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

Instructor: Dr Benedikt Löwe
Vakcode: MolCL6
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.

Preliminary course syllabus.
September 6
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
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).

Last update : December 13th, 2005