Schedule of topics and
Week 1: Survey of What is Ahead.
Reading: "What is Logic?" on pages 3-6 in the Nolt textbook. A Very Brief History of Mathematical Logic. History of Propositional Logic. Finish chapter 1 in Nolt. Here is the author's list of errors in his book; his .mht file opens in Internet Explorer using Java, but not in Firefox or in Chrome. Here is my additional list of errors.
Week 2: Propositional Logic: Syntax and Semantics.
Reading: Chapters 2 and 3 in Nolt. Techniques of Translation into Propositional Logic.
Week 3-5: Propositional Logic: Inference and Metatheory.
Reading: Chapters 4 and 5 in Nolt, but skip section 4.5 except for its last three paragraphs.
Week 6: Predicate Logic with Identity and Functions: Syntax.
Reading: Chapter 6 in Nolt.
Weeks 7-8: Predicate Logic: Semantics.
Reading: Chapter 7 in Nolt. Skip 7.4, but be able to assess validity of sequents on p. 221.
Week 9: Predicate Logic: Inference, the Logic of Binary Relations, Soundness, Completeness, Implicit Assumptions, Inexpressibility.
Reading: Browse Chapters 8 and 9 in Nolt.
The Logic of Binary Relations.
Week 10: Predicate Logic: Church's Thesis, Undecidability and the Halting Problem, Decidable Fragments.
Reading: Browse chapter 10 in Nolt.
Week 11: Formal Systems.
and the Nature of Mathematical Truth." Reading in Hofstadter: Introduction: A Musico-Logical Offering; Chapter 1: The MU-puzzle; Chapter 2: Meaning and Form in Mathematics; Chapter 3: Figure and Ground.
Weeks 12-13: Consistency, Completeness and Recursive Structures.
Reading: Contracrostipunctus; Chapter 4: Consistency, Completeness and Geometry; Gödel, Escher, Bach: A Mental Space Odyssey (only the first 3/4 of Lecture 3 of the M.I.T. lectures on chapter 4 of GEB). (optional: Chapter 5: Recursive Structures and Processes);
Chapter 7: The Propositional Calculus.
Weeks 14-15: Gödel's Incompleteness Theorems.
Reading: Chapter 8: Number Theory; Chapter 9: Mumon and Gödel, pp. 259-275; Gödel's First Incompleteness Theorem; Chapter 14 (On Formally Undecidable Propositions of TNT and Related Systems), the section "Gödel's Second Theorem."
The above schedule of course topics may be changed somewhat as we
progress through the semester, but these changes, if any, are not
expected to affect the schedule of
the homeworks and tests.
back to the main syllabus
May 5, 2013