Abstract
I argue that Aristotle’s late-antique commentators read into his theory of demonstration the notion of tekmeriodic proofs in attempt to integrate into the theory of demonstration the assumption that the principles of demonstration should be evident. In so doing, I trace the late antique commentators’ view to Alexander of Aphrodisias’ discussion of the principles of demonstration, showing how his assumption that the principles of demonstration should be evident underlies their notions of tekmeriodic proofs.
Résumé
On examine pourquoi les commentateurs d’Aristote dans l’Antiquité tardive lisent dans sa théorie de la démonstration le concept de preuve tekmeriodique. Il s’agit, selon nous, d’une tentative visant à intégrer à cette théorie la supposition que les principes de la démonstration doivent être évidents. Pour justifier cette thèse, nous examinons l’étude des preuves du Tekmerion de Simplicius jusqu’à Alexandre d’Aphrodisie qui considérait les axiomes évidents et envisageait qu’ils puissent prouver des principes de l’être.
Zusammenfassung
In diesem Beitrag wird behauptet, dass die spätantiken Aristoteles-Kommentatoren in dessen Lehre vom Beweis das Konzept des tekmérion hineininterpretieren, um sie mit der Behauptung zu verbinden, die Prinzipien des Beweisens müssten unbezweifelbar sein. Dabei wird die Perspektive der spätantiken Kommentatoren von Simplicius bis zu Alexander von Aphrodisias’ Diskussion der Prinzipien des Beweisens zurückverfolgt, um zu verdeutlichen, inwieweit dessen Forderung nach unbezweifelbaren Prinzipien des Beweisens die Grundlage für das Konzept tekmeriodischer Belege bei den spätantiken Kommentatoren bildet.
Resumen
Examinamos por qué los comentaristas de Aristóteles en la Antiguidad tardía leen en su teoría de la demostración el concepto de prueba tekmeriódica. Se trata, creemos, de una tentativa que quiere integrar a esta teoría la suposición de que los principios de la demostración tenían que ser evidentes. Para justificar esta tesis, examinamos el estudio de pruebas de Tekmerion de Simplicius hasta Alejandro d’Afrodisías que consideraba los axiomas cómo evidentes y contemplaba la posibilidad que pudiesen probar los principios del ser.
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Orna Harari, born in 1969, is Senior Lecturer at the departments of Classics and Philosophy (Tel Aviv University). Her research concerns the reception of Aristotle’s theory of demonstration in the late-antique commentary tradition. Amongst her recent publications, one finds, “Simplicius on Tekmeriodic Proofs” (Studies in History and Philosophy of Science, 43, 2012).
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Harari, O. The principles of demonstration and tekmeriodic proofs in the late-antique commentary tradition. Rev synth 134, 249–266 (2013). https://doi.org/10.1007/s11873-013-0219-6
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DOI: https://doi.org/10.1007/s11873-013-0219-6