Unit 1: Introduction to simple logical systems

Tue Jan 16 | Bach, Escher, Gödel (Overview)
Strange Loops, Self-reference and Paradox, Logic Puzzles |
Slides (Bach)*
Accompaniment Slides (Gödel)* |

Thu Jan 18 | Why Set Theory and Logic? Why Symbolic Reasoning?
Classification Problems and Equivalence Relations, Venn Diagrams, Formal Logic, Infinite Sets Introduction: A Musico-Logical
Offering
Good King Wenceslas |
Notes/SQ
Music Slides* |

Tue Jan 23 | Zeno and Infinity
Consistency and Completeness, Geometric Series and the Infinite Hotel (Number Theory & Infinity) Three-part Invention
Discuss Problem Set 1 |
Notes/SQ
Infinite Hotel Music Slides* Slides (algebra)* Problem Set 1 |

Thu Jan 25 | The MU Puzzle
Characteristic Ingredients of Formal Systems, Practice with MIU system, Reasoning Inside / Outside the System, Decision Procedures. Chapter I: MU-Puzzle
Begin discussing Problem Set 2.1-4 (including MU-Puzzle program) |
Notes/SQ
Problem Set 2 MU-Program |

Tue Jan30 | Carroll’s Paradox
“Infinite regress”, Modus Ponens. Two-part Invention; Chapter
II: Meaning and Form in Mathematics
Bach Two-part Invention
#4
Discuss Problem Set 2 |
Notes/SQ
Music Slides* Problem Set 2 |

Thu Feb 1 | Meaning and Form in Mathematics
Variables and axiom Schema, isomorphisms and meaning, the Requirement of Formality, proof and generalization. More Chapter II: Meaning and Form in Mathematics
Discuss Problem Set 3 |
Problem Set 3 |

Sun Feb 4 | Exam #1 |