Gottfried Wilhelm Leibniz (1646–1716) was a German philosopher and mathematician (and jurist, linguist, historian, inventor, etc.) famous for discovering differential calculus and developing the ‘infinitesimals’ notation we use today. He also invented a calculating machine, and was fascinated with the binary system for number expression. He was a rationalist idealist in philosophy known for an ontology with a plurality of simple ‘monads’, and for his metaphysical principles: ‘sufficient reason’, ‘identity of indiscernibles’, and ‘preestablished harmony’.
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.
Translations
Here is the beginning of a collection of translations of Leibniz’s key writings on the analysis situs. The collection is set to be published by Oxford University Press, hopefully by early 2025, as part of the series New Texts in the History of Philosophy, which they publish on behalf of the British Society for the History of Philosophy. I am 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.
This is the first lengthy and coherent text that Leibniz wrote and shared on the analysis situs. This draft does not yet include figures.
Initial draft complete, revised draft for upload soon. Email for a copy.
Translation projected. Latin text from Mugnai’s book.
Translation projected. Latin text is unpublished draft by Mathesis group.
Translation projected. Latin text is unpublished draft by Mathesis group.
Translation projected. Latin text is unpublished draft by Mathesis group.
Extant translation in Loemker. A revision here is projected.
Initial draft complete, revised draft for upload soon. Email for a copy.
This draft does not yet include figures.
Translation projected.
Extant translation in Loemker. A revision here is projected.
This text is likely among the last that Leibniz wrote before his death. This draft does not yet include figures.
There is only one published collection of Leibniz’s writings on this topic, by J. Echeverría, but the temporal scope is narrow and the original Latin is translated there to French. The (original language) Akademie-Ausgabe will include new volumes on this topic, but these editions aim for manuscript accuracy and comprehensive inclusion, making them very difficult to appreciate for all but professional Leibniz scholars.
This book project intends to collect the best representatives from a broad timeframe in 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 interesting to philosophers of mathematics, of language, and of space. Historians of early modern math, and of geometry in general, should find it useful as well.
The bulk of Leibniz’s work here, and the special focus of my collection, is not mathematically technical. It reveals many questions and challenges that arise during a 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. This 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. Study of this project is key to understanding Leibniz’s method in general.
Research and Writing on Leibniz
ToC, Abstract, and Intro for my BPhil Thesis. Email for a complete copy.
A short essay introducing the idea that a mathematical category gives a good model for Leibniz’s ontology.