Talmudic Chaos v. Halakhic Linearity in the Logic of Judaism

In 2011 we published an article, "In Search Of The Logic Of Judaism: From Talmudic Chaos To Halakhic Linearity," which you can download and read from the link here.   

We used mathematical ideas to differentiate the linear organization of the halakhah from non-linear thinking of the Talmud. Our abstract says: 

In this paper we examine some common views of scholars concerning the idea of the halakhah in Judaism. We then explain why their methods failed to account for the main philological and historical evidence regarding the term from the Talmudic texts. Then we suggest as a heuristic explanation that the logic of the Talmud defies linearity and can be discussed productively using chaos theory.

The authors in this volume cover varied topics with sophistication and erudition. The publisher's page provides details about the book, as copied below. 

Schumann, Andrew, Tzvee Zahavy, Avi Sion, Aviram Ravitsky, Stefan Goltzberg,  Judaic Logic

Title:	Judaic Logic
Series:	Judaism in Context 8
Publisher:	Gorgias Press
ISBN:	978-1-61719-194-7
Language:	English
Format:	Hardback, Black, 6 x 9 in

1. Introduction, Andrew Schumann
2. In Search of The Logic of Judaism: From Talmudic Chaos To Halakhic Linearity, Tzvee Zahavy
3. Maimonides’ Use of Logic In The Guide of The Perplexed, Joseph A. Buijs
4. Structure And Sources of The Hebrew Commentary on Petrus Hispanus's Summulae Logicales By Hezekiah Bar Halafta, Alias Bonenfant De Millau, Mauro Zonta
5. Aristotelian Logic and Talmudic Methodology: The Commentaries on the 13 Hermeneutic Principles and Their Application of Logic, Aviram Ravitsky
6. A Fortiori Reasoning In Judaic Logic, Avi Sion
7. The A Fortiori Argument In The Talmud, Stefan Goltzberg
8. Sense In Making: Hermeneutical Practices of The Babylonian Talmud Against The Background of Medieval And Contemporary Views, Sergey Dolgopolski
9. Judaic Syllogistics: The Baba Qama From The Logical Point Of View, Andrew Schumann
10. Symbolic Computation And Digital Philosophy In Early Ashkenazic Kabbalah, Yoel Matveyev 

The Publisher's Description of the book tells us: 

Judaism differs considerably from other theistic religions. One of the main features is that Jewish religious laws are not dogmatic but based on specific legal reasoning. This reasoning was developed by the first Judaic commentators of the Bible for inferring Judaic laws from the Pentateuch. The book is about Judaic reasoning from the standpoint of modern logic. Its first goal is to define Judaic logic. This logic was aimed to be a methodology for deducing religious laws. The idea that this methodology can be viewed as original logic that is not less deductive than Aristotle’s logic did not emerge until the Late Middle Ages. At that time Medieval Hebrew works about Judaic reasoning were influenced by Arabo-Islamic philosophy as well as by Latin Scholastic logic. In this volume we discuss different forms of influence of the Aristotelian logic on developing the Talmudic methodology. Then we aim to sketch semantics for the Judaic reasoning, explicating Talmudic case study and Rabbinic situation analysis to develop general approaches to formalizing Judaic logic. This consideration of Judaic logic has relevance for modern logic and analytic philosophy and may be compared with the contribution made by the formalization of Ancient Greek logical systems to 20th-century logic and language philosophy.