This article addresses the problem of automatically extracting legal indices which express the important contents of legal documents. Legal indices are not limited to single-word keywords and compound-word keywords, they are also clause keywords. We approach index extraction using structural information of Japanese sentences, i.e. chunks and clauses. Based on the assumption that legal indices are composed of important tokens from the documents, extracting legal indices is treated as a problem of collecting chunks and clauses that contain as many important (...) tokens as possible. Each token is assigned a weight which is a statistical score, e.g. TF–IDF and Okapi BM25, to indicate its importance. The importance of a chunk or clause is determined based on the average weight of tokens included in that chunk or clause. Then, highly weighted chunks and clauses are recognized as the indices for legal documents. The experimental results on Japanese National Pension Act data show that our proposed method achieves better performance than TextRank, the most popular unsupervised method in extracting single-word and compound-word keywords. In addition, this approach is also applicable to extract clause keywords with high performance. (shrink)

Different animal groups exhibit a surprisingly diversity of sex determination systems. Moreover, even systems that are superficially similar may utilize different underlying mechanisms. This diversity is illustrated by a comparison of sex determination in three well‐studied model organisms: the fruitfly Drosophila melanogaster, the nematode Caenorhabditis elegans, and the mouse. All three animals exhibit male heterogamety, extensive sexual dimorphism and sex chromosome dosage compensation, yet the molecular and cellular processes involved are now known to be quite unrelated. The similarities must have (...) arisen by convergent evolution. Studies of sex determination demonstrate that evolution can produce a variety of solutions to the same basic problems in development. (shrink)

In der 1970 gegründeten Reihe erscheinen Arbeiten, die philosophiehistorische Studien mit einem systematischen Ansatz oder systematische Studien mit philosophiehistorischen Rekonstruktionen verbinden. Neben deutschsprachigen werden auch englischsprachige Monographien veröffentlicht. Gründungsherausgeber sind: Erhard Scheibe (Herausgeber bis 1991), Günther Patzig (bis 1999) und Wolfgang Wieland (bis 2003). Von 1990 bis 2007 wurde die Reihe von Jürgen Mittelstraß mitherausgegeben.

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos (...) theory, topology, mathematical physics, and the solution of Fermat's Last Theorem.Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises will stretch the more advanced reader. (shrink)

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos (...) theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises will stretch the more advanced reader. (shrink)

This book presents a systematic reconstruction of Leibniz’s dynamics project (c. 1676-1700) that contributes to a more comprehensive understanding of the concepts of physical causality in Leibniz’s work and 17th century physics. It argues that Leibniz’s theory of forces privileges the causal relationship between structural organization and physical phenomena instead of body-to-body mechanical causation. The mature conception of Leibnizian force is not the power of one body to cause motion in another, but a kind of structural causation related to the (...) configuration of integral systems of bodies in physical evolution. By treating the immanent philosophy of Leibniz’s dynamics, this book makes explicit the systematic aims and inherent limits of Leibniz's physical project, in addition to providing an alternative vision of the scientific understanding of the physical world in the late 17th and early 18th century. (shrink)

Leibniz studies is a distinctive kind of joy. The seventeenth-century polymath made remarkable impacts in a wide-ranging number of domains and their subdomains. The attempt to study one domain in d...

This paper focuses on Leibniz’s conception of modality and its application to the issue of natural laws. The core of Leibniz’s investigation of the modality of natural laws lays in the distinction between necessary, geometrical laws on the one hand, and contingent, physical laws of nature on the other. For Leibniz, the contingency of physical laws entailed the assumption of the existence of an additional form of causality beyond mechanical or efficient ones. While geometrical truths, being necessary, do not require (...) the use of the principle of sufficient reason, physical laws are not strictly determined by geometry and therefore are logically distinct from geometrical laws. As a consequence, the set of laws that regulate the physical laws could have been created otherwise by God. However, in addition to this, the contingency of natural laws does not consist only in the fact that God has chosen them over other possible ones. On the contrary, Leibniz understood the status of natural laws as arising from the action internal to physical substances. Hence the actuality of physical laws results from a causal power that is inherent to substances rather than being the mere consequence of the way God arranged the relations between physical objects. Focusing on three instances of Leibniz’s treatment of contingency in physics, this paper argues that, in order to account for the contingency of physical laws, Leibniz maintained that final causes, in addition to efficient and mechanical ones, must operate in physical processes and operations. (shrink)

