The Normativity of Formal Orders and Procedures in the Ancient World: A Comparison between Mathematical and Judicial Rule Systems

The project “Normativity of formal structures and procedures in the ancient world – A comparison of mathematical and judicial systems” is part of a larger project covering the time period from the ancient world (including Egypt and Mesopotamia) to the modern era. Systems of legal norms (constitutions, law collections, judicial texts for teaching purposes) and mathematical theorems or systems of mathematical rules both represent formal structures which are valuable for specific legal theory and epistemological aspects, as they are of a high inner coherence which enables deductions, aiming at enabling unique decisions for the solution of specific problems. Within both areas (law and mathematics), the existence of a formal structure is characterized by specific superior norms (below referred to as: meta-norms) which guide the structure and application of the system of norms/rules.

The guidance provided by such meta-norms, which are the basis for a formal understanding of judicial and mathematical structures and procedures, is a characteristic feature of a modern idea of law and mathematics. It was mainly devised and established in the first decades of the 20th century within the context of scientific and cultural concepts of the modern era. Hans Kelsen (for the domain of legal theory) and David Hilbert (for the domain of mathematics) are key figures in this development.

However – and this is where our current project starts from – even very early stages of written judicial and mathematical systems and procedures display certain formal structures. This is also apparent in further domains, where knowledge was put in written form. The formation but also the historical and cultural variation of these meta-norms which are linked to the setup and use of formal structures and procedures in law and mathematics may (and must) therefore be considered as a historical process of longue durée. To understand this process in its important stages better is the aim of our project.

The project analyses the normativity of formal structures and procedures with reference to ancient Egyptian, Mesopotamian, Hittite, Greek and Roman judicial and mathematical texts. Systems of norms which were generated by the earliest literate cultures indicate requirements for the normativity and characteristic aspects of formal structures, e.g. with respect to the language (grammar) used to express them. They prompt us to reflect about the terms “coherence” and “abstraction” and enable us to gain insights into the validity and acceptance of norms in pre-modern cultures and the procedures through which they were enforced.

The study of the systems of rules of ancient cultures that used writing provides fundamental insights into the conditions for the emergence and acceptance of formally structured systems of norms. Such features as the importance of casuistic practices, regional and chronological changes and the need for consistency and coherence in their logical structure make it possible to draw conclusions about the nature of normative systems in question that may also be useful in research on later and even on recent developments. The close collaboration with Prof. Moritz Epple and Prof. Guido Pfeifer fostered the discussion of the results beyond the boundaries of our project.

Discussion of the research topic and the selection of suitable source material took place at an introductory workshop in April 2013. This workshop also served as preparation for the international conference held in March 2015. The papers delivered at this conference were then discussed in a further workshop held in February 2016. This served to make interconnections between the chapters of the corresponding volume that is currently being prepared for publication.

Pre-modern mathematical and judicial texts exhibit distinctive formal structures whose normativity can be identified as early as in the texts from Mesopotamia and Egypt and enables conclusions to be drawn about the division of their content (e.g. the analysis of the Codex Hammurapi by Jim Ritter and that of the Codex Urnamma by Hans Neumann). Significant differences can be found between written legal texts from Egypt and from Mesopotamia (Annette Imhausen). Using Hittite (Daliah Bawanypeck), Greek (Markus Asper), and Roman (Peter Gröschler) legal texts and texts from Ptolemaic Egypt (Katelijn Vandorpe, Mark Depauw) several possibilities are presented about how normativity (linguistic features, formulas, specific design of writing material) was used to promote putative permanent validity and authority. In addition, Guido Pfeifer documented the use of mathematical values within Mesopotamian legal texts as a further connection between the two subject areas.
A publication that will be summing up the results of the project, is currently in preparation and will be published in a project volume in the series KEF (Kārum – Emporion – Forum. Beiträge zur Wirtschafts-, Rechts- und Sozialgeschichte des östlichen Mittelmeerraums und Altvorderasiens) of the Ugarit publishing house.


The most important events of this project:

Lectures: Hans Neumann (Münster) and Jim Ritter (Paris), Wissensordnungen im Codex Ur-Namma und im Codex Hammurapi (Colloquium History of Science), Cluster of Excellence "The Formation of Normative Orders", Goethe University, Frankfurt am Main,  May 10, 2016.

Workshop: The Normativity of formal structures, Cluster of Excellence "The Formation of Normative Orders", Goethe University, Frankfurt am Main, February 4–5, 2016.

Lecture: Markus Asper (Berlin), On the Authority of Normative Texts. Inscriptional Law and Mathematical Literature in Ancient Greece (Colloquium History of Science), Cluster of Excellence "The Formation of Normative Orders", Goethe University, Frankfurt am Main, December 15, 2015.

International Workshop: Die Normativität formaler Ordnungen und Prozeduren in der Antike und im Mittelalter: Mathematische und rechtliche Regelsysteme im Vergleich, Cluster of Excellence "The Formation of Normative Orders", Goethe University, Frankfurt am Main, March 17–19,  2015.

Workshop: Normativity of formal structures and procedures in the ancient world. A comparison of mathematical and juridical systems, Cluster of Excellence "The Formation of Normative Orders", Goethe University, Frankfurt am Main, April 11–13, 2013.

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