Gödel's solitary work was the single most important factor in the development of precise theories of formal languages, which, through the coding that he invented, can be handled by a machine. His work led to precise notions of algorithmic computability from which a direct path leads to the first theoretical ideas of a computer in the work of Alan Turing in 1936 and John von Neumann some years later.
The development of logic and foundational study has been known to us only in broad outlines until Jean van Heijenoort's pioneering work. He published in 1967 a collection of original papers under the title From Frege to Gödel: The Development of Mathematical Logic 1879-1931. There was, however, no attempt at organised historical work with the sources. Such detailed work is still in a very early state and crucial sources for the development of logic remain unexplored.
Deep intellectual history cannot be achieved if only published work is considered. Comparison to a parallel and partly overlapping development is illuminating. Quantum mechanics, as well as foundations of mathematics, received a decisive impetus around the year 1900, with Planck's discovery of the quantum of action, and the discovery of Russell's paradox and Hilbert's idea of formalisation. All of these developments led to a well-established theoretical account by the early 1930s, right before the Nazi takeover in Germany: quantum mechanics in the second part of the 1920s in the work of the Göttingers Heisenberg and Born, logic and foundations with the full development of first-order logic by the early 1930s by the Göttingers Hilbert, Bernays, and Gentzen, assisted mainly by Gödel's striking discoveries.
Historical work on the development of quantum mechanics began in the 1960s in a massive effort in which every conceivable source was unearthed and made available in several hundred microfilm reels, the Archive for the History of Quantum Physics.
Sadly, nothing of this kind was ever done with logic and foundations. Our present information society owes a part of its existence to a well-hidden but essential line of development. There are several thousand pages of notes by Gödel waiting to be studied, written in a long-forgotten, difficult stenographic script. Similarly, extensive notes for lecture courses during the crucial years, written by Paul Bernays, the central driving force in foundational study around 1930, as well as over five thousand contemporaneous letters exist in the Bernays archive. These have been exploited only sporadically. The fate of many other sources, such as the papers of Gerhard Gentzen and Rose Rand, has been similar.
The main aims of our project are twofold:
Understanding Gödel's unpublished papers requires a combination of mastery of the logical details and the application of professional standards of historical-foundational research to the source material, which, in addition, is only accessible to a reader trained in stenographic writing. So far, much of this work remains to be done. There are two exceptions: the transcription of Gödel's so-called "Zilsel lecture" in Vienna in January 1938 and his Göttingen lecture on the consistency of the continuum hypothesis of December 1939, both published in the third volume of Gödel's Collected Works. Both of these texts were lecture notes, relatively finished in comparison to the private notes. More recently, much effort has been dedicated to producing transcriptions of Gödel's philosophical notebooks that he called "Max Phil," or Philosophical Maxims, in order to better understand Gödel the philosopher. Our project will provide ample material for future generations of philosophers and logicians to complement the picture given by the Philosophical Maxims as well as other works of Gödel's published so far.
The project consists of theoretically oriented basic research. It uses special methods for the study of mostly unpublished primary sources, the contemporary methods of logic and foundational study to aid in their interpretation, up-to-date formal methods for the development of research themes suggested by the sources, and scholarly methodological standards of historical-foundational research.
The main sources comprise a number of series of notebooks, all written in shorthand and logical symbolism, left virtually untouched except for the Max Phil series:
Gödel's notebooks have some overlap in themes, ideas and results that are presented in Max Phil or Resultate Grundlagen often appearing in less finished form in the Arbeitshefte, to give an example. Gödel was meticulous about keeping his notebooks, and they contain detailed lists of contents from which we can infer that he did reread them. There is a separate list of "Progress" entries, in which he summed both his achievements and objectives in numbered points in the Arbeitshefte.
As of early Spring 2019, our current projects include the following: