Article ID: CBB164105590

Abū Hāšim Al-Ǧubbāʾī, algèbre et inférence (2020)

unapi

Cet article vise à restituer la doctrine du « signe du manifeste au caché » d'Abū Hāšim al-Ğubbāʾī (888-933). Il montre qu'Abū Hāšim a tendu à interpréter ce signe comme une inférence, dont il a reconnu deux types principaux : le type-1 (la « communauté de preuve », al-ištirāk fī al-dalāla) procède par déduction analytique de concepts en neutralisant les conditions de réalisation de ces derniers, c'est-à-dire leur soubassement ontologique. C'est, typiquement, la procédure la plus directement consonante avec l'ontologie modale d'Abū Hāšim. Le type-2 (la « communauté de cause », al-ištirāk fī al-ʿilla) exhibe un même rapport de causalité au plan du connu et au plan de l'inconnu et considère que la causalité au plan du connu est elle-même la cause de la causalité au plan de l'inconnu. Cette partition parfaitement inédite dans la philosophie et le kalām est en revanche préfigurée dans la doctrine de la preuve exposée par al-Ḫwārizmī dans son Algèbre. Al-Ḫwārizmī distingue en effet entre la preuve « par la cause » (bi-al-ʿilla), qui consiste à transférer une certaine déduction géométrique au plan de l'algèbre et la preuve « par l'expression » (bi-al-lafẓ) qui opère directement sur les expressions algébriques, qu'elle réduit analytiquement. En se fondant sur un texte d'Abū Hāšim consacré à la connaissance humaine qui paraît se référer à l’œuvre d'al-Ḫwārizmī, l'article suggère pour finir que le parallèle conceptuel étroit entre la doctrine de la preuve d'al-Ḫwārizmī et la doctrine du signe d'Abū Hāšim pourrait ne pas être une simple coïncidence. Deux appendices ont été ajoutés. Le premier traite de la lecture par al-Fārābī de la théorie de l'inférence d'Abū Hāšim. Le second, en s'appuyant sur toutes les données disponibles, établit pour la première fois les dates correctes et précises de la vie d'Abū Hāšim., AbstractThis article aims to unravel the doctrine of the “sign from the manifest to the hidden” of Abū Hāšim al-Ğubbāʾī (888-933). It shows that Abū Hāšim tended to interpret this sign as an inference, of which he recognized two main types: Type-1 (the “community of evidence”, al-ištirāk fī al-dalāla) proceeds by analytical deduction of concepts by neutralizing the conditions of their realization, i. e. their ontological basis. This is, typically, the procedure most directly consonant with Abū Hāšim's modal ontology. Type-2 (the “community of cause”, al-ištirāk fī al-ʿilla) exhibits the same causal relationship at the known and unknown levels and considers causality at the known level to be itself the cause of causality at the unknown level. This partition was completely new in philosophy and kalām at the time of Abū Hāšim, but it is foreshadowed in al-Ḫwārizmī’s Algebra. In this book, al-Ḫwārizmī distinguishes between proof “by cause” (bi-al-ʿilla), which consists in transferring a certain geometric deduction to algebra, and proof “by expression” (bi-al-lafẓ), which operates directly on algebraic expressions, which it reduces analytically. A text by Abū Hāšim devoted to human knowledge that seems to refer to the work of al-Ḫwārizmī suggests, finally, that the close parallel between al-Ḫwārizmī’s doctrine of proof and Abū Hāšim's doctrine of the sign may not be a mere coincidence. Two appendices have been added. The first deals with al-Fārābī’s reading of Abū Hāšim's theory of inference. The second, based on all available data, establishes for the first time the correct and precise dates of Abū Hāšim's life.This article aims to restore the doctrine of the "sign from the manifest to the hidden" of Abū Hāšim al-Ğubbāʾī (888-933). It shows that Abū Hāšim tended to interpret this sign as an inference, of which he recognized two main types: type-1 (the "community of proof", al-ištirāk fī al-dalāla) proceeds by analytical deduction of concepts by neutralizing the conditions for the realization of the latter, that is to say their ontological foundation. It is, typically, the procedure most directly consonant with Abū Hāšim's modal ontology. Type-2 (the "community of cause", al-ištirāk fī al-ʿilla) exhibits the same relation of causality on the plane of the known and on the plane of the unknown and considers that the causality on the plane of the known is itself the cause of causality at the level of the unknown. This partition, completely new in philosophy and kalām, is on the other hand prefigured in the doctrine of proof exposed by al-Ḫwārizmī in his Algebra. Al-Ḫwārizmī indeed distinguishes between proof “by cause” (bi-al-ʿilla), which consists in transferring a certain geometric deduction to the plane of algebra, and proof “by expression” (bi-al-ʿilla). lafẓ) which operates directly on algebraic expressions, which it reduces analytically. Based on a text by Abū Hāšim on human knowledge that appears to refer to the work of al-Ḫwārizmī, the article concludes by suggesting that the close conceptual parallel between al-Ḫwārizmī's doctrine of proof Ḫwārizmī and Abū Hāšim's sign doctrine might not be a mere coincidence. Two appendices have been added. The first deals with al-Fārābī's reading of Abū Hāšim's theory of inference. The second, drawing on all available data, establishes for the first time the correct and precise dates of Abū Hāšim's life.

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB164105590/

Similar Citations

Article Naoya Iwata; (2021)
Aristotle on Geometrical Potentialities (/isis/citation/CBB103445778/)

Article Fiorentino, Francesco; (2007)
Causalità, infinito e sostanza in Francesco d'Ascoli (/isis/citation/CBB001020537/)

Chapter Caroti, Stefano; (2006)
Nicolas d'Autrécourt, la génération, la corruption et l'altération (/isis/citation/CBB001020317/)

Thesis La Nave, Federica; (2005)
Belief Without Proof from Ancient Geometry to Renaissance Algebra (/isis/citation/CBB001560809/)

Article Srećko Kovač; (2020)
On causality as the fundamental concept of Gödel’s philosophy (/isis/citation/CBB991048612/)

Book Karen Bennett; (2017)
Making Things Up (/isis/citation/CBB739865359/)

Article Waldegg, Guillermina; (2001)
Ontological Convictions and Epistemological Obstacles in Bolzano's Elementary Geometry (/isis/citation/CBB000101855/)

Book Yrjönsuuri, Mikko; (2001)
Medieval Formal Logic: Obligations, Insolubles and Consequences (/isis/citation/CBB000102010/)

Article Nascimento, Carlos Arthur Ribeiro do; (2008)
Avicena e as Ciências Mistas (/isis/citation/CBB000950536/)

Book Dominique Tournès; (2022)
Histoire du calcul graphique (/isis/citation/CBB952248492/)

Article Leïla Hamouda; Yassine Hachaichi; (2021)
Note sur l'extraction de la racine carrée d'un entier chez ibn Al-Hayṯam et comparaison avec Al-Baġdādī (/isis/citation/CBB183440774/)

Chapter Hélène Bellosta; (2012)
La destinée arabe des Données d’Euclide (/isis/citation/CBB209738412/)

Article Oaks, Jeffrey A.; (2011)
Al-Khayyām's Scientific Revision of Algebra (/isis/citation/CBB001210380/)

Authors & Contributors
Moyon, Marc
Bellosta, Hélène
Caroti, Stefano
Chemla, Karine Carole
Cohoe, Caleb
Corry, Leo
Journals
Arabic Sciences and Philosophy
Archive for History of Exact Sciences
Archivum Franciscanum Historicum
British Journal for the History of Philosophy
Circumscribere: International Journal for the History of Science
Endeavour: Review of the Progress of Science
Publishers
Harvard University
Kluwer Academic
Oxford University Press
Università degli Studi di Siena
Edizioni Cadmo
Cassini (Publisher)
Concepts
Geometry
Algebra
Philosophy
Mathematics
Ontology
Causality
People
Aristotle
Euclid
Abu Bakr al-Qadi
al-Khayyam, Ghiyath al-Din Abul Fateh Omar Ibn Ibrahim
Avicenna
Bolzano, Bernard
Time Periods
Medieval
14th century
13th century
Ancient
Renaissance
11th century
Places
China
Greece
Italy
Czech Republic
Europe
Mediterranean region
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment