B.Phil. Seminar Volker Halbach and Joel Hamkins
Logic and Philosophy of Logic

Hilary term 2021, Fridays 9-11, online on Zoom

https://us02web.zoom.us/j/81223003837?pwd=SlpPRU13YXljdDIwUzJwM3FLVUQ1UT09

Meeting ID: 812 2300 3837

Passcode: 198063 

At the beginning of each class we will introduce the topic by presenting an article or book chapter, which all participants will be expected to have read in advance. This will be followed by a discussion. Here is our preliminary plan:

week 1: The theory of syntax and diagonalization • Volker Halbach will use these slides. There are too many pages, but we'll see how far we get. I would like to explain how Gödel diagonalization works without having to go through arithmetization. The slides are based on parts of a book I am writing. Please let me know if you would like to receive a pdf of the two relevant chapters. They cover a little more than the slides on which I will concentrate.

week 2: Applications of diagonalization: semantic paradoxes and incompleteness theorems •Volker Halbach will continue with his slides.

week 3: Several fixed-point theorems with applications •Joel Hamkins has prepared a paper A review of several fixed-point theorems, with applications.

week 4: We look at the notion of self-reference in metamathematics. Volker Halbach will present parts of the following paper: Self-Reference in Arithmetic I+II, Review of Symbolic Logic 7 (2014), 671-691 and 692-712 • preprint containing both parts. The slides are here.

week 5: We will talk about Melvin Fitting's paper, "Russell's paradox, Gödel's theorem" Chapter in book: Raymond Smullyan on self reference, 47–66,Outstanding Contributions to Logic, 14, Springer, Cham, 2017. An electronic version of the book is available here on SOLO.

week 6: structured propositions • Arthur Wu will introduce the paper A Theory of Structured Propositions by Andrew Bacon.

week 7: consistency strength I • Joel Hamkins will present his paper Nonlinearity in the hierarchy of large cardinal consistency strength

week 8 consistency strength II • Joel Hamkins will present his paper Nonlinearity in the hierarchy of large cardinal consistency strength