CartCategory Theory for Arts and Humanities Instructor: Édgar A. Valenzuela NuncioProgram: WorkshopCredit(s): 1Date: August 9, 16, 23, 30Time: 14:00-16:30 ET
DESCRIPTION: Whether orders, morphisms, algebras, or mappings, the appearance of categories in pure and applied mathematics is ubiquitous. Because of its synthetic nature, its acceptance has foreshadowed the set-theoretic foundational approach to mathematics: that which would otherwise have been a behemoth construction using purely an “analytical” method like set theory, or subject-specific techniques, has become a dynamic foundational medium. Its diagrammatic appeal is undeniable—this is why we see its importance more and more outside of a purely mathematical context.
By Cx Tx, we mean a placeholder: Critical Thinking, Culture Theory, Cybernetics Theory, Conspiracy Theory, CosmoTechnics, Cthulhuism, etc. Attendees are required to devise an input for Cx Tx.
This Workshop is an introduction to category theory as a thinking tool. Attendees are required to showcase their learnings through an interdisciplinary project. Participants are guided to complete a mixed media: categorical formality ⊕ Cx Tx. Be it a 3D animation or an academic essay, the work must be accompanied by proper formality and an improper Cx Tx, respectively.
Session 1: Categories and Functors / Objects, arrows, and functors through formality and intuition, basic literature and tools, category-theoretic building blocks, functoriality as translation tool, Cecilia Vicuña’s Palabrarmas (arm-words), breadcrumbs for project development
Readings Spivak, Category Theory for Scientists, pp. 15–22, 69–101, 113–128 (recommended but not required)
Session 2: Natural Transformation through Cybernetics / Adjunctions and natural transformations, formalizing autopoietic systems using category theory, systems theory and cybernetics, Cartesian closed categories, relational biology, Allende’s cybernetic vision for Chilean politics
Readings: Louie, “Relational Biology” (2017), Louie, “Essays on More Than Life Itself” (2011)
Session 3: Categories of Models / The abstract notion of model from the semantic approach in logic, model theory and mathematical logic, relational, classical, paraconsistent, and paracomplete models, Badiou’s reading of materialist epistemology, semantic link to abstract logics, interdisciplinary construal of model theory
Readings: Badiou, The Concept of Model, chapter 2 (p. 9) and chapters 4–10 (pp. 14–55)
Session 4: Set Theory co-contra Category Theory / The foundational dichotomy between set theory and category theory, NBG and ZFC formalizations, Zalamea’s synthetic approach, Kantian reading of analytic versus synthetic, Vopěnka’s Hypothesis, toward a full synthetic approach to foundational projects
Readings: Zalamea, Synthetic Philosophy of Contemporary Mathematics, introduction (pp. 3–18), chapter 1 (pp. 21–48), chapter 3 (pp. 109–129)
IMAGE: A Thousand Plateaus, First English Translation, University of Minnesota Press, 1987
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