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Core Logic
2004/2005; 1st Semester
Institute for Logic, Language & Computation
Universiteit van Amsterdam

Instructor: Dr Benedikt Löwe
Vakcode: MolCL6
ECTS: 6
Time: Wednesday 13:15 - 17:00
Place: P.017
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: The first part of the course will cover the history of logic from Aristotle to the nineteenth century. In the second part, we will cover important areas of modern logic, in particular applications of modal logic, and logical methods in linguistics, philosophy and mathematics.

Organization.

Preliminary course syllabus.
September 8
  • 13-15. Organisation of the Course. Logic in the different scientific disciplines.
  • 15-17. MoL Room Committee Elections. Q/A Session of the Student Mentors.
  • Homework Set #1: PDF File (Deadline: September 15th, 2004.)
  • Lecture Slides #1: PDF File
September 15
  • 13-15. Origins of logic: Greek mathematics (Euclid) and Greek disputations. The Square of Oppositions. Aristotelian syllogistics.
  • 15-17. Guest Lecture. Jeroen Bons (Utrecht), The History of Rhetoric.
  • Homework Set #2: PDF File (Deadline: September 22nd, 2004.)
  • Lecture Slides #2: PDF File
  • The 24 valid moods.
September 22
  • 13-15. More on syllogistics. Aristotelian Modal Logic. Stoic and Megarian Logic. Boëthius.
  • 15-17. Practice Session. Syllogistics.
  • Homework Set #3: PDF File (Deadline: September 29th, 2004.)
  • Lecture Slides #3: PDF File
September 29
October 6
  • 13-15. More on Abelard. The Universities. Logic in the late middle ages (XIIIth and XIVth century). Some game-theoretic interpretations of logic: Dialogic logic.
  • Practice Session. Games and logic.
  • Homework Set #5: PDF File (Deadline: October 13th, 2004.)
  • Lecture Slides #5: PDF File
  • P.V.Spade, Why Don't Mediaeval Logicians Ever Tell Us What They're Doing? Or, What Is This, A Conspiracy?, preprint 2000: PDF File
October 13
  • 13-15. Termistic logic. Insolubles. Obligationes.
  • Guest Lecture. Jaap Maat (Amsterdam), Logic in the XVIIth century.
  • Homework Set #6: PDF File (Deadline: October 20th, 2004.)
  • Lecture Slides #6: PDF File
  • Guidelines for writing summaries
  • Slides of the Guest Lecture "Logic in the XVIIth century": PDF-File
October 20
  • 13-15. The great changes between 1450 and 1550. Leibniz ("calculemus"). De Morgan. Boole. Boolean algebras as mathematizations of reasoning.
  • Practice Session. Partial orders, lattices, Boolean algebras.
  • Homework Set #7: PDF File (Deadline: November 3rd, 2004.)
  • Lecture Slides #7: PDF File
October 27 No classes (EXAM WEEK).
November 3
  • 13-15. Algebraic approaches to logic in the XIXth century. The birth of modern logic. First-order logic.
  • Practice Session. Basics of first order logic.
  • Homework Set #8: PDF File (Deadline: November 10th, 2004.)
  • Lecture Slides #8: PDF File
November 10
  • 13-15. Foundations of Mathematics. The Grundlagenkrise der Mathematik.
  • Guest Lecture. Yde Venema (Amsterdam), Algebraic Logic / Duality.
  • Homework Set #9: PDF File (Deadline: November 17th, 2004.)
  • Lecture Slides #9: PDF File
  • David Hilbert, Mathematische Probleme. Vortrag, gehalten auf dem internationalen Mathematiker-Kongreß zu Paris 1900. PDF-File.
November 17
November 24
  • 13-15. Recursion Theory. Theoretical Computer Science and Complexity Theory. Independence Results in Set Theory.
  • 15-17. Guest Lecture. Leen Torenvliet (Amsterdam), Mathematical Logic and its relation to the P=NP problem.
  • Homework Set #11: PDF File (Deadline: December 1st, 2004.)
  • Lecture Slides #11: PDF File
  • Robert I. Soare, Computability and recursion, Bulletin of Symbolic Logic 2 (1996), p.284-321 (PS-file)
December 1
  • 13-15. Proof Theory. Tarski. Model Theory. The modern view of modal logic: Kripke models and frames.
  • 15-17. Guest Lecture. Johan van Benthem (Amsterdam), Information Update in Communication.
  • Homework Set #12: PDF File (Deadline: December 8th, 2004.)
  • Lecture Slides #12: PDF File
  • Johan van Benthem, 'One is a lonely number': on the logic of communication, ILLC Publications PP-2003-07; PDF-File
December 8
  • 13-15. Applications of Modal Logic. An overview of recent developments in mathematical logic.
  • 15-17. Guest Lecture. Thomas Müller (Oxford), Temporal logic and the logic of agency: PDF-File
  • Homework Set #13: PDF File (Deadline: December 15th, 2004.)
  • Lecture Slides #13: 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 15
  • 13-15. Theories and formalisms for truth.
  • 15-17. Guest Lecture. Maarten de Rijke (Amsterdam). Search.
  • Thomas Bolander, Self-Reference and Logic, Phi News 1 (2002), p.9-44: PDF File.
December 22 No classes (EXAM WEEK).
Last update : December 15th, 2004