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PHIL 149 - Special Topics in Philosophy of Logic and Mathematics: Nonclassical Logic Professor Wesley Holliday Tuth 11-12:30 UC Berkeley, Fall 2018 Dwinelle 88

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PHIL 149 - Special Topics in Philosophy of Logic and Mathematics: Nonclassical Logic Professor Wesley Holliday Tuth 11-12:30 UC Berkeley, Fall 2018 Dwinelle 88 PHIL 149 - Special Topics in Philosophy of Logic and Mathematics: Nonclassical Logic Professor Wesley Holliday TuTh 11-12:30 UC Berkeley, Fall 2018 Dwinelle 88 Syllabus Description A logical and philosophical exploration of alternatives to the classical logic students learn in PHIL 12A. The focus will be on intuitionistic logic, as a challenger to classical logic for reasoning in mathematics, and quantum logic, as a challenger to classical logic for reasoning about the physical world. Prerequisites PHIL 12A or equivalent. Readings All readings will be available on the bCourses site. Requirements { Weekly problem sets, due on Tuesdays in class (45% of grade) { Term paper of around 7-8 pages due December 7 on bCourses (35% of grade) { Final exam on December 12, 8-11am with location TBA (20% of grade) Class, section, and Piazza participation will be taken into account for borderline grades. For graduate students in philosophy, this course satisfies the formal philosophy course requirement. Graduate students should see Professor Holliday about assignments. Sections All enrolled students must attend a weekly discussion section with our GSI, Yifeng Ding, a PhD candidate in the Group in Logic and the Methodology of Science. Contact Prof. Holliday | [email protected] | OHs: TuTh 1-2, 246 Moses Yifeng Ding | [email protected] | OHs: Tu 2-4, 937 Evans Schedule Aug. 23 (Th) Course Overview Reading: none. 1/5 Part I: Review of Classical Logic Aug. 28 (Tu) Review of Classical Natural Deduction Videos: Prof. Holliday’s videos on natural deduction. Aug. 30 (Th) Nonconstructive Proofs Reading: Chapter 1, Section 2 of Constructivism in Mathematics by Anne Sjerp Troelstra and Dirk van Dalen. Part II: Logic as Algebra Sept. 4 (Tu) Ordered Sets Reading: 1.1, 1.2, 1.4, 1.14, 1.15, 1.16, 1.21, 1.23 of Introduction to Lattices and Order by Brian A. Davey and Hilary A. Priestley. Sept. 6 (Th) Lattices Reading: pp. 33-37, 39-41 (ending with 2.12) of Introduction to Lattices and Order by Davey and Priestley. Sept. 11 (Tu) Distributive Lattices Reading: pp. 85-92 of Introduction to Lattices and Order by Davey and Priestley. Sept. 13 (Th) Boolean Algebras Reading: pp. 93-95 of Introduction to Lattices and Order by Davey and Priestley. Sept. 18 (Tu) Logic as Algebra I Reading: Section 5.1 and Appendix B of Modal Logic by Patrick Blackburn, Maarten de Rijke, and Yde Venema. Sept. 20 (Th) Logic as Algebra II Reading: same as previous session. Part III: Intuitionistic Logic Sept. 25 (Tu) The BHK Interpretation Reading: Section 5.1 of Logic and Structure by Dirk van Dalen, Section 1 of “Intuitionistic Logic” by van Dalen (Handbook of Philosophical Logic), and “On the Interpretation of Intuitionistic Logic” by Andrei Kolmogorov. Sept. 27 (Th) Intuitionistic Propositional and Predicate Logic Reading: Section 5.2 of Logic and Structure by van Dalen. Oct. 2 (Tu) Heyting Algebras Reading: pp. 173-174 and 177 of Distributive Lattices by Raymond Balbes and Philip Dwinger. Oct. 4 (Th) Heyting Algebras Reading: same as previous session. Oct. 9 (Tu) Intuitionistic Kripke Semantics I Reading: Section 5.3 of Logic and Structure by van Dalen. Oct. 11 (Th) Intuitionistic Kripke Semantics II Reading: same as previous session. Oct. 16 (Tu) Intuitionistic Arithmetic Reading: Section 11.4 of “Intuitionistic Logic” (The Blackwell Guide to Philosophical Logic) by van Dalen and Section 7.5 of “Intuitionistic Logic” (Handbook of Philosophical Logic) by van Dalen 2/5 Oct. 18 (Th) The Intuitionist Critique I Reading: Section 1 of “The Logic of Brouwer and Heyting” by Joan Rand Moschovakis and Chapter 1 of Intuitionism: An Introduction by Arend Heyting. Oct. 23 (Tu) The Intuitionist Critique II Reading: “The Philosophical Basis of Intuitionistic Logic” by Michael Dummett and pp. 1-21 of Elements of Intuitionism by Michael Dummett. Oct. 25 (Th) Translations Reading: Section 3.5 of “Intuitionistic Logic” by Nick Bezhanishvili and Dick de Jongh, pp. 216-220 of Philosophy of Logics by Susan Haack, and Section 3.3 of Varieties of Logic by Stewart Shapiro. Part IV: Quantum Logic Ocr. 30 (Tu) Ortholattices and Quantum Logic I Reading: Sections 7-10, 11, and 