478 research outputs found
Note on the Grothendieck operations and the Betti realization
Get PDFThe purpose of this note is to show that the Betti realization of motives is compatible with Grothendieck's six operations and the nearby cycles functors, which in the motivic world, were previously studied by the author. We first review the construction of the Betti realization. Then, we establish some general criteria which, applied to the Betti realization, give the compatibilities we seek except for the one concerning the nearby cycles functors. The latter will be treated in a separate section
EMILIO BETTI VERSUS HANSAS-GEORGAS GADAMERIS: HERMENEUTINIO PRASMĖS SUPRATIMO DILEMA
Get PDFStraipsnio tikslas – apibrėžti Emilio Betti vartojamas sąvokas, eksplikuoti pagrindines jo metodinės hermeneutikos nuostatas, nurodyti esmines jam rūpimas hermeneutinių tyrimų problemas ir išryškinti Betti „metodinės hermeneutikos“ bei Hanso Georgo Gadamerio „filosofinės hermeneutikos“ esminius skirtumus ir nesutarimus. Betti priėjo kaltinamąją išvadą, kad Gadameris interpretuojamojo autoriaus objektyvią reikšmę pavertė interpretuojančiojo subjektyviu ir istoriškai kintančiu reikšmingumu, atvedusiu į reliatyvizmą. Straipsnyje pirmiausia įrodinėjama, kad autoriaus arba „objekto autonomijos“ prasminis krūvis prieš Betti valią dėl „perimančio rūpinimosi“ pranyksta ir persikelia į interpretatoriaus, kuris yra įsigyvenęs į objektyvumą, sąmonės plotmę. Taip jis tampa priklausomas nuo interpretatoriaus rekonstruojančių užmojų, kuriuos lydi tam tikri metodologiniai sumanymai. Kai Betti pabrėždamas „objekto autonomijos“ svarbą teigė, jog „svetimos dvasios“ objektyvumas pasiekiamas per interpretatoriaus kongenialų įsigyvenimą į ją – Aš įsigyvenimą į Tu, – jis tam tikru atžvilgiu „svetimai dvasiai“ ne suteikė objektyvųjį „svorį“, bet jį atėmė. Kitaip tariant, ne sustiprino, bet susilpnino dvasios autonomiją. Antra, nepagrįsta laikoma Betti išvada, kad gadameriškasis interpretatorius, remdamasis „pilnaties numatymu“, užgrobia tiesos monopoliją, kuri jam tampa jei ne nuosavybe, tai kontrolės instancija. Trečia, nepagrįsta laikoma Betti išvada, jog Gadamerio „filosofinė hermeneutika“ paneigia „objekto autonomiją“ ir todėl veda prie reliatyvizmo. Gadamerio „filosofinė hermeneutika“ numato teksto prasminio turinio autonomiją – ne tik interpretatoriaus, bet ir kūrybos autoriaus bei pirminio skaitytojo atžvilgiu. Ketvirta, teigiama, jog Gadamerio hermeneutinio supratimo efektas yra tas, kad jis ne subjektyviai iškreipia prasmės ar tiesos objektyvumą, kaip norėjo parodyti Betti, bet išskleidžia ir apnuogina interpretacijos subjektyvumą – kaip teisėtą arba neteisėtą – to, kas buvo parašyta ar pasakyta, atžvilgiu.
Pagrindiniai žodžiai: interpretacija, supratimas, prasmė, E. Betti „metodologinė hermeneutika“, H. G. Gadamerio „filosofinė hermeneutika“.
Emilio Betti versus Hans-Georg Gadamer: the Dilemma of Hermeneutical Understanding of Meaning
Arūnas Mickevičius
Summary
The paper aims to define the terms used by Emilio Betti, explicate the basic attitudes and the essential problems of his methodical hermeneutics, and highlight fundamental differences and disagreements between Betti’s “methodical hermeneutics” and Hans-Georg Gadamer’s “philosophical hermeneutics”. Betti came to the indictment that Gadamer turned the objective meaning of the author to subjective and historical significance which had led to relativism. The paper first argues that objective meaning of the author or the “autonomy of the object”, against the will of Betti, disappears and moves to the realm of consciousness of the interpreter. When Betti claimed, emphasizing “autonomy of the object”, that objectivity of the “alien spirit” is achieved through the interpreter’s congeniality, he has not strengthened but weakened the autonomy of the spirit. Second, Betti is wrong in stating that Gadamer’s interpreter, referring to the “anticipation of the fullness”, occupies the monopoly of the truth of which he becomes the instance of ownership or control. Third, Betti is wrong in stating that Gadamer’s “philosophical hermeneutics” denies the autonomy of the object, and thus leads to relativism. Gadamer’s “philosophical hermeneutics” provides the autonomy of the text not only with respect to the interpreter, but also with respect to the creativity of the author and the primary reader. Fourth, the article states that the effect of Gadamer’s hermeneutical understanding is that it does not subjectively distort the meaning of truth or objectivity, as Betti wanted to show, but expands and exposes the subjectivity of interpretation – as a legitimate or illegitimate – with respect to what has been written or said.
Keywords: interpretation, understanding, meaning, E. Betti’s methodological hermeneutics, H.G. Gadamer’s philosophical hermeneutics
YAUMIDDIN DALAM PERSPEKTIF TEORI HERMENEUTIKA EMILIO BETTI
No full textAbstrak: Paper ini menggunakan pendekatan kajian pustaka yang bersumber dari buku, jurnal, dan literatur lainnya yang masih ada relevansinya dengan topik ini. Tujuan dari paper ini ialah berusaha untuk menginterprestasikan kata yaumuddin dalam QS. Al-Fatihah: 4 dipandang dari teori hermeneutika Emilio Betti. Hasil kajian literatur menunjukkan bahwa menurut Emilio Betti kajian terhadap teks erat kaitannya dengan kegiatan interpretasi meaning yang terkandung di dalam teks tersebut. Meaning senantiasa merujuk pada objektifitas pemikiran sang penafsir. Oleh karenanya, interpretasi teks hendaknya bersifat gerakan penafsiran yang melibatkan aspek kebahasaan, latar belakang historis dan pengenalan terhadap si pengarang secara bersama-sama. Metode hermeneutika Betti lebih menekankan pada rekonstruksi makna berbekal cakrawala intelektual penafsir (subjek) menggunakan model interprestasi reproduktif. Berdasarkan teori Betti tersebut, teks yaumiddin pada QS. Al-Fatihah: 4 berarti hari ditiupnya sangsakala, dimana hari yang tidak seorang pun dapat membela orang lain, sehingga hari itu dinamakan juga sebagai hari keputusan dan hari pembalasan oleh Allah SWT.Kata Kunci: Emilio Betti, Objektifitas, Rekonstruksi, dan Reproduktif.Abstract: This paper uses lierature research approach which sourced from books, journals, and other literature that still have relevance to this topic. This paper seeks to interpret the word “yaumiddin†in QS. Al-Fatihah: 4 from the perspective of Emilio Betti hermeneutic theory. The results of study showed that in a perspective of Betti the text closely related to the activities of interpretation of the meaning contained in the text. Meaning always refers to the objectivity of the interpreter thought. Therefore, the interpretation of the text should be the movement of interpretation that involves linguistic aspects, historical background and introduction to the author together. Betti hermeneutical method is more emphasis on the reconstruction of the intellectual horizons of meaning armed interpreter (subject) using a model of reproductive interpretation. Based on Betti theory that text “yaumiddin†on QS. Al-Fatihah: 4 means the day he blew the trumpet, where the day that no one can defend someone else, so the day was named as well as the decisions and the Day of Judgment by Allah SWT.Keywords: Emilio Betti, Objectivity, Reconstructive and Reproductive.</jats:p
La resistencia lingüística en “Como el cristal al romperse”. El español como refugio lingüístico, cultural y emocional
Get PDFEl cuento de Luz Selenia Vázquez “Como el cristal al romperse” (1983) profundiza en las complejidades de la experiencia migrante latina en los Estados Unidos. A través de la protagonista, Lupe Carrera, la autora explora las tensiones entre dos culturas y dos idiomas. Este artículo analiza cómo el cambio de código refleja la lucha interna de la protagonista por reconciliar su identidad bicultural dentro de una sociedad que a menudo la margina. Se argumenta que la lengua sirve ya sea como una herramienta de resistencia ya sea como un refugio de la alienación.
Luz Selenia Vázquez’s short story “Como el cristal al romperse” (1983) delves into the complexities of the Latina migrant experience in the United States. Through the protagonist, Lupe Carrera, the author explores the tensions between two cultures and languages. This article analyzes how code-switching reflects the protagonist’s internal struggle to reconcile her bicultural identity within a marginalizing society. It argues that language serves as both a tool for resistance and a refuge from alienation.Luz Selenia Vázquez’s short story “Como el cristal al romperse” (1983) delves into the complexities of the Latina migrant experience in the United States. Through the protagonist, Lupe Carrera, the author explores the tensions between two cultures and languages. This article analyzes how code-switching reflects the protagonist’s internal struggle to reconcile her bicultural identity within a marginalizing society. It argues that language serves as both a tool for resistance and a refuge from alienation.
El cuento de Luz Selenia Vázquez “Como el cristal al romperse” (1983) profundiza en las complejidades de la experiencia migrante latina en los Estados Unidos. A través de la protagonista, Lupe Carrera, la autora explora las tensiones entre dos culturas y dos idiomas. Este artículo analiza cómo el cambio de código refleja la lucha interna de la protagonista por reconciliar su identidad bicultural dentro de una sociedad que a menudo la margina. Se argumenta que la lengua sirve ya sea como una herramienta de resistencia ya sea como un refugio de la alienación
GRAPH INVARIANTS AND BETTI NUMBERS OF REAL TORIC MANIFOLDS
No full textFor a graph G, the graph cubeahedron □_G and the graph associahedron △_G are simple convex polytopes which admit (real) toric manifolds. In this paper, we introduce a graph invariant, called the b-number, and show that the b-numbers compute the Betti numbers of the real toric manifold X^R(□_G) corresponding to □_G. The b-number is a counterpart of the notion of anumber, introduced by S. Choi and the second named author, which computes the Betti numbers of the real toric manifold X^R(△_G) corresponding to △_G. We also study various relationships between a-numbers and b-numbers from the viewpoint of toric topology. Interestingly, for a forest G and its line graph L(G), the real toric manifolds X^R(△_G) and X＾R(□_＜L(G)＞) have the same Betti numbers
BETTI NUMBERS OF SHIMURA CURVES AND ARITHMETIC THREE--ORBIFOLDS
No full textInternational audienceWe show that asymptotically the first Betti number b1 of a Shimura curve satisfies the Gauss--Bonnet equality 2π(b1 − 2) = vol where vol is hyperbolic volume; equivalently 2g−2 = (1+o(1)) vol where g is the arithmetic genus. We also show that the first Betti number of a congruence hyperbolic 3--orbifold asymptotically vanishes relatively to hyperbolic volume, that is b1/ vol → 0. This generalises previous results obtained by the first author, on which we rely, and uses the same main tool, namely Benjamini--Schramm convergence.Nous démontrons une égalité de Gauss--Bonnet asymptotique pour les surfaces provenant de réseaux arithmétiques. En dimension 3 nous démontrons que les nombres de Betti des orbi-variétés arithmétiques hyperboliques sont négligeables par rapport au volume. Les démonstrations reposent sur un résultat de convergence au sens de Benjamini--Schramm des 2- et 3-orbi-variétés hyperboliques arithmétiques généralisant un travail du premier auteur
GRAPH INVARIANTS AND BETTI NUMBERS OF REAL TORIC MANIFOLDS
