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Home , Algebraic logic, George Boole

Algebraic and Its Critics The from Leibniz to Frege University of Chicago Spring Quarter 2014

Instructor: Marko Malink Course ID: PHIL 39406 E-mail: [email protected] Location: 302 Cobb Office Hours: T, 1:30-3:30 pm, Walker 202B Times: TR, 12:00-1:20pm Instructor: Anubav Vasudevan E-mail: [email protected] Office Hours: T, 1:30-3:30 pm, Walker 202D

Course Description: The study of logic in the second half of the 19th century was dominated by an algebraic approach to the subject. This tradition, as exemplified in ’s Laws of Thought, aimed to develop a of deductive reasoning based on the standard algebraic techniques employed in arithmetic. In this course, we will trace the historical development of the algebraic tradition in logic, beginning with the early attempts of Leibniz to formulate a . We will then consider various aspects of the algebraic systems of logic developed in the 19th century in the works of Boole, Jevons, DeMorgan, Peirce, and Schröder, and conclude with an examination of Frege’s critique of Boole’s system in to his own Begriffsschrift. Readings: All readings will be made available for download through the “Chalk” course website (to access Chalk, navigate to chalk.uchicago.edu and login using your CNetID and password). If you are not able to access the Chalk site please let us know, so that we can grant you access manually. Course Requirements: Undergraduate students are required to write two papers: a 5-7 page midterm paper and a 8-10 page final paper. These two papers will be worth 80% of the final grade. The remaining 20% of the final grade will be assessed on the basis of participation in class. The midterm paper should address a topic related to the material discussed in weeks 1-4 of the course, and is due on Monday, April 28. The final paper should address a topic related to the material discussed in weeks 5-10 of the course, and is due on Friday, June 6. Graduate students are required to write one paper (15-20 pages in length) on any related topic, due on Friday, June 6. Syllabus: Week 1. Introduction and April 1: Introduction April 3: Aristotle’s Syllogistic - Aristotle, Prior Analytics, R. Smith (tran.), ch. 1-2 and 4-7, pp. 1-12. - M. Malink, Aristotle’s Modal Syllogistic, Harvard University Press 2013, ch. 1-6, pp. 19-101. Week 2. Leibniz April 8: Leibniz I G.W. Leibniz, General about the Analysis of Concepts and of Truths (1686), in G.H.R. Parkinson (tran. and ed.), Leibniz: Logical Papers, Oxford University Press 1966, pp. 47-87. April 10: Leibniz II Optional: W. Lenzen, ‘Leibniz’ Logic’, in D.M. Gabbay and J. Woods (eds.), Handbook of the History of Logic, Volume 3. The Rise of Modern Logic: from Leibniz to Frege, Elsevier 2004, pp. 1-83. Week 3. Boole April 15: Boole I G. Boole, The Mathematical Analysis of Logic (1847), pp. 14-48. April 17: Boole II G. Boole, (1854), chapters 1-3, pp. 1-51. Week 4. Boole and Jevons April 22: Boole III G. Boole, The Laws of Thought (1854), ch. 4-5,15, pp. 52-79. April 24: Jevons - W.S. Jevons, Pure Logic (1864), ch. 4-10, 14-15, pp. 41-62, 88-103. - I. Grattan-Guinness, ‘The Correspondence between George Boole and Stanley Jevons, 1863-64,’ History and of Logic, vol. 12, issue 1 (1991), pp. 16-19, 23-31 (ltrs. 1-8) Optional: T. Hailperin, ‘Boole’s isn’t ’, Magazine, vol. 54, no. 4 (1981), pp. 172-184. Week 5. De Morgan April 29: De Morgan I - A. De Morgan, ’On the : II’ (1864), in W. Stark (ed.), On the Syllogism and other Logical Writings, Yale University Press 1966, pp. 50-68. - D. Merrill, and the Logic of Relations, Kluwer Academic Publishers 1990, ch. 3 (‘Generalizing the Copula’), pp. 48-78. May 1: De Morgan II - A. De Morgan, ’On the Syllogism: III’ (1864), in W. Stark (ed.), On the Syllogism and other Logical Writings, Yale University Press 1966, §§1–6, pp. 74-91. - D. Merrill, Augustus De Morgan and the Logic of Relations, Kluwer Academic Publishers 1990, ch. 4 (’The Problem of Form and Matter’), pp. 89-112. Week 6. Peirce May 6: Peirce I C.S. Peirce, ‘Description of a Notation for the Logic of Relatives’ (1870), in C. Hartshorne and P. Weiss (eds.), Collected Papers of , vol. 3, Cambridge University Press (1933), pp. 85-98. May 8: Peirce II - C.S. Peirce, ‘Description of a Notation for the Logic of Relatives’ (1870), pp. 85-98. Optional: G. Brady, From Peirce to Skolem, Elsevier 2000, ch. 2 (‘Peirce’s Calculus of Relatives: 1870’), pp. 23-50. Week 7. Peirce May 13: Peirce III C.S. Peirce, ‘The Logic of Relatives’ (1883), in C. Hartshorne and P. Weiss (eds.), Collected Papers of Charles Sanders Peirce, vol. 3, Cambridge University Press (1933), pp. 195-209. May 15: Peirce IV Optional: G. Brady, From Peirce to Skolem, Elsevier 2000, ch. 4 (‘Peirce on the Algebra of Relatives’), pp. 95-112. Week 8. Schröder vs. Frege May 20: Schröder vs. Frege I - E. Schröder, ‘Review of G. Frege’s Conceptual Notation’, in T.W. Bynum (tran. and ed.), : Conceptual Notation and Related Articles, Oxford University Press 1972, pp. 218-232. - G. Frege, ‘On the Aim of the Conceptual Notation’, in T.W. Bynum (tran. and ed.), Gottlob Frege: Conceptual Notation and Related Articles, Oxford University Press 1972, pp. 90-100. - G. Frege, ‘Boole’s Logical Formula-Language and my Concept-Script’, in G. Frege, Posthumous Works, ed. by H. Hermes, F. Kambartel, F. Kaulbach, tran. by P. Long & R. White, Blackwell Press 1979, pp. 47-52. May 22 Schröder vs. Frege II - G. Frege, ‘Boole’s Logical Calculus and the Concept-Script’, in G. Frege, Posthumous Works, ed. by H. Hermes, F. Kambartel, F. Kaulbach, tran. by P. Long & R. White, Blackwell Press 1979, pp. 9-46. - J. can Heijenoort, ‘Logic as Calculus and Logic as Language’, Synthese 17 (1967), pp. 324-330. - V. Peckhaus, ‘Calculus Ratiocinator vs. Characteristics Universalis? The Two Traditions in Logic, Revisited’, History and 25 (2004), 3-14. Week 9. Schröder vs. Frege and Tarski May 27: Schröder vs. Frege III - H. Sluga ‘Frege Against the Booleans’, Notre Dame Journal of Formal Logic 28 (1987), pp. 80-98 Optional: W. Goldfarb, ‘Logic in the Twenties: The Nature of the Quantifier’, Journal of Symbolic Logic 44 (1979), pp. 351-68. May 29: Tarski I TBA Week 10. Tarski June 3: Tarski II TBA Contacting the Instructors: If you wish to set up an appointment outside of our regularly scheduled office hours, please send us an e-mail, briefly describing your question and proposing a time at which we can meet. For filtering purposes, all course-related e-mails should include the expression ‘algebra’ somewhere in their subject line. This will ensure that your message will be replied to with the least possible delay. Except during scheduled office hours, phone calls are to be limited to time-sensitive queries or other emergencies.