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Core Logic 2005/2006; 1st Semester Institute for Logic, Language & Computation Universiteit van Amsterdam

Instructor: Dr Benedikt Löwe
Vakcode: MolCL6
ECTS: 6
Time: Tuesday 14-17
Place: P.227
Course language: English
Teaching Assistant: Dipl.-Math. Stefan Bold (sbold@science.uva.nl)
Intended Audience: M.Sc. students of Logic

Prerequisites: Basic knowledge of logic. (If students feel that they don't satisfy this criterion, they should take the course "Basic Logic" in addition to Core Logic.)

Goal of this course. This course is the obligatory course for the M.Sc. Programme in Logic in the first semester. It is the time and place to meet for all of the logic students. In addition to that, the course should give a broad historical overview of logic in general, and with particular emphasis of the areas of research that the ILLC is involved in.

Content of the course: This course will cover the history of logic from Aristotle to the XXIst century. We will discuss the Greeks, the Middle Ages, Enlightenment, Leibniz, the dawn of mathematical logic in the XIXth century, and then the diversification of logic in mathematics, computer science and philosophy in the XXth century. In the second half of the semester we will present relevant modern research areas.

Organization. The course will be organized in Lectures and Colloquia (with invited guest speakers). The grade will be determined by weekly homework (264 points) and written summaries of guest lectures (90 points). Your grade will depend on your total number of points (out of 354). 180 points will be enough to pass the course.

• Homework. There will be 12 homework sets, each worth 22 points. The homework sets are due one week after they are handed out. Homework will be graded by Stefan Bold. You can either hand it in during the lecture or send it as a PDF file to him by e-mail on or before the day of the deadline.
• Summaries. There will be a number of guest lectures for which you are supposed to write 100-200 word summaries. The deadline for the summaries is one week after the guest lecture. Note that the upper limit of the numbers of words is strict, and points will be deducted for longer summaries. If you are not acquainted with writing summaries, here is a quick guide to writing summaries with a lot of details and links.

  Each summary will be graded on a 0-15 scale for both content and style (15-13: "excellent"; 12-10: "good"; 9-6: "OK"; 5-0: "not OK"). As a consequence, each summary will have between 0 and 30 points. Your three best scores on summaries are added up to give the total summary score out of 90. (Yes, this does mean that you can pick the three guest lectures that you find most interesting.)

  • Grading of content. For this, we shall check your summary against the list of all important points from the lecture, weighted by the order of importance. It is not enough to merely mention a point made, but to embed it into the argumentative structure of the summary, so just dropping names in a parenthetical remark won't be enough. Note that due to the word limit of 200 words, you cannot include all of the important points, so you will have to make a choice.
  • Grading of style. The grade for style is based on the clarity of the thesis statement, your choice of the "red thread", the general set-up of the summary, the argumentative structure of individual sentences, stylistic issues, grammar and spelling. As an indication, you can check the GRE Scoring Guidelines and the GRE Samples for essay writing with grades. (As a rough guideline, benchmark 6 would be 'excellent', benchmark 5 between 'excellent' and 'good', benchmark 4 between 'good' and 'OK', benchmark 3 'OK', and benchmark 2 and benchmark 1 'not OK'.) Please keep in mind that the example essays are much longer than the summaries you are supposed to write (the example essays for the good and excellent grades are all more than 400 words long).

Preliminary course syllabus.

