The Political Perfection of Original Judaism: Pedagogical Governance and Ecclesiastical Power in Mendelssohn's Jerusalem
Moses Mendelssohn famously penned his Jerusalem; or, On Religious Power and Judaism in response to a public challenge. Mendelssohn had declared “ecclesiastical power” to be a contradiction in terms, and had thus come out strongly against the use of coercion in religious life, and against the ban of excommunication by rabbinic authorities, in particular. In the anonymously published The Search for Light and Right, August Cranz defies Mendelssohn to explain how he could reconcile this liberal view of religion with his continued commitment to—and his insistence that Jews were still obligated to observe—Jewish law. “As reasonable as all you say [about religious power] may be, to just that degree it contradicts the faith of your fathers . . . and the principles of its church . . . expressly set down in the books of Moses,” Cranz argues. “The theocratic ruling staff drove the whole people . . . with force and punishment.” True, Cranz concedes, exile reduced the capacity of Jewish authorities to enforce Jewish law, “but these ecclesiastical laws are there even if their exercise is no longer a must.” Cranz challenges Mendelssohn to explain his apparently irreconcilable commitments: “How can you persist in the faith of your fathers and shake the whole structure by clearing away its cornerstones, dear Mr. Mendelssohn, when you contest the ecclesiastical law given as divine revelation through Moses?”
Faith and Freedom: Moses Mendelssohn's Theological-Political Thought
DEDICATION ABBREVIATIONS PREFACE INTRODUCTION 1. God is Good: The Harmony between Judaism and Enlightenment Philosophy 2. Philosophy and Law: Shaping Judaism for the Modern World 3. Either/Or: Jacobi's Attack on the Moderate Enlightenment 4. Enlightenment Reoriented: Mendelssohn's Pragmatic Religious Idealism CONCLUSION BIBLIOGRAPHY
How to do a p-descent on an elliptic curve
In this paper, we describe an algorithm that reduces the computation of the (full) p-Selmer group of an elliptic curve E over a number field to standard number field computations such as determining the (p-torsion of) the S-class group and a basis of the S-units modulo pth powers for a suitable set S of primes. In particular, we give a result reducing this set S of 'bad primes' to a very small set, which in many cases only contains the primes above p. As of today, this provides a feasible algorithm for performing a full 3-descent on an elliptic curve over Q, but the range of our algorithm will certainly be enlarged by future improvements in computational algebraic number theory. When the Galois module structure of E[p] is favorable, simplifications are possible and p-descents for larger p are accessible even today. To demonstrate how the method works, several worked examples are included.