この間、Brill の catalogue を見ていると、次のような本の近刊情報が載っていた。
- Khaled El-Rouayheb Relational Syllogisms and the History of Arabic Logic, 900-1900, Brill, Islamic Philosophy, Theology and Science. Texts and Studies, 80, Due in July 2010
Relational inferences are a well-known problem for Aristotelian logic. This book charts the development of thinking about this anomaly, from the beginnings of the Arabic logical tradition in the tenth century to the end of the nineteenth. Based in large part on hitherto unstudied manuscripts and rare books, the study shows that the problem of relational inferences was vigorously debated in the thirteenth, fourteenth and fifteenth centuries. In the course of the seventeenth and eighteenth centuries, Ottoman logicians (writing in Arabic) came to recognize relational inferences as a distinct kind of 'unfamiliar syllogism' and began to investigate their logic. These findings show that the development of Arabic logic did not - as is often supposed - come to an end in the fourteenth century. On the contrary, Arabic logic was still being developed by critical and fecund reflections as late as the eighteenth and nineteenth centuries.
だそうです。ちょっと驚いた。Arabic Logic というのはヨーロッパの Medieval Logic の前段階ぐらいにしか認識しておりませんでしたが、19世紀ぐらいまで行われていたのだ、それはすごいな、知らなかった。ちなみに relational syllogisms とは、次のようなもののことだそうです。
He [Galen] also introduced the so-called relational syllogisms, examples of which are “A is equal to B, B is equal to C; therefore A is equal to C” and “Dio owns half as much as Theo; Theo owns half as much as Philo. Therefore Dio owns a quarter of what Philo owns.” (Gal. Inst. Log. 17–18). All relational syllogisms Galen mentions have in common that they are not reducible in either Aristotle’s or Stoic syllogistic, but it is difficult to find further formal characteristics that unite them all.
これは、Susanne Bobzien - Logic, history of: Ancient logic: Later Antiquity - in: Donald M. Borchert (ed.) - Encyclopedia of Philosophy. Second Edition - New York, Macmillan, 2006, Vol. 5、からの抜粋で、Formal Ontology Homepage の “Theory and History of Ontology”というページから取ってきました。
スコラ哲学が現在も、あるいはついこの間まで行われていたということはあるようなので(松本正夫先生)、別に驚くほどのことでもないのかもしれませんが…。
今の Relational Syllogisms and the History of Arabic Logic, 900-1900 という本が入っている series には、以下のような本もあります。
- Amir Ljubović The Works in Logic by Bosniac Authors in Arabic, Brill, Islamic Philosophy, Theology and Science. Texts and Studies, 77, 2008
The book offers and explains the hypothesis that the end of the 13th century does not denote the “final stage” and the “stage of decay” of Arabic logic as the “Aristotelian logic” continues its life and development in the following period in Bosnia and Herzegovina either as a subject within the educational system, or as general propaedeutics for each scientific thought where it had skilled interpreters. The book proves that the people of Bosnia and Herzegovina used almost the same way to compose writings in the field of logic: one in Latin within West-European cultural and theological tradition, and the others in Arabic, within Arabic-islamic tradition.
随分細かい話ですね。これも Arabic Logic 延命の話のようです。
加えて、先日、College Publications の homepage を見ていると、新しい本の series が刊行されるとの情報が出ていた。どのような本かというと、次のような本です。
- Michael Abraham, Dov Gabbay and Uri J. Schild Non-deductive Inferences in the Talmud, College Publications, Studies in Talmudic Logic Series, 2010
We analyse the three basic non-deductive rules of Talmudic inference; namely Kal Vachomer (Argumentum A Fortiori) and the two kinds of Binyan Av (Analogy and Induction). We construct a unified Matrix Abduction model which explains all the major instances of these rules in the Talmud.
シリーズ タルムード論理学研究。すごい！
Series の概略は以下の通り。
Studies in Talmudic Logic
Series edited by Michael Abraham, Dov Gabbay and Uri Schild
The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries a ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic.
This book series on Talmudic Logic,aims to present logical analysis of Talmudic reasoning using modern logical tools.The series begins with the systematic analysis of Talmudic inference rules. The first book shows that we can present Talmudic reasoning intuitions as a systematic logical system basic to modern non-deductive reasoning , such as Argumentum A Fortiori, Abduction and Analogy. The second book offers a systematic common sense method for intuitively defining sets and claims that this method adequately models the Talmudic use of the rules Klal uPrat.The also criticizes modern Talmudic research methodology.
Forthcoming books will deal with additional topics like Deontic logic , and Temporal logic , Agency and processes in the Talmud and more.
The aims of the series are two fold:
1. To import into the Talmudic study modern logical methods with a view to help understand complicated Talmudic passages, which otherwise cannot be addressed.
2. To export from the Talmud new logical principles which are innovative and useful to modern contemporary logic.
すごすぎるな。
さらに加えて、以下の論文も、たまたま Studia Logica の homepage で見かけて驚いた。
- M. Abraham , Dov M. Gabbay and U. Schild “Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal Vachomer) using Matrix Abduction,” in: Studia Logica, vol. 92, no. 3, 2009
よくわからないが、どうやら最新の動向のようですね。今、Arabic Logic よりも、Talmudic Logic の方が新しい、という訳でしょうか？ 先端すぎて勉強がついていかないです…。
以上は夜中に急いで書き下したので、誤字脱字や勘違いなどが含まれていましたらすみません。
疲れました。寝ます。おやすみなさい。
