Here is the New Foundations Home Page (NF home page is extremely out of date and needs to be edited, note to self August 2014). Here is the universal set bibliography (an expansion of the bibliography of Forster's NF book). Here are the notes from M502, Logic and Set Theory, which may be turning into a book. For information about my claim to have proved the consistency of New Foundations, see below.
Here find the slides for my recent talk at the College of Idaho. I'm very pleased with the construction of the reals given there, using neither ordered pairs nor equivalence classes!
Here is my new separate page on the artificial language Loglan.
Here is a day by day schedule for both my classes.
Here is the current official document. This is the "new" version, with index, references and conclusion added. I think it is in shape to be the flagship version now. The previous major version of the document describing the proof is here. I am preserving the previous major version because more people are familiar with it and because the new version probably still has a lower index as a draft. The new version is not motivated by any errors detected in the old version, but by the fact that the old version is very complex and hard to follow; the new version is still complex and hard to follow, but the nastiness is getting down to the essential core that cannot in the end be removed. Comments and questions (on either document) from those who understand the technical issues are very welcome; I apologize in advance for the still difficult state of the text, and I am sure that I don't yet have all the bugs out.
Here is the alternative version (the simplified one). This is still a possibly negative-indexed draft, but it looks quite promising, all around much simpler than the argument in the main document above. I did fix the bug I complained about earlier, but I have not yet written down the final bits of the argument in this version. I know how the closing part goes; it simply must be written down carefully for the rather different situation in the alternative construction.
If you have an amateur philosophical interest in NF, I do not think it likely that you will get anything out of this very technical and not yet very polished document (in either version), and I am not likely to answer your questions about it. Be advised that in my opinion (which I know is not universal) the famed NF consistency problem has nothing at all to do with philosophical issues which Quine's set theory might be taken to address: I think that NFU addresses these issues to exactly the same extent and its consistency and mathematical strength have been settled issues since 1969.
Here is the talk I gave on New Foundations to the department at Boise State on September 10, 2013. Philosophical interests in NF might be served by these slides, and also by the notes on Frege's logic which appear below. This is my most recent explicitly philosophical essay about Quine-style set theory.
Here find an outline of how to fix the foundational system of Frege using stratification in the style of Quine.
Here find my current notes on Dana Scott's lovely and weird result that ZFC minus extensionality has the same strength as Zermelo set theory.
Here is the May 19th 2011 (submitted) version of the paper I am writing about Zuhair al-Johar's proposal of "acyclic comprehension", with Zuhair and Nathan Bowler as co-authors, a perhaps surprising reformulation of stratified comprehension.
Here is the Jan 20 2012 draft of the paper I am writing about a simpler form of symmetric comprehension, strong versions of which give extensions of NF with semantic motivation and a weaker version of which gives a new consistent fragment of NF inessentially stronger than NF3, for which I give a model construction. The problem of modelling the versions that yield NF seems to be very hard (as usual). This version is ready for submission.
Here find the note submitted Dec 30 2013 on my result that the set H(|X|) of all sets hereditarily smaller in size than a set X exists, not using Choice. It is surprising to me that this is not an obvious result, but the references for partial results that I have been able to find are recent, so perhaps it is new.
Here is a recent version of my manual of logical style, a teaching tool (or would-be teaching tool) with which I am constantly tinkering to try to give students some idea how to approach the precipice of writing a proof.Here is a draft paper on mathematics in three types (mostly, on defining functions in three types) based on a presentation at BEST 2009. Here are the notes for the talk I gave on this subject in Edmonton on Sept 11 2012.
Here is a version of my paper on the curious fact that the urelements in the usual models of NFU turn out to be inhomogeous, because the membership relation on the underlying model-with-automorphism of the usual set theory turns out to be definable in NFU terms. This version corrects a couple of annoying typos in the published version.
I will put a link to my SEP article on Alternative Axiomatic Set Theories here.
Here are my notes on efficient bracket abstraction.
Here are the notes for the visit of Peter Seymour.
Materials relating to the visit of Olivier Esser are here.
Here's a link to the Department of Mathematics and Computer Science Home Page here at Boise State!
Here is a letter of mine discussing the set theory of Ackermann. Here are some not very serious notes on a pocket set theory. Here is a later version (DVI file).
Here is the official web site of the Loglan Institute.. Here is the mirror of the Loglan web site here at Boise State. There is access to a wide variety of information, documents and software through these links.
Here is my new separate page on Loglan, where you can find pointers to my current Loglan projects.