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Erschienen in:
Towards an Efficient Implementation of an Accurate SPH Method Kapitel lesen Erstes Kapitel lesen

2020 | OriginalPaper | Buchkapitel

Paradoxes of the Infinite and Ontological Dilemmas Between Ancient Philosophy and Modern Mathematical Solutions

verfasst von : Fabio Caldarola, Domenico Cortese, Gianfranco d’Atri, Mario Maiolo

Erschienen in: Numerical Computations: Theory and Algorithms

Verlag: Springer International Publishing

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Abstract

The concept of infinity had, in ancient times, an indistinguishable development between mathematics and philosophy. We could also say that his real birth and development was in Magna Graecia, the ancient South of Italy, and it is surprising that we find, in that time, a notable convergence not only of the mathematical and philosophical point of view, but also of what resembles the first “computational approach” to “infinitely” or very large numbers by Archimedes. On the other hand, since the birth of philosophy in ancient Greece, the concept of infinite has been closely linked with that of contradiction and, more precisely, with the intellectual effort to overcome contradictions present in an account of Totality as fully grounded. The present work illustrates the ontological and epistemological nature of the paradoxes of the infinite, focusing on the theoretical framework of Aristotle, Kant and Hegel, and connecting the epistemological issues about the infinite to concepts such as the continuum in mathematics.

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Vorheriges Kapitel A Multi-factor RSA-like Scheme with Fast Decryption Based on Rédei Rational Functions over the Pell Hyperbola
Nächstes Kapitel The Sequence of Carboncettus Octagons
Fußnoten
1
If there are n new guests the simplest choice is to use the function https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-39081-5_31/478615_1_En_31_IEq2_HTML.gif , instead, in case of an infinite countable number, the function https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-39081-5_31/478615_1_En_31_IEq3_HTML.gif (see [22, 39]).
 
2
The unimaginable numbers are numbers extremely large so that they cannot be written through the common scientific notation (also using towers of exponents) and are behind every power of imagination. To write them some special notations have been developed, the most known of them is Knuth’s up-arrow notation (see [30]). A brief introduction to these numbers can be found in [10], while more information is contained in [7, 11, 25].
 
3
See Physics, 204a8–204a16, in [4, Vol. I].
 
4
See Metaphysics, IX.6, 1048a-b, in [4, Vol. I].
 
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Metadaten
Titel
Paradoxes of the Infinite and Ontological Dilemmas Between Ancient Philosophy and Modern Mathematical Solutions
verfasst von
Fabio Caldarola
Domenico Cortese
Gianfranco d’Atri
Mario Maiolo
Copyright-Jahr
2020
Buch
Numerical Computations: Theory and Algorithms

Print ISBN: 978-3-030-39080-8

Electronic ISBN: 978-3-030-39081-5

Copyright-Jahr: 2020

DOI
https://doi.org/10.1007/978-3-030-39081-5_31