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2013-10-01Berichte und sonstige Texte DOI: 10.18452/13567
Die zeitliche Differenzierung
dc.contributor.authorThaliath, Babu
dc.date.accessioned2017-06-17T15:49:28Z
dc.date.available2017-06-17T15:49:28Z
dc.date.created2013-10-13
dc.date.issued2013-10-01
dc.identifier.otherhttp://www.academia.edu/4734391/The_Temporal_Differentiation
dc.identifier.urihttp://edoc.hu-berlin.de/18452/14219
dc.description.abstractIn its historical development, the notion of infinitesimal proved to be an ambiguous entity both in philosophy as well as in mathematics. The Aristotelian distinction between actual and potential infinity seemed to be predicated upon mechanical considerations (owing to its original relation to Zeno´s paradox). The discourse or debate on the mode of existence of the infinitesimal developed within the context of theoretical philosophy, mathematics, and mathematical sciences, as represented in the invention of the method of calculus by Newton and Leibniz. These contradicting notions of infinity, historically bequeathed, were synthesized into the early-modern concept of limits. The discretion of the limit did not exclude the potential infinitesimal but, on the contrary, presupposed it in the infinite continuity of a process of diminution. The historical origins of such a synthesis can be observed in the late Middle Ages, namely in Nicolaus Cusanus´notion of infinite processes and their discrete bounds, as represented in his geometrical demonstrations of the doctrine coincidentia oppositorum. However, the introduction of the principle of limits in the original geometric-mathematical method of differentiation led to a problem in the philosophy of mathematics. The infinitesimal was originally created in an infinitely continuous process of differentiation, but this (once admitted) element of potential infinitesimal was eliminated in a method of limits in favour of a discrete entity of differential, i.e. in favour of actual infinitesimal. This strategic elimination would also mean the elimination of two basically indispensable factors, or elements, from the limit process in differential calculus, namely the movement and the time (immanent in the movement). Moreover, the predetermination of the limit seems to be a problematic assumption in the original and historically established mode of differentiation. In reality, however, the actual limit itself evolves from a movement of an infinite retardation. When the limit is not predetermined in discretion but generates itself in a process-mode, it rehabilitates the (originally eliminated) potential infinitesimal in a method of temporal differentiation. An adequate substantiation of the self-generating principle of limit, that integrates the factors of space, time, and movement, becomes possible through the synthesis of actual and potential infinity.eng
dc.language.isoger
dc.publisherHumboldt-Universität zu Berlin, Philosophische Fakultät I
dc.subjectNewtonger
dc.subjectLeibnizger
dc.subjectInfinitesimalrechnungger
dc.subjectDifferentialrechnungger
dc.subjectPotential-Unendlich Kleineger
dc.subjectAktual-Unendlich Kleineger
dc.subjectLimesger
dc.subjectGrenzwertverfahrenger
dc.subjectCauchyger
dc.subjectCusanusger
dc.subjectcoincidentia oppositorumger
dc.subjectAristotelesger
dc.subjectZenos paradoxger
dc.subjectZeitliche Differenzierungger
dc.subjectEpistemologieger
dc.subjectPhilosophie der Mathematikger
dc.subjectNewtoneng
dc.subjectLeibnizeng
dc.subjectCalculuseng
dc.subjectDifferential Calculuseng
dc.subjectPotential Infinitesimaleng
dc.subjectActual Infinitesimaleng
dc.subjectActual and Potential Infinityeng
dc.subjectLimitseng
dc.subjectLimit-Processeng
dc.subjectCauchyeng
dc.subjectCusanuseng
dc.subjectcoincidentia oppositorumeng
dc.subjectAristotleeng
dc.subjectZeno´s paradoxeng
dc.subjectTemporal Differentiationeng
dc.subjectEpistemologyeng
dc.subjectPhilosophy of Mathematicseng
dc.subject.ddc000 Allgemeines, Wissenschaft
dc.subject.ddc510 Mathematik
dc.subject.ddc100 Philosophie
dc.subject.ddc530 Physik
dc.titleDie zeitliche Differenzierung
dc.typereport
dc.identifier.urnurn:nbn:de:kobv:11-100212914
dc.identifier.doihttp://dx.doi.org/10.18452/13567
local.edoc.anmerkungDiese Abhandlung basiert auf den mathematischen Untersuchungen in den Monographien, die ich im Rahmen meiner Promotion (in Freiburg i. Br.)und Postdoc (in Berlin/Cambridge) veröffentlicht habe, nämlich: "Perspektivierung als Modalität der Symbolisierung" (Dissertation, 2005) und "Natur und Struktur der Kräfte" (2010).
local.edoc.fp-subtypeother
local.edoc.type-nameBerichte und sonstige Texte
local.edoc.institutionPhilosophische Fakultät I
dc.description.versionNot Reviewed

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