DOWNLOADABLE LECTURE NOTES

1. The Formalization of Mathematics, February, 1997, 11 pages.  TalkFormMath12pt[1].2.97

2. Ramsey Theory and Enormous Lower Bounds, April 5, 1997, 11 pages.  TalkRamThyEnLB

3. Transfer Principles in Set Theory, May 7, 1997, 21 pages.   TransPrin12pt050797

4. Axiomatization of Set Theory by Extensionality, Separation, and Reducibility, October 5, 1997, 12 pages.  TalkAxiomSetThy

5. From Russell’s Paradox to Higher Set Theory, October 10, 1997, 13 pages.  FromRusselltoSetThy

6. Finite Trees and the Necessary Use of Large Cardinals, January 10, 1998, 8 pages. FiniteTreesLC

7. Unprovable Theorems in Discrete Mathematics, April 26, 1999, 10 pages.  TalkUnpThmDisMath

8. A Theory of Strong Indiscernibles, April 28, 1999, 2 pages.  ThyStrongIndis

9. A Complete Theory of Everything: satisfiability in the universal domain, October 10, 1999, 15 pages. ACompThyEver101099

10. Decreasing Chains of Algebraic Sets, November 12, 1999, 12 pages. ChainsAlgSets

11. Discrete Independence Results, November 16, 1999, 13 pages.  DisIndResults

12. The Mathematical Meaning of Mathematical Logic, April 21, 2000, 14 pages.  MathMeanMathLogic042100

13. Does Mathematics Need New Axioms?, May 30, 2000, 13 pages.  NewAxioms_12pt.6.5.00

14. A Logician Looks at Programming, May 31, 2000, 4 pages. ALogicianLooks

15. Foundations of Mathematics: past, present, and future’ May 31, 2000, 8 pages. fom12pt5.31.00

16. Enormous Integers in Real Life, June 1, 2000, 11 pages.  EnormousInt.12pt.6_1_00

17. Lecture notes on baby Boolean relation theory, October 3, 2001, 11 pages.  BabyBRT100301

18. Does normal mathematics need new axioms?, October 26, 2001, 12 pages.  DoesMathNeed102601

19. Lecture notes on term rewriting and computational complexity, November 7, 2001, 12 pages.  TermRew110701

20. Lecture notes on enormous integers, November 22, 2001, 11 pages.  EnormousInt112201

21. Issues in the foundations of mathematics, Godel Lecture, Association for Symbolic Logic, June 2, 2002, 14 pages.  GodelLect060202

22. Demonstrably necessary uses of abstraction, Hans Rademacher Lectures, University of Pennsylvania, September 17-20, 2002, 53 pages.  RADEM092602

23. Adventures in the foundations of mathematics, VIGRE Lectures, Ohio State University, April 28-May 7, 2003, 64 pages.  VIGRE050903

24. Unprovable theorems, April 19, 2005, 11 pages.  UnprovThms052605

25. Clay Millenium Problem: P = NP, Mathematics Colloquium, Ohio State University, October 20, 2005, 19 pages.  P=NP10290512pt

26. What you cannot prove 1: before 2000, December 19, 2005, 18 pages.  CCRTalk1.121905

27. Forty years on his shoulders, Goedel Centenary, April 25, 2006, 9 pages.  Fortyyears12pt042506

28. Remarks on Goedel Phenomena and the field of reals, Goedel Centenary, April 27, 2006, 6 pages.  GodelPh042406′

29. Remarks on the unknowable, Goedel Centenary, April 28, 2006, 6 pages.  Unknow052206

30. Adventures in the Verification of Mathematics, Computer Science Colloquium, Ohio State University, June 8, 2006, 19 pages.  CStalk060806

31. Search for Consequences, Logic Colloquium ’06, August 9, 2006, Nijmegen, Netherlands, 15 pages.  SearchConseq080906

32. Goedel’s Legacy in Mathematical Philosophy, Logic Colloquium ’06’, August 9, 2006, Nijmegen, Netherlands, 6 pages.  GodelLegPanelNij0809061

33. Contemporary perspectives on Hilbert’s second problem and the Goedel incompleteness theorems, AMS panel, New Orleans, January 6, 2007, 7 pages.  Hilb2panel020107

34. Computer assisted certainty, Computer Science Lecture Series, University of Kentucky, January 25, 2007, 17 pages.  Certainty020107

35. Concept Calculus, Mathematical Methods in Philosophy, Banff, Canada, February 21, 2007, 9 pages.  BanffLect022407

36. Limitations on our understanding of the behavior of simplified physical systems, Science, Reason, and Truth, San Marino, August 17-19, 2007, 26 pages.  See Publications. SanMarino081807

37. Concept Calculus’ APA Panel on Logic in Philosophy, APA Eastern Division Annual Meeting, Baltimore Maryland, January 2, 2008, 17 pages. Supercedes 1/1/2008 and earlier versions.  BaltLect010208

38. ‘LOGIC: Interdisciplinary Adventures in Mathematics, Philosophy, Computer Science, and Education’, University Distinguished Lecture, The Ohio State University, April 23, 2008, 16 pages. Streaming video at http://www.osu.edu/facultystaff/university_awards/2007/lecturer.php  DistLectOSU042308

39. Concept Calculus, Carnegie Mellon University, March 26, 2009, Pure and Applied Logic Colloquium.  ConcCalcCMU032909

40. Boolean Relation Theory, Carnegie Mellon University, March 27, 2009, Mathematical Logic Seminar.  BRT,CMU032909

41. Decision Problems in Strings and Formal Methods, Carnegie Mellon University, Theory/POP Seminar, March 27, 2009.  DecProbStrCMU032909

42. Foundational Adventures for the Future, Honoree Lecture at the Foundational Adventures Conference in honor of Harvey Friedman’s 60th Birthday, Columbus Ohio, May 14-17, 2009. Lecture delivered May 15, 2009.  HonoreeLecture

43. Concept Calculus, Department of Philosophy, MIT, November 4, 2009, 22 pages.  ConcCalcMIT110409

44. Decision Procedures for Verification, Joint Theory of Computation and Programming Language Seminar, Computer Science, Harvard University, October 9, 2009, 28 pages. Also delivered at the MIT Computer Science Department, November 4, 2009.  DecProbStrHarvard100909

45. Strict Reverse Mathematics, Reverse Mathematics Workshop, University of Chicago, November 7, 2009, 19 pages.  StrictRevMath110709:08

46. Unprovable Theorems, Mathematics/Philosophy talk at Harvard University, October 8, 2009. Also delivered at the Boston Mathematics Colloquium, MIT, November 5, 2009. 30 pages.  UnpThms110509

47. Shocking(?) Unprovability, Lecture at the Mathematics Department of The Ohio State University, April 16, 2010. 1 hour. 20 pages.  ShockOSU041610

48. Aspects of Constructive Set Theory and Beyond, Amsterdam Conference on Set Theory, Classical and Constructive, 1 hour, May 6, 2010, 20 pages.  ConStThyAmst050610pdf

49. Concrete Incompleteness from EFA Through Large Cardinals, May 10, 2010, Institute for Logic, Language, and Computation, University of Amsterdam, 2 hours. 31 pages. ConIncompAmst051010

50. Concrete Mathematical Incompleteness, University of Cambridge, UK, November 8, 2010. Minor revisions November 18, 2010. 28 pages.  ConcMathIncCamb111810

51.  Boolean Relation Theory, University of Cambridge, UK, November 10, 2010. Minor revisions November 18, 2010. 38 pages.  BRTCamb111810′

52. Adventures In Logic For Undergraduates. Lecture Series. 5 Lectures, Ohio State University. Lecture 1: Logical Connectives, January 18, 2011  LogicalConn012610  Lecture 2: Logical Quantifiers, January 25, 2011  LogicalQuan012611  Lecture 3: Turing Machines, February 1, 2011  TuringMach020211  Lecture 4: Goedel’s Blessing and Goedel’s Curse, February 8, 2011  GoedelBlessCurse020811  Lecture 5: Foundations of Mathematics, February 15, 2011  Foundations021611 VIDEOS available at YouTube site https://www.youtube.com/channel/UCdRdeExwKiWndBl4YOxBTEQ/feed?view_as=public

53. Past, Present, and Future Directions in the Foundations of Mathematics. Trends in Logic, Kurt Goedel Society, Vienna Academy of Sciences, Vienna, Austria, April 29, 2011, 1 hour. 37 pages.  ViennaFounds042811

54. An Appreciation of Hilary’s Mathematical Work, delivered June 1, 2011 at Philosophy in an Age of Science, Conference in Honor of Hilary Putnam’s 85th Birthday. Revised June 7, 2011. 14 pages.  PutnamTalk060711

55. Maximality and Incompleteness, deelivered March 1, 2012, at the Brandeis-Harvard-MIT-Northeastern Joint Mathematics Colloquium, at Harvard. 1 hour. Revised March 5, 2012. 31 pages.  MaxIncHarv030512

56. Are the Usual Axioms Sufficient?, delivered March 10, 2012 at Patrick Suppes’ 90th Birthday Celebration, at Stanford. 20 minutes. 15 pages.  Suppes90th030712

57. Goedel’s Second Theorem: Its Meaning and Use, delivered March 17, 2012 at AMS Special Session, on The Legacy of Goedel’s Second Incompleteness Theorem for the Foundations of Mathematics, Washington DC, 45 minutes. 30 pages.  GodelSecond0311712+08

58. Incompleteness 1, Invitation to Mathematics Series, Department of Mathematics, Ohio State University, April 25, 2012. 20 pages.  INC1,InvToMath042512

59. Incompleteness II, Invitation to Mathematics Series, Department of Mathematics, Ohio State University, May 2, 2012. 21 pages.  INC2.InvToMath050212

60. Logic: Interdisciplinary Adventures in Mathematics, Philosophy, Computer Science, and Theology, Keynote lecture, Institutional Honorary Doctorate, Ghent University, Ghent, Belgium, September 4, 2013,  56 pages. Logic-Inter082813keynote’

61. Concept Calculus, Institutional Honorary Doctorate, Ghent University, Ghent, Belgium, September 5, 2013,  26 pages. ConcCal090113

62. A Foundationalist Looks at the Piano, Mostowski Centenary, Warsaw, Poland, October 18, 2013, 13 pages. FoundPianoWar10.18.13a

63. Foundational Investigations in Mathematics and Philosophy, May 8, 2014, Public Lecture, Princeton Philosophy Department, 10 pages. PrincTalk060614

64. Perspectives on Formal Verification, January 21, 2016, one hour Keynote lecture, The Fifth International Conference On Certified Programs And Proofs, St. Petersburg, Florida, delivered January 18, 2016, 11 pages.  VerifConf012116

65. An Approach to the Formal Representation of Mathematical Propositions, February 3, 2016, Semantic Representation of mathematical Knowledge Workshop, Fields Institute, Toronto, Canada, 14 pages. DigialLibrary020716

66. Extending Functions, September 22, 2016, 13 pages. August 5, 2016 talk at the workshop Model Theory: From fields to Hardy Fields, held at the Fields Institute in Toronto in honor of Lou van den Dries 65th birthday. torontotalk092216

67. Adventures in Incompleteness, January 24, 2017, Logic Seminar, Stanford University, 11 pages. AdvIncomp020117-10ur5y4

68. Adventures in Incompleteness, March 1, 2017, Distinguished Lecture, Mathematics, Philosophy, and Computer Science, University of Texas at Austin, 45 pages (24 point). UTAustin030117-1dkk31s  16 pages (12 point) AdvIncomp03011712pt-1k0z6to Movie: http://mediasite.aces.utexas.edu/UTMediasite/Play/8187d66a626f48d2a1b0be57ca17833