Overview of Randall Holmes's Home Page

There is a section of personal data (with random links), (or you can see my curriculum vita 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. Here is my latest theorem proving project, an implementation of a variant of Automath. Information about my book (including the errata slip) is here.

Here is the New Foundations Home Page (NF home page is extremely out of date and needs to be edited, note to self August 2014).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.

Utilities

utilities

Teaching Stuff

NF Consistency Proof

I currently claim to have a proof of the consistency of New Foundations.

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 a rather different presentation of the argument, still in an early draft, which I think might resolve some of the intelligibility issues of the main draft. If it fulfils its early promise, it may become the main document.

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, 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.

New: my book to be available on-line in a new edition

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 PDF version is the result of a first pass through the text in November 2012 with the aim of preparing an official online second edition. I thank my publishers for their kindness in allowing me to maintain an online version, both to conveniently publicize error corrections and to make the work available now that it is out of print. Since I am currently actively working on editing an official second edition (I really am, as of November 2012), communications about errors and infelicities would be very welcome!

Drafts of Current Work

Here find an outline of a proposed approach to semantics for the Principia Mathematica (PM) of Russell and Whitehead using the type and substitution algorithms in my paper on automated polymorphic type inference in PM. Here find some notes on PM with page references related to the same analysis.

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.

Miscellaneous Documents

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 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.

Other Stuff

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!

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).

Loglan, an artificial human language

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.

Here is my new separate page on Loglan, where you can find pointers to my current Loglan projects.

Watson Theorem Prover Project

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.

Education in Virtual Worlds?

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 in 2009 (?). 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'm currently practicing my Loglan in weekly conversation meetings in Second Life, but not there much otherwise; I remain interested in doing some experiments on representing Calculus III concepts in the 3D virtual world.

The Strictly False Programming Language (frivolous)

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].

The Definition of Planet (frivolous)

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 lately proposed by the IAU are not so good.