Leibniz

Analysis Situs

Leibniz’s fascination with symbol systems led, after his success with calculus, into a lifelong project to develop an artificial symbolic language to express geometric quality or ‘shape’. He called it analysis situs, his characteristica geometrica. He opposed the Cartesian school that relied on a reduction of geometric shape to geometric quantity through the use of coordinate systems. He objected that the universal language of quantity, namely arithmetic and algebra, is not well tailored to the subject of geometric quality, and exclusive use of this reduction leads to many difficulties. He hoped his new system would be more convenient for writing, hence remembering and communicating, facts about shapes. He thought it should have a role in pure geometry, which is concerned with ‘natural’ shapes like points, lines, and circles, and a role in architecture, biology, and engineering, or anywhere shapes are recorded and communicated.

Translation Project

This project shares work on a collection of translations of writings of G. W. Leibniz on his analysis situs. Most of these writings currently have no English edition. The collection is set to be published by Oxford University Press, hopefully in 2027, as part of the New Texts in the History of Philosophy series, which they publish on behalf of the British Society for the History of Philosophy.

We aim to collect representative essays from across the entire period of Leibniz’s life. I hope it will give easy access to Leibniz professionals wondering what the analysis situs was really about, and it should be useful for philosophers interested in mathematics, computation, language, and space. Historians of early modern math, and of geometry in general, should find it useful as well.

I am the editor and a translator; David Jekel is another translator. Notes, comments, criticisms, corrections, and any other contributions are warmly welcomed by email. We are happy to receive philosophical reflections or remarks on the subject matter as well.

None of the essays is yet available in finalized form in the official Academy Edition. We carefully studied Leibniz’s manuscripts for each essay. For many of these essays there are now transcriptions resulting from the Mathesis and Philiumm projects in advance of eventual publication in the Academy Edition. Gerhardt’s transcriptions remain the best available for the SGL, AGP, and IRMM. Before the Mathesis and Philiumm transcriptions became available, we worked with Mugnai and Echeverría’s CGGs, and Echeverría’s CG, and our project is indebted to their early work.

The analysis situs is a key to understanding Leibniz’s method in general. The bulk of Leibniz’s work here, and the special focus of this collection, is not mathematically technical. It reveals many questions and challenges that arise from Leibniz’s devoted effort to create a new symbolic language system, which effort was indeed of only limited success, even if the idea was of unlimited prescience. The idea of ‘symbolic language system’ is the mainstem river running through Leibniz’s life’s work, with longest and most consistent effort devoted to the analysis situs.

Useful Links

Archiv Repositorium – Digital resources offered from the Leibniz Library in Hannover
Leibniz Online – Links to old texts online, compiled by the Edition office in Münster
Leibniz Catalog – Search Leibniz writings by metadata
Leibniz Edition – Homepage of the Academy Edition

Texts and Translations

• ‘Typed’ links take you to a page in the official PDF hosted by the GWL Library.
• ‘Hand’ PDFs are the manuscripts after I have split the bifolia and arranged them in reading order.
• ‘Stamped’ PDFs are the transcription files with markings directing readers to ranges (page and top/mid/bot) of the Hand files. Together, these allow one to easily verify any of our readings.

✓ drafting revision, ✓✓ polishing revision, ✓✓ final review

Research and Writing on Leibniz