Get PDFFor a graph G, the graph cubeahedron □_G and the graph associahedron △_G are simple convex polytopes which admit (real) toric manifolds. In this paper, we introduce a graph invariant, called the b-number, and show that the b-numbers compute the Betti numbers of the real toric manifold X^R(□_G) corresponding to □_G. The b-number is a counterpart of the notion of anumber, introduced by S. Choi and the second named author, which computes the Betti numbers of the real toric manifold X^R(△_G) corresponding to △_G. We also study various relationships between a-numbers and b-numbers from the viewpoint of toric topology. Interestingly, for a forest G and its line graph L(G), the real toric manifolds X^R(△_G) and X＾R(□_＜L(G)＞) have the same Betti numbers
Einleitung der Herausgeber
Get PDFThis book presents the long-awaited critical edition of an unpublished manuscript of 277 pages containing Twardowski’s lecture notes on logic given in German at the University of Vienna. As to length, language and topic, this text is unique among the works of the author, who is renowned for his Zur Lehre vom Inhalt und Gegenstand der Vorstellungen (1894), an influential but short book that has been out of stock for a long time already. In Logik Twardowski’s ideas are exposed in a much more extensive and interestingly revised form. The rest of Twardowski’s production is in Polish, a language inaccessible to many readers
L^2-Betti numbers of locally compact groups and their cross section equivalence relations
No full text© 2015 American Mathematical Society. We prove that the L2-Betti numbers of a unimodular locally compact group G coincide, up to a natural scaling constant, with the L2-Betti numbers of the countable equivalence relation induced on a cross section of any essentially free ergodic probability measure preserving action of G. As a consequence, we obtain that the reduced and unreduced L2-Betti numbers of G agree and that the L2-Betti numbers of a lattice Γ in G equal those of G up to scaling by the covolume of Γ in G. We also deduce several vanishing results, including the vanishing of the reduced L2-cohomology for amenable locally compact groups.sponsorship: The first author was supported by ERC Starting Grant VNALG-200749. The second author was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92). The third author was supported by ERC Starting Grant VNALG-200749, Research Programme G.0639.11 of the Research Foundation - Flanders (FWO), and KU Leuven BOF research grant OT/08/032. (ERC|VNALG-200749, Danish National Research Foundation through the Centre for Symmetry and Deformation|DNRF92, Research Foundation - Flanders (FWO)|G.0639.11, KU Leuven BOF|OT/08/032, Villum Fonden|00007423)status: Publishe
L²-Betti numbers arising from the lamplighter group
Get PDFWe apply a construction developed in a previous paper by the authors in order to obtain a formula which enables us to compute l²-Betti numbers coming from a family of group algebras representable as crossed product algebras. As an application, we obtain a whole family of irrational l²-Betti numbers arising from the lamplighter group algebra Q[Z(2) (sic) Z]. This procedure is constructive, in the sense that one has an explicit description of the elements realizing such irrational numbers. This extends the work made by Grabowski, who first computed irrational l(2)-Betti numbers from the algebras Q[Z(n) (sic) Z], where n >= 2 is a natural number. We also apply the techniques developed to the generalized odometer algebra (O)((n) over bar), where (n) over bar is a supernatural number. We compute its *-regular closure, and this allows us to fully characterize the set of O((n) over bar)-Betti numbers.Both authors were partially supported by DGI-MINECO-FEDER through the Grants MTM2014-53644-P and MTM2017-83487-P, and by the Generalitat de Catalunya through the Grant 2017-SGR-1725. The second named author was also partially supported by DGI-MINECO-FEDER through the Grant BES-2015-071439 and by the research funding Brazilian agency CAPES and by the ERC Starting Grant "Limits of Structures in Algebra and Combinatorics" No. 805495
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