September 6	14-16. Organisation of the Course. Logic in the different scientific disciplines. 16-17. Q/A Session of the Student Mentors. Homework Set #1: PDF File (Deadline: September 13th, 2005.) Lecture Slides #1: PDF File Entry "Logic" in Wikipedia (Discussion) Thomas Hofweber, Logic and Ontology, in: Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Summer 2005 Volker Peckhaus, 19th century logic between philosophy and mathematics, Bulletin of Symbolic Logic 5 (1999), p. 433-450.
September 13	14-16. Origins of logic: Greek mathematics (Euclid) and Greek disputations. The Square of Oppositions. Aristotelian categories. 16-17. Guest Lecture. Rens Bod (Amsterdam), Unifying Models of Language, Music and Vision. PDF File. Homework Set #2: PDF File (Deadline: September 20th, 2005.) Lecture Slides #2: PDF File
September 20	14-16. Aristotelian syllogistics. Aristotelian Modal Logic. 16-17. Guest Lecture. Maricarmen Martínez (Amsterdam), Content-dependent reasoning. PDF File. Homework Set #3: PDF File (Deadline: September 27th, 2005.) Lecture Slides #3: PDF File Fred Richman, Equivalence of Syllogisms, Notre Dame Journal of Formal Logic 45 (2004), p.215-233; PDF File The 24 valid moods.
September 27	14-16. Aristotelian Temporal Logic. Stoic and Megarian Logic. Neoplatonism. Boëthius. Logic and Theology in the Middle Ages. 16-17. Guest Lecture. Marian Counihan (Amsterdam), Logic meets psychology. . PDF File. . Lecture Slides #4: PDF File Homework Set #4: PDF File (Deadline: October 4th, 2005.) Christopher J. Martin, The Logic of Negation in Boethius, Phronesis 36 (1991), p. 277-304: PDF File.
October 4	14-16. Logic and Theology in the Middle Ages (ctd.). Logic as ars sermocinalis. Trivium and Quadrivium. Anselm of Canterbury. The early middle ages. Peter Abelard. 16-17. Guest Lecture. Wolfram Hinzen (Amsterdam), Philosophy of Language and Mind. Homework Set #5: PDF File (Deadline: October 11th, 2005.) Lecture Slides #5: PDF File Paul Vincent Spade, Why Don't Mediaeval Logicians Ever Tell Us What They're Doing? Or, What Is This, A Conspiracy?, preprint 2000: PDF File Hans Thijssen, Condemnation of 1277, in: Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Spring 2003 Edition)
October 11	14-16. The Universities. Logic in the late middle ages (XIIIth and XIVth century). Termistic logic. Insolubles. 16-17. Guest Lecture. Jaap Maat (Amsterdam), Logic in the XVIIth century. Homework Set #6: PDF File (Deadline: October 18th, 2005.) Lecture Slides #6: PDF File Lynn H. Nelson, The Avignon Papacy, 1305-1378, course notes for History 108, "Introduction to Medieval History" at Kansas University.
October 18	14-16. Some game-theoretic interpretations of logic: Dialogic logic. Obligationes. The great changes between 1450 and 1550. Leibniz ("calculemus"). 16-17. Guest Lecture. Yde Venema (Amsterdam), Logic and Algebra. Homework Set #7: PDF File (Deadline: November 1st, 2005.) Lecture Slides #7: PDF File
October 25	No classes (EXAM WEEK).
November 1	14-16. Algebraic approaches to logic in the XIXth century. De Morgan. Boole. Boolean algebras as mathematizations of reasoning. Geometry as a prototype for abstract mathematics. 16-17. Guest Lecture. Göran Sundholm (Leiden). The Expulsion of the Judging Subject from Logical Paradise: The History of Logic from Aristotle until the Present Day. Homework Set #8: PDF File (Deadline: November 8th, 2005). Lecture Slides #8: PDF File
November 8	14-16. Naïve Set Theory as an example for abstract mathematics. First-order logic: Frege, Hilbert, Gödel. 16-17. Guest Lecture. Eric Pacuit (Amsterdam), Games, Puzzles, Logic. PDF File. Homework Set #9: PDF File (Deadline: November 15th, 2005.) Lecture Slides #9: PDF File
November 15	14-16. Foundations of Mathematics. The Grundlagenkrise der Mathematik. Axiomatization of Set Theory. 16-17. Guest Lecture. Jelle Zuidema (Amsterdam), Formal Models of the Evolution of Language: PDF File. Homework Set #10: PDF File (Deadline: November 22nd, 2005.) Lecture Slides #10: PDF File David Hilbert, Mathematische Probleme. Vortrag, gehalten auf dem internationalen Mathematiker-Kongreß zu Paris 1900. PDF-File. Richard Zach, Hilbert's "Verunglückter Beweis," the first epsilon theorem, and consistency proofs, History and Philosophy of Logic 25 (2004), p.79-–94. Richard Zach, The practice of finitism: Epsilon calculus and consistency proofs in Hilbert's Program, Synthese 137 (2003), p.211-259.
November 22	14-16. Gödel's Incompleteness Theorems. Proof Theory. Computability: Turing and the Halting Problem. The Church-Turing Thesis. Recursion Theory. Church and his students. 16-17. Guest Lecture. Khalil Sima'an (Amsterdam), Language Use and Uncertainty. PDF File. Homework Set #11: PDF File (Deadline: November 29th, 2005.) Lecture Slides #11: PDF File Robert I. Soare, Computability and recursion, Bulletin of Symbolic Logic 2 (1996), p.284-321 (PS-file)
November 29	14-16. Model Theory. Tarski. Set Theory. The modern view of modal logic: Kripke models and frames. Homework Set #12: PDF File (Deadline: December 13th, 2005.) Lecture Slides #12: PDF File 16-17. Guest Lecture. Johan van Benthem (Amsterdam), Logics of Communication and Interaction.
December 6	Class cancelled.
December 13	14-16. Applications of Modal Logic: standard translation, intuitionistic logic, provability logic. An overview of recent developments in mathematical logic. 16-17. Guest Lecture. Albert Visser (Utrecht): Varieties of arithmetical experience. (Deadline for summary: December 20th in mailbox S.Bold or by e-mail to sbold@science.uva.nl.) Lecture Slides #13: PDF File Joel D.Hamkins, A simple maximality principle, Journal of Symbolic Logic, 68 (2003), p.527-550: PDF File. Sam Buss, Alekos Kechris, Anand Pillay, Richard Shore, The prospects for mathematical logic in the twenty-first century, Bulletin of Symbolic Logic 7 (2001), p.169-196 (PS-file) W. Hugh Woodin, The continuum hypothesis I, Notices of the American Mathematical Society 48 (2001), p.567-576: PDF-File W. Hugh Woodin, The continuum hypothesis II, Notices of the American Mathematical Society 48 (2001), p.681--690: PDF-File
December 20	No classes (EXAM WEEK).

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Last update : December 13th, 2005