page being updated Jan 2011. removing various anachronisms.
There is a section of personal data (with random links), (or you can see my curriculum vita (with publication list) ) a section on my theoretical research in Quine's "New Foundations" and related systems . Here is the page for my current theorem proving project Marcel. There is access to documents from the latter two sections. Information about my book (including the errata slip) is here.
Here is the New Foundations Home Page. 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.
Here is my Google Calendar.
Old courses: Follow this link
I have permission from my publisher to post a revised version of my book Elementary Set Theory with a Universal Set (which has gone out of print) online. This will correct the known errors. A provisional version (which does correct the errors (the ones I know about, at any rate) but has not been fine-tuned editorially) is found here for now; this now includes suggestions of various correspondents. There is also a PDF version. I don't believe that the index will be correct in either of these versions.
Since I am currently actively working on editing an official second edition, any comments from readers about errors and infelicities would be very welcome!
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.
Just what the section title says. These are various drafts I keep in public view. Some very old things have been hanging around here for quite a while: as I update in January 2011 I am removing most of them, but I may add more.
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 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.
I will put a link to my SEP article on Alternative Axiomatic Set theory 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.
If you want to send mail to me at holmes@math.boisestate.edu, feel free!
Here's a link to the Department of Mathematics and Computer Science Home Page here at Boise State!
If you get here the wrong way and none of the local links seem to work, despair not: click here and things should improve dramatically.
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).
For several years, I have been the “chief executive officer” (a grander designation than is perhaps appropriate) of The Loglan Institute, the nonprofit organization which attempts to guide the development of the artificial language Loglan. This language was originally proposed by James Cooke Brown in the 1950's as a vehicle for testing the Sapir-Whorf hypothesis (look it up!) A specific peculiarity of this language is that it is (at least in intention) syntactically unambiguous: the official version of the language is unambiguously machine parsable. The language is intended to be highly logical: it is to some extent an implementation of first-order logic in a spoken language.
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.
Just as Esperanto has its Ido, so Loglan has its Lojban. This sister language is still in some ways quite similar: it has a larger community and more activity. The Logical Language Group which oversees Lojban and The Loglan Institute are on good terms at this time, whatever may have been true in the past. I think the original language still has something to offer, and the existence of two languages may provide some opportunities as well.
Here is the link to the page for my old theorem prover project Watson: Watson theorem prover page. I am planning to incorporate some features of this system into my current project. This project was funded for some time by the Department of Defense; I have not worked directly on it for years, but I have not forgotten about it entirely.
Note the question mark. I'm not gung ho on this subject, but I have spent some time investigating the question of whether and how well mathematics (and other content) could be taught in online environments such as Second Life. I participated in the class Teaching and Learning in Second Life taught by Lisa Dawley in the Boise State Educational Technology Program last term. I think a major (perhaps the major) technical problem with teaching math in SL has to do with the difficulty of freehand drawing in SL, and I developed a tool in Second Life which (almost) addresses this. There is a blog entry about a presentation on this problem. In spring 2010 I taught a class in SL called Teaching Mathematics in Virtual Worlds, through the Educational Technology Department here. I will put up some links about this as I update this page
I have designed an eccentric programming language (Strictly False) an extension of Wouter van Oortmerssen's elegant False programming language. The source (in Standard ML) is here and the documentation (PDF) is here.. Any BSU student who writes a program in False or Strictly False which does something interesting can come and see me for praise [you can get a DOS False interpreter off the site I cite; to run my interpreter (and my language is definitely more powerful), you need Moscow ML].
Definitions are important to mathematicians, and fools rush in where angels fear to tread, so here find my modest proposal for the definition of "planet" with comments on why the definitions currently proposed by the IAU are not so good.