This article aims to interpret Leibniz’s dynamics project through a theory of the causation of corporeal motion. It presents an interpretation of the dynamics that characterizes physical causation as the structural organization of phenomena. The measure of living force by mv2 must then be understood as an organizational property of motion conceptually distinct from the geometrical or otherwise quantitative magnitudes exchanged in mechanical phenomena. To defend this view, we examine one of the most important theoretical discrepancies of Leibniz’s dynamics with (...) classical mechanics, the measure of vis viva as mv2 rather than ½ mv2. This “error”, resulting from the limits of Leibniz’s methodology, reveals the systematic role of this quantity mv2 in the dynamics. In examining the evolution of the quantity mv2 in the refinement of the force concept from potentia to actio, I argue that Leibniz’s systematic limitations help clarify dynamical causality as neither strictly metaphysical nor mechanical but a distinct level of reality to which Leibniz dedicates the “dynamica” as “nova scientia”. (shrink)

On Tibetan Buddhist doctrines and philosophy according to Sa-skya-pa tradition.

Different animal groups exhibit a surprisingly diversity of sex determination systems. Moreover, even systems that are superficially similar may utilize different underlying mechanisms. This diversity is illustrated by a comparison of sex determination in three well‐studied model organisms: the fruitfly Drosophila melanogaster, the nematode Caenorhabditis elegans, and the mouse. All three animals exhibit male heterogamety, extensive sexual dimorphism and sex chromosome dosage compensation, yet the molecular and cellular processes involved are now known to be quite unrelated. The similarities must have (...) arisen by convergent evolution. Studies of sex determination demonstrate that evolution can produce a variety of solutions to the same basic problems in development. (shrink)

This article aims to treat the question of the reality of Leibniz’s infinitesimals from the perspective of their application in his account of corporeal motion. Rather than beginning with logical foundations or mathematical methodology, I analyze Leibniz’s use of an allegedly “instantiated” infinitesimal magnitude in his treatment of dead force in the Specimen Dynamicum. In this analysis I critique the interpretive strategy that uses the Leibnizian distinction, drawn from the often cited 1706 letter to De Volder, between actual and ideal (...) for understanding the meaning of Leibniz’s infinitesimal fictionalism. In particular, I demonstrate the ambiguity that results from sticking too closely with the idea that ideal mathematical terms merely “represent” concrete or actual things. In turn I suggest that, rather than something that had to be prudentially separated from the realm of actual things, the mathematics of infi nitesimals was part of how Leibniz conceived of the distinction between the actual and ideal within the Specimen Dynamicum. (shrink)

In this article, I address two different kinds of equivocations in reading Leibniz’s fictional infinite and infinitesimal. These equivocations form the background of a reductive reading of infinite and infinitesimal fictions either as ultimately finite or as something whose status can be taken together with any other mathematical object as such. The first equivocation is the association of a foundation of infinitesimals with their ontological status. I analyze this equivocation by criticizing the logicist influence on 20th century Anglophone reception of (...) the syncategorematical infinite and infinitesimal. The second equivocation is the association of the rigor of mathematical demonstration with the problem of the admissibility of infinite or infinitesimal terms. I analyze this by looking at Leibniz’s constructive method and apagogic argument style in his quadrature method. In treating these equivocations, I critique some assumptions that underlie the reductive reading of Leibniz’s fictionalism concerning infinite and infinitesimals. In turn, I suggest that these infinitesimal “fictions” pointed to a problematic within Leibniz’s work that was conceived and reconsidered in Leibniz’s work from a range of different contexts and methods. (shrink)

This paper argues that Cantorian transfinite cardinality is not a necessary assumption for the ontological claims in Badiou’s L’Être et l’Événement. The necessary structure for Badiou’s mathematical ontology in this work was only the ordinality of sets. The method for reckoning the sizes of sets was only assumed to follow the standard Cantorian measure. In the face of different and compelling forms of measuring non-finite sets, it is argued that Badiou’s project can indeed accommodate this pluralism of measurement. In turn, (...) this plurality of measurement implies that Badiou’s insistence on the “subtraction of the one”, the move to affirm the unconditioned being of the “inconsistent multiple”, results in the virtuality of the one, a pluralism of counting that further complicates the relationship between the one and the multiple in the post-Cantorian era. (shrink)