17 of “The Logic of Quantum Mechanics” by Garrett Birkhoff and John Von Neumann and pp. 129-138 (up to Definition 4) of “Quantum Logics” by Maria Luisa Dalla Chiara and Roberto Giuntini. Nov. 1 (Th) Ortholattices and Quantum Logic II Reading: same as previous session. Nov. 6 (Tu) Relational Semantics for Quantum Logic I Reading: “Semantics of the Minimal Logic of Quantum Mechanics” by H. Dishkant, “Semantic Analysis of Orthologic” by Robert Goldblatt, and pp. 138-146 of “Quantum Logics” by Dalla Chiara and Giuntini. Nov. 8 (Th) Relational Semantics for Quantum Logic II Reading: same as previous session. Nov. 13 (Tu) Is Logic Empirical? I Video: “Probability & Uncertainty: the quantum mechanical view of nature” by Richard Feynman Reading: “Is Logic Empirical?” by Hilary Putnam. Nov. 15 (Th) Is Logic Empirical? II Reading: “Is Logic Empirical?” by Michael Dummett. Nov. 20 (Tu) Is Logic Empirical? III Reading: pp. 382-383 and p. 388 of “Probability in Quantum Mechanics” by L. E. Ballentine and “The Labyrinth of Quantum Theory” by Tim Maudlin. Nov. 22 (Th) No Class (Thanksgiving) Nov. 27 (Tu) Is Logic Empirical? IV Reading: Section 6.5 of The Boundary Stones of Thought by Ian Rumfitt. Nov. 29 (Th) Course Reflections Reading: none. Dec. 12 (W) Final Exam, 8-11am, location TBA 3/5 Course Policies LaTeX For your problem sets, neatly handwritten submissions are fine. However, we recommend that you try LaTeX for typing your problem sets. LaTeX will beautifully typeset all of the logical symbols that you need to use in this course. Not only is this nice for those grading your work, but also it should help you to create clear and well-organized content. Knowing how to use LaTeX is a useful skill for other courses too. For help getting started with LaTeX, see Professor MacFarlane’s LaTeX page for Phil 142: johnmacfarlane.net/142/latex.html. Academic Integrity “Any test, paper or report submitted by you and that bears your name is presumed to be your own original work that has not previously been submitted for credit in another course unless you obtain prior written approval to do so from your instructor. In all of your assignments, including your homework or drafts of papers, you may use words or ideas written by other individuals in publications, web sites, or other sources, but only with proper attribution. “Proper attribution” means that you have fully identified the original source and extent of your use of the words or ideas of others that you reproduce in your work for this course, usually in the form of a footnote or parenthesis.” —Report of the UCB Academic Dishonesty and Plagiarism Subcommittee, June 18, 2004 { Students who are found to have plagiarized or cheated in the course will receive an F. Extensions and Late Work { Extensions will be granted only in case of medical and family emergencies. { Late problem sets without prior notification of an emergency will not be accepted. { Your lowest score on a problem set during the semester will be dropped. { Term papers submitted after the deadline will immediately lose one grade step (e.g., from B+ to B) and an additional step every 24 hours thereafter. Regrades { You have one week after a problem set is returned to request a regrade of a problem. { Requests must come with a written explanation of why you would like a regrade. { When a problem is regraded, the score may go up, down, or remain the same. { Regrade requests are for problem sets only. Term papers will not be regraded. Accommodations for Students with Disabilities If you have a letter of accommodation from the Disabled Students Program, please let us know as soon as possible so that we can do whatever we can to help you in the course. 4/5 Our Policy on Sexual Violence and Harassment Sexual violence and sexual harassment have no place in a learning environment. Therefore, in alignment with Title IX of the Education Amendments of 1972, it is the policy of the University of California (Sexual Harassment and Sexual Violence Policy) to prohibit sexual harassment, sexual assault, domestic/dating violence, and stalking. The UC Sexual Violence and Sexual Harassment Policy requires that the University immediately implement interim remedies and permanent support measures, when necessary, for victims/survivors. If you or someone you know experiences sexual violence or harassment, there are options, rights, and resources, including assistance with academics, reporting, and medical care. Visit survivorsupport.berkeley.edu or call the 24/7 Care Line at 510-643-2005. 5/5.
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