple times in the week, to give you an opportunity to ask questions and receive help in-person outside of class time. If you prefer to meet at a different time, please contact me to arrange that.

Accessibility

Students with disabilities are legally entitled to reasonable accommodations to ensure equal access to education. I am committed to providing you with equal access to this class, and am happy to work with you to ensure reasonable accommodations. Because the accommodations offered are usually forward-looking modifications, it is important to get them set up as soon as possible.

Anyone who feels they may need accommodation based on the impact of a disability should contact Jeannie Altshuler, Director of Accessibility and Academic Support, in the Win Commons (jaltshuler@simons-rock.edu; 413-528-7383).

The Americans with Disabilities Act defines a disability as a medical condition that substantially limits one or more major life activities—including things like walking, sleeping, taking care of yourself, learning, and regulating your emotions—or major bodily functions. If you have a medical condition—including mental health conditions—that significantly interferes with your schoolwork, you probably qualify. You do not need to disclose your condition to your instructors to receive accommodations.

Academic Honesty

You are expected to know and uphold the college’s policies on academic honesty as described in the Student Handbook. Mathematics classes form part of the core base of skills you need to succeed in many later classes, and you are harming yourself if you try to avoid learning the material for this class.

The use of ChatGPT or other AI tools is prohibited. Submitted work using these tools will receive a zero, with no chance for making up the lost points. I reserve the right to escalate the consequences for repeated violations.

You are encouraged to collaborate with classmates for homework, but the work you submit is expected to be your own. If you do work with others, please say so and give their names with your submitted homework.

Other Campus Resources

The Wellness Center Health and Counseling Services, as the name says, offers health and counseling services.

The Win Student Resources Commons offers academic support, tutoring, accessibility, and career advice.

Schedule

Notice of Changes

This syllabus is subject to change. If this happens, you will be informed of any additions or changes.