In his note [5] Hausner states a simple combinatorial principle, namely: $$(H)\left\{ {\begin{array}{*{20}c} {if f is a function a non - empty finite set \sigma into itself, p a} \\ {prime, f^p = i_\sigma and \sigma _0 the set of fixed points of f, then } \\ {\left| \sigma \right| \equiv \left| {\sigma _0 } \right|(mod p).} \\\end{array}} \right.$$ .He then shows how this principle can be used to prove:Fermat's little theorem,Cauchy's theorem for finite groups,Lucas' theorem for binomial numbers.Letε=(0,1, (...) ...),ℱ 1−1 the family of all one-to-one functions from a subset ofε intoε andℳ 1−1 the family of all p.r. (i.e., partial recursive) one-to-one functions from a subset ofε intoε. A subsetα of ε is finite, ifα is not equivalent to a proper subset under a function inℱ 1−1. The setα is calledisolated, if it is not equivalent to a proper subset under a function inℳ 1−1. An isolated set can also be defined as a subset ofε which has no infinite r.e. (i.e., recursively enumerable) subset. While every finite set is isolated, there are $c = 2^{\aleph _0 }$ infinite sets which are isolated; these sets are calledimmune. It is the purpose of this paper to generalize (H) to a principle (H*) for isolated sets and to show how (H*) can be used to prove generalizations of Fermat's little theorem and Cauchy's theorem for finite groups. We have been unable to generalize Lucas' theorem in a similar manner. (shrink)

The contribution of the generation of Tâbi’un in the formation of Islamic sciences in general and in the development of hadith in particular is known. Various studies have been done on the quality of this contribution. Being a part of such an aim is among the targets of this study as well. Not to conducted any work on the hadithism of especially Abdullah b. Abbas' student and after him Atâ ibn Abi Rabah who the most famous teacher of the Mecca (...) school was another encouraging reason. While examining the life and scientific personality of Ata who was one of the early personalities, it has been tried to reach some results with the information obtained from the sources from the first period, especially the fatwa and rumors belonging to him. Atâ who was leading an observable, active political life, lived in the intellectual and social turmoil that emerged in the early period. Atâ who drawing attention with his educator personality, added his own experiences to the scientific heritage he received from the companions in the first instance Ibn Abbas, and had been passed it on to the next generations. Being a fatwa authority in Makkah mufti and pilgrimage organizations for many years is one of his important experiences. In addition to being well-known for his devotion to the Sunnah, he has been taken place between those known among the generation of Tâbi’un with his fatwa and ijtihad. Ata, who is a critical hadith reciter, is accepted as the absolute authority in the hadith. The fact that he was one of the first to make talfiq in the hadith shows that he knew the diversity of the sources he reported and the many tarikh of the narrations. He wrote narrations and encouraged writing of hadith. He contributed to the development of hadith terms with some of the hadith concepts he used and drew attention with the abundance of mursal hadiths. (shrink)

This book covers the author's conception of God aside from any religion. He does not come from a religious view in order to transmit the truest conception of God that he is capable of because any religion, whatever it might be, always claims God for itself in an exclusionary fashion. In other words, you must be a follower of the chosen faith before God will accept you into his kingdom. Wells rejects this view. Any man or woman who accepts God's (...) love as one person connecting to their own creator, is fine. An intermediary, despite what they might crow from whatever pulpits they use, is not necessary. We are all God's children. We are all seeking the same God, so to be dogmatic within a certain exclusionary faith is small-minded and petty. If you want to grow up, spiritually, then this book is for you. (shrink)

Studying Mesilat Yesharim with Hadar Goldin.

Open peer commentary on the article “Religion: A Radical-Constructivist Perspective” by Andreas Quale. Upshot: Quale offers a way of categorizing religious discourse based on radical constructivism. This commentary raises questions about the inter-relation of cognitive and non-cognitive knowledge, the role of testimony in learning about religion, and whether knowledge and belief have different roles in cognitive and non-cognitive knowledge, and suggests that Quale’s analysis opens a tolerant perspective on religious discourse.

Geschichte der neueren Philosophie ist ein unveränderter, hochwertiger Nachdruck der Originalausgabe aus dem Jahr 1895. Hansebooks ist Herausgeber von Literatur zu unterschiedlichen Themengebieten wie Forschung und Wissenschaft, Reisen und Expeditionen, Kochen und Ernährung, Medizin und weiteren Genres. Der Schwerpunkt des Verlages liegt auf dem Erhalt historischer Literatur. Viele Werke historischer Schriftsteller und Wissenschaftler sind heute nur noch als Antiquitäten erhältlich. Hansebooks verlegt diese Bücher neu und trägt damit zum Erhalt selten gewordener Literatur und historischem Wissen auch für die Zukunft bei.