Course Modules

Course Overview

Course Overview
Module Completed Module In Progress Module Locked
Course Overview 1173294  
  • Attachment
    Syllabus Syllabus
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  • Context Module Sub Header

    Textbook

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  • External Url
    P. Smith, Introduction to Godel's Theorems P. Smith, Introduction to Godel's Theorems
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  • Context Module Sub Header

    Additional Readings

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  • External Url
    G. Boolos, J. P. Burgess, and R. Jeffrey, Computability and Logic G. Boolos, J. P. Burgess, and R. Jeffrey, Computability and Logic
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  • External Url
    P. Raatikainen, Godel's Incompleteness Theorems, Stanford Encyclopedia of Philosophy P. Raatikainen, Godel's Incompleteness Theorems, Stanford Encyclopedia of Philosophy
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  • External Url
    Have fun this semester! Have fun this semester!
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Introduction to Incompleteness (1/26)

Introduction to Incompleteness (1/26)
Module Completed Module In Progress Module Locked
Introduction to Incompleteness (1/26) 1173320  
  • Attachment
    Introductory Slides: The Many Routes to Godel's Theorems Introductory Slides: The Many Routes to Godel's Theorems
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  • Attachment
    Reading: R. Smullyan, The general idea behind Godel's proof Reading: R. Smullyan, The general idea behind Godel's proof
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  • Context Module Sub Header

    Historical and Philosophical Background

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  • External Url
    Hilbert's Program, Stanford Encyclopedia of Philosophy Hilbert's Program, Stanford Encyclopedia of Philosophy
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  • External Url
    Kurt Godel, Stanford Encyclopedia of Philosophy Kurt Godel, Stanford Encyclopedia of Philosophy
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  • External Url
    R. Zach, Hilbert's program then and now R. Zach, Hilbert's program then and now
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  • Attachment
    Chapter 1: Godel's Life and Work, in In the Light of Logic by S. Feferman Chapter 1: Godel's Life and Work, in In the Light of Logic by S. Feferman
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  • Context Module Sub Header

    Introductions to Godel's Theorems

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  • External Url
    What is Godel's Theorem?, Scientific American What is Godel's Theorem?, Scientific American
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  • External Url
    Godel, Turing and Friends, Lecture by Scott Aaronson Godel, Turing and Friends, Lecture by Scott Aaronson
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  • External Url
    Video: Kurt Gödel and the Limits of Mathematics. Mark Colyvan (P1) Video: Kurt Gödel and the Limits of Mathematics. Mark Colyvan (P1)
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  • External Url
    Video: Kurt Godel and the Limits of Mathematics. Mark Colyvan (P2) Video: Kurt Godel and the Limits of Mathematics. Mark Colyvan (P2)
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  • Attachment
    G. Boolos, Godel's Second Incompleteness Theorem Explained in Words of One Syllable, Mind, Mind, Vol. 103. 1994 G. Boolos, Godel's Second Incompleteness Theorem Explained in Words of One Syllable, Mind, Mind, Vol. 103. 1994
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Basic Concepts (1/31, 2/2, 2/7)

Basic Concepts (1/31, 2/2, 2/7)
Module Completed Module In Progress Module Locked
Basic Concepts (1/31, 2/2, 2/7) 1173321  
  • Context Module Sub Header

    Mathematical Background - Sets, Relations and Functions

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  • Attachment
    Mathematical Methods for Linguistics, Chapters 1 - 3 Mathematical Methods for Linguistics, Chapters 1 - 3
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  • Context Module Sub Header

    Functions, Enumerations, Diagonalization Arguments

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  • Context Module Sub Header

    [IGT] Chapter 2

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  • Attachment
    Open Logic Textbook - Functions Open Logic Textbook - Functions
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  • Attachment
    Open Logic Textbooks - Enumerations Open Logic Textbooks - Enumerations
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  • Context Module Sub Header

    First Order Logic, Revisited

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  • Attachment
    E. Pacuit, Notes on First Order Logic E. Pacuit, Notes on First Order Logic
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  • Attachment
    Boolos, Burgess and Jeffrey, Chapters 9-10, A Precis on First-Order Logic (Syntax and Semantics) Boolos, Burgess and Jeffrey, Chapters 9-10, A Precis on First-Order Logic (Syntax and Semantics)
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  • Context Module Sub Header

    Formal Arithmetic, First Steps

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  • Attachment
    Worksheet 1 - Introduction to Formal Arithmentic Worksheet 1 - Introduction to Formal Arithmentic
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  • Context Module Sub Header

    Mathematical Induction

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  • Attachment
    Open Logic Textbook - Induction Open Logic Textbook - Induction
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Exam 1 (2/9)

Exam 1 (2/9)
Module Completed Module In Progress Module Locked
Exam 1 (2/9) 1175491  
  • Attachment
    Review sheet (questions for the exam will be taken from this review sheet). Review sheet (questions for the exam will be taken from this review sheet).
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Computability, Primitive Recursive Functions, Recursive Functions (2/14, 2/16, 2/21)

Computability, Primitive Recursive Functions, Recursive Functions (2/14, 2/16, 2/21)
Module Completed Module In Progress Module Locked
Computability, Primitive Recursive Functions, Recursive Functions (2/14, 2/16, 2/21) 1175492  
  • Context Module Sub Header

    [IGT] Chapters 3, 4 and 14

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  • Attachment
    Computability and Logic: Chapter 6: Recursive Functions Computability and Logic: Chapter 6: Recursive Functions
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  • Attachment
    Worksheet 2 - Primitive Recursive Functions Worksheet 2 - Primitive Recursive Functions
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Formal Arithmetic (2/23, 2/28)

Formal Arithmetic (2/23, 2/28)
Module Completed Module In Progress Module Locked
Formal Arithmetic (2/23, 2/28) 1175493  
  • Context Module Sub Header

    [IGT] Chapters 9 - 13

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Q is PR-Adequate (3/2, 3/7)

Q is PR-Adequate (3/2, 3/7)
Module Completed Module In Progress Module Locked
Q is PR-Adequate (3/2, 3/7) 1175494  
  • Context Module Sub Header

    [IGT] Chapters 5, 16, 17

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  • Attachment
    Computability and Logic: Section 16.2: Q is PR-adquate Computability and Logic: Section 16.2: Q is PR-adquate
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Arithmetization of Syntax (3/9, 3/14, 3/16)

Arithmetization of Syntax (3/9, 3/14, 3/16)
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Arithmetization of Syntax (3/9, 3/14, 3/16) 1175495  
  • Context Module Sub Header

    [IGT] Chapters 19 & 20

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  • Attachment
    Computability and Logic: Chapter 15: Arithematization Computability and Logic: Chapter 15: Arithematization
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NO CLASS - SPRING BREAK (3/19 - 3/26)

NO CLASS - SPRING BREAK (3/19 - 3/26)
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NO CLASS - SPRING BREAK (3/19 - 3/26) 1175497  

Diagonalization Theorem, First Incompleteness Theorem (3/28, 3/30, 4/4)

Diagonalization Theorem, First Incompleteness Theorem (3/28, 3/30, 4/4)
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Diagonalization Theorem, First Incompleteness Theorem (3/28, 3/30, 4/4) 1175496  
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    [IGT] Chapters 21 - 24

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  • External Url
    Godel's Incompleteness Theorem, Section 2 (SEP) Godel's Incompleteness Theorem, Section 2 (SEP)
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Second Incompleteness Theorem (4/6)

Second Incompleteness Theorem (4/6)
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Second Incompleteness Theorem (4/6) 1175514  
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    [IGT] Chapters 31, 32

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  • External Url
    Godel's Incompleteness Theorem, Section 3 (SEP) Godel's Incompleteness Theorem, Section 3 (SEP)
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Undecidability and Incompleteness (4/11, 4/18)

Undecidability and Incompleteness (4/11, 4/18)
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Undecidability and Incompleteness (4/11, 4/18) 1176532  
  • Context Module Sub Header

    Computability and Incompleteness: [IGT] Chapters 40 - 43

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LECTURE CANCELED (4/13) - Away at the Pacific APA

LECTURE CANCELED (4/13) - Away at the Pacific APA
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LECTURE CANCELED (4/13) - Away at the Pacific APA 1175515  

Lob's Theorem and Provability Logic (4/20, 425)

Lob's Theorem and Provability Logic (4/20, 425)
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Lob's Theorem and Provability Logic (4/20, 425) 1175587  
  • Context Module Sub Header

    [IGT] Chapters 33 & 34

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  • Attachment
    Computability and Logic: Chapter 27: Provability Logic Computability and Logic: Chapter 27: Provability Logic
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Epistemic Arithmetic and Absolute Provability (4/27, 5/2)

Epistemic Arithmetic and Absolute Provability (4/27, 5/2)
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Epistemic Arithmetic and Absolute Provability (4/27, 5/2) 1175588  
  • External Url
    P. Koellner, Godel's Disjunction P. Koellner, Godel's Disjunction
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Student Presentations (5/4, 5/9/ 5/11)

Student Presentations (5/4, 5/9/ 5/11)
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Student Presentations (5/4, 5/9/ 5/11) 1175589  
  • Context Module Sub Header

    Presentation Topics

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  • Context Module Sub Header

    Speed-Up Theorems: [IGT] Chapter 28

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    Second-Order Arithmetic: [IGT] Chapter 29

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    Isaacson's Thesis: [IGT] Chapter 30

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  • Context Module Sub Header

    Truth and Provability: [IGT] Chapter 23

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  • External Url
    H. Gaifman, Naming and Diagonalization, From Cantor to Godel to Kleene, Logic Journal of the IGPL, 14: 709–728, 2006 H. Gaifman, Naming and Diagonalization, From Cantor to Godel to Kleene, Logic Journal of the IGPL, 14: 709–728, 2006
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  • External Url
    N. Yanofsky, A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points, Bulletin of Symbolic Logic, 2003 N. Yanofsky, A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points, Bulletin of Symbolic Logic, 2003
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  • Attachment
    Kirzman and Raz: Surprise Exam & The Second Incompleteness Theorem Kirzman and Raz: Surprise Exam & The Second Incompleteness Theorem
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  • Attachment
    P. Egre, The Knower Paradox in the Light of Provability Interpretations of Modal Logic, Journal of Logic, Language and Information, 2005 (This is a long paper, so you'll need to focus on a specific section) P. Egre, The Knower Paradox in the Light of Provability Interpretations of Modal Logic, Journal of Logic, Language and Information, 2005 (This is a long paper, so you'll need to focus on a specific section)
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  • Attachment
    T. Franzen, The Popular Impact of Godel's Incompleteness Theorems, Notices of the AMS, 2006 T. Franzen, The Popular Impact of Godel's Incompleteness Theorems, Notices of the AMS, 2006
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  • External Url
    P. Raattkainen, On the Philosophical Relevance of Godel's Incompleteness Theorems, Publié dans Revue internationale de philosophie, 2005 P. Raattkainen, On the Philosophical Relevance of Godel's Incompleteness Theorems, Publié dans Revue internationale de philosophie, 2005
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  • Attachment
    M. Davis, What did Godel believe? M. Davis, What did Godel believe?
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  • External Url
    S. Shapiro, Idealization, Mechanism, and Knowability, Chapter 8 in Godel's Disjunction, 2016 S. Shapiro, Idealization, Mechanism, and Knowability, Chapter 8 in Godel's Disjunction, 2016
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  • External Url
    T. Williamson, Absolute Provability and Safe Knowledge of Axioms, Chapter 10 in Godel's Disjunction, 2016 T. Williamson, Absolute Provability and Safe Knowledge of Axioms, Chapter 10 in Godel's Disjunction, 2016
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  • Attachment
    B. Buldt, The Scope of G¨odel’s First Incompleteness Theorem (This is a long paper, so you will have to focus on 1-2 sections) B. Buldt, The Scope of G¨odel’s First Incompleteness Theorem (This is a long paper, so you will have to focus on 1-2 sections)
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minimum score must view must submit must contribute