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The Arché Grundgesetze Translation Project
Gottlob Frege

The Team

The core team is:

Philip Ebert
Marcus Rossberg
Roy T. Cook (technical consultant)
Crispin Wright (project co-ordinator)

We are proud to annouce the following consultants of the translation project:

Dr Michael Beaney (York University)
Professor Gottfried Gabriel (Universität Jena)
Professor Michael Hallett (McGill University)
Professor Richard G. Heck, Jr. (Brown University)
Professor Michael Kremer (Chicago)
Professor Wolfgang Künne (Universität Hamburg)
Professor Robert May (UC Davis)
Professor Eva Picardi (Università di Bologna)
Professor Thomas Ricketts (University of Pittsburgh)
Professor Peter Simons, FBA (Leeds University)
Professor Jason Stanley (Rutgers University)
Professor Peter Sullivan (Stirling University)
Professor Jamie Tappenden (University of Michigan)
Professor Christian Thiel (Universität Erlangen)
Professor Kai Wehmeier (University of California, Irvine)

Technical advisors for typesetting and LaTeX:

Dr J.J. Green (University of Sheffield)
  Creation of a font for Frege’s function symbols.
Professor Richard G. Heck, Jr. (Brown University)
  Advice concerning LaTeX and XML; modification of the begriff.sty.
Rob McInnes (University of St Andrews)
  Creation of a graphic interface for typesetting Frege’s Begriffsschrift formalism with XML and LaTeX output, the latter using begriff.sty.
Guðmundur Andri Hjálmarsson (University of St Andrews)
  Improvement of the graphic interface for typesetting Frege’s Begriffsschrift formalism; general IT advice and assistance.
Dr Josh Parsons (University of Otago)
  Creation of the begriff.sty for typesetting Frege’s Begriffsschrift formalism.
Dr William Stirton (Edinburgh University)
  Technical advice and assistance for typesetting of Frege’s Begriffsschrift formalism.


From October 2005 to May 2006, the project is funded by a continuation of the AHRC Research Grant for Arché’s project on The Logical and Metaphysical Foundations of Classical Mathematics, originally scheduled to run from October 2000 to September 2005. From June 2006 it will be funded for a further 24 months by a Research Grant by the Leverhulme Trust.
The Six Basic Laws

Background and Project Description

The importance of Frege’s ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework within which his technical contributions were conceived and developed has been so deep that he has a strong case to be regarded as the inventor of much of the agenda of modern analytical philosophy itself. English is, of course, the dominant medium of Frege scholarship, as it is of analytical philosophy in general. Two of Frege’s three principal books – the Begriffsschrift (1879) and Grundlagen der Arithmetik (1884) – have been available in English translation for many years, as have all the most important of his other, article-length writings. His major work, however, the Grundgesetze der Arithmetik, published in two volumes (1893 and 1903), has never been completely translated into English.

Grundgesetze was to have been the summit of Frege’s life’s work – a rigorous demonstration within the system of Begriffsschrift how the fundamental laws of the classical pure mathematics of the natural and real numbers could be derived from principles which, in Freges view, were purely logical. As is familiar, a letter received from Bertrand Russell shortly before the publication of the second volume made Frege realise that Axiom V of his system, governing identity for value-ranges, led to contradiction.

Despite this contradiction, developments initiated in work by the late George Boolos and by Crispin Wright in the 1980s, showed that much of the main thrust of Frege's project can be salvaged. The broad upshot of this work was that the replacement of Axiom V in the system of Grundgesetze by what came to be known as Hume’s Principle, associating one-one corresponding concepts with the same cardinal number, provided for, first, a consistent theory in which classical number theory could be developed and, second, a theory of considerable philosophical interest.
Hume's Principle
The last 20 years have seen substantial philosophical and technical advances in this programme, with extensions to real and complex analysis and significant fragments of set-theory. Much of the work has been done under the auspices of the AHRC-funded project on The Logical and Metaphysical Foundations of Classical Mathematics, which has been running at Arché since 2000 under the leadership of Crispin Wright, and in which Roy Cook, Philip Ebert and Marcus Rossberg have participated.

Despite the progress in the area of Neo-Fregean philosophy of logic and mathematics and a newly sparked interest in Frege’s original work, there is still no complete and uniform translation of his main work. Grundgesetze has only been partially and eclectically translated. The existing translations are not collected in one volume, and the translation of Frege’s technical terms is not standardised. Although most of the untranslated material in volume I consists of formal proofs, Frege adds in almost every case important explanations, clarifications and guidance in short passages of prose. The untranslated sections of volume II contain crucial philosophical passages. Here, Frege criticises his contemporaries for their conceptions of the real numbers and of the notions of continuity and magnitude. Most prominent amongst these are Cantor and Weierstrass. Since we are still lacking a precise picture of Frege’s formal characterisation of the real numbers (Frege’s volume III has never been published and his manuscript, if it ever existed, is presumably lost with most of his Nachlass), a full understanding of these criticisms seems invaluable for a reconstruction of Frege’s approach to real analysis. The formal parts of volume II which again contain extensive elucidations are concerned with the final sections of his account of arithmetic. In the latter chapters, Frege starts to construct the formal framework for his account of analysis by giving, for example, his characterisation of the notion of magnitude.


Our paramount objective is, of course, to produce the most accurate, fluent and philosophically informed rendition possible of Frege’s text. A substantial philosophical introduction and analytical table of contents will be included.

A Companion Volume of original philosophical essays on Grundgesetze will be produced to coincide in publication with the translation itself. The essays, by the team of translators and advisers, and other invited scholars with interests in Frege’s philosophy of mathematics and its modern descendants, will be encouraged to provide both analytical exposition of the leading ideas of Frege’s book and critical development of them. Expressions of interest are invited via contact, in the first instance, with Arché.

A dedicated Grundgesetze section, hereby initiated, will be developed on this website to accompany the work of translation and the Companion. The site will be divided into open- and restricted-access sections. The principal purpose of the open-access pages will be to offer users assistance in understanding and working in Frege’s Begriffsschrift notation, and to provide further information about Frege’s writings and the secondary literature. An online tutorial for reading, writing, and reasoning in Begriffsschrift will be provided. A typesetting programme to represent Begriffsschrift formulae within LaTeX (including an XML option) is already available for download here:

Software Download


Two workshops are planned to take place within the lifetime of the project.

The first workshop was based on a full first draft of the translation of the first volume and took place in November 2007. The following photographs are from the first workshop.

Grundgesetze Workshop

(From left to right, back to front) Mike Beaney, Steve Read, Robert May, Marcus Rossberg, Crispin Wright, Gottfried Gabriel, Michael Hallett, Eva Picardi, Roy Cook, Elia Zardini, Kai Wehmeier and Philip Ebert.

Grundgesetze Workshop

(Clockwise from bottom left) Michael Hallett, Roy Cook, Marcus Rossberg, Philip Ebert, Robert May, Crispin Wright, Gottfried Gabriel, Mike Beaney, Eva Picardi, Kai Wehmeier, William Stirton and Elia Zardini

The second workshop is planned to take place at the end of the project, in 2008.

Further details will be posted as they become available.

Expressions of interest for participation in the workshops are invited. Please contact Arché.


The finished translation, in English only but in a form preserving the pagination of the original German Pohle editions (1893 and 1903), will be published by Oxford University Press.
A rule of inference