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Core Logic
2006/2007; 1st Semester
Institute for Logic, Language & Computation
Universiteit van Amsterdam

Instructor: Dr Benedikt Löwe
Vakcode: MolCL6
Time: Wednesday 14-17
Place: I.001 (map to find building I)
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
  • 14-15. Q/A Session of the Student Mentors.
  • 15-17. Organisation of the Course. Logic in the different scientific disciplines.
  • Homework Set #1: PDF File (Deadline: September 13th, 2006.)
  • Lecture Slides #1: PDF File
  • 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. Jeroen Bons (Amsterdam), TBA.
  • Homework Set #2: PDF File (Deadline: September 20th, 2006.)
  • Lecture Slides #2: PDF File
  • Dmitri Panchenko, Thales and the Origin of Theoretical Reasoning, Configurations 1 (1993), p.387-414
September 20
  • 14-16. Aristotelian syllogistics. Aristotelian Modal Logic.
  • 16-17. Guest Lecture. Sara Uckelman (Amsterdam), How does a modern logician work on historical problems? (PDF file of the slides)
  • Homework Set #3: PDF File (Deadline: September 27th, 2006.)
  • 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 in life: or when logic meets cognition, from the ivory tower. PDF file of the slides.
  • Lecture Slides #4: PDF File
  • Homework Set #4: PDF File (Deadline: October 4th, 2006.)
  • Alan Code, Aristotle's response to Quine's objections to modal logic, Journal of Philosophical Logic 5 (1976), p. 159-186: PDF File.
  • 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. The Universities.
  • 16-17. Guest Lecture. Jelle Zuidema (Amsterdam), Formal Models of the Evolution of Language: PDF File.
  • Homework Set #5: PDF File (Deadline: October 11th, 2006.)
  • 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
  • Michael A. Covington, Scientia Sermocinalis: Grammar in Medieval Classifications of the Sciences, in: Nicola McLelland, Andrew Linn (eds.), Flores grammaticae: Essays in Memory of Vivien Law, p.49-54; PDF File
October 11
  • 14-16. The Universities (ctd). Logic in the late middle ages (XIIIth and XIVth century). Termistic logic. Insolubles.
  • 16-17. Guest Lecture. Jan-Willem Romeijn (Amsterdam), Probability and Logic: PDF file.
  • Homework Set #6: PDF File (Deadline: October 18th, 2005.)
  • Lecture Slides #6: PDF File
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. Jaap Maat (Amsterdam), Logic in the XVIIth century: PDF file.
  • Homework Set #7: PDF File (Deadline for Exercises 22, 23, and 24: November 8th, 2006. Deadline for Exercise 25: November 15th, 2006)
  • Lecture Slides #7: PDF File
October 25 No classes (EXAM WEEK).
November 1 Class Cancelled (MSc Logic Accreditation Visitation).
November 8
  • 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. Stephen Read (St. Andrews), Thomas Bradwardine and a fourteenth-century solution to the semantic paradoxes.
  • Homework Set #8: PDF File (Deadline: November 15th, 2006).
  • Lecture Slides #8: PDF File
November 15
  • 14-16. Naïve Set Theory as an example for abstract mathematics. First-order logic: Frege, Hilbert, Gödel.
  • 16-17. Guest Lecture. Ulle Endriss (Amsterdam), Multiagent Resource Allocation: PDF file.
  • Homework Set #9: PDF File (Deadline: November 22nd, 2006.)
  • Lecture Slides #9: PDF File
November 22
  • 14-16. Foundations of Mathematics. The Grundlagenkrise der Mathematik.
  • No Guest Lecture.
  • Homework Set #10: PDF File (Deadline: November 29th, 2006.)
  • Lecture Slides #10: PDF File
November 29
December 6
  • 14-16. Proof Theory. Computability: Turing and the Halting Problem. The Church-Turing Thesis. Recursion Theory. Model Theory. Tarski. Set Theory. The modern view of modal logic: Kripke models and frames.
  • Homework Set #12: PDF File (Deadline: December 13th, 2006.)
  • 16-17. Guest Lecture. Yde Venema (Amsterdam), Coalgebra. PDF file.
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. Johan van Benthem (Amsterdam), TBA.
December 20 No classes (EXAM WEEK).

Last update : December 12th, 2006