The examination paradox and formal prediction : Notas de Matemáticas, 6

In treating paradoxes which are formulated in common language, one is sometimes tempted to go too far, by making a mathematical model that demonstrates in a correct way the fundamental assertion of the paradox or its negation. But this is not always relevant, because in several cases the point is to...

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Detalles Bibliográficos
Autor principal: Bosch, Jorge Eduardo
Formato: Publicacion seriada
Lenguaje:Inglés
Publicado: 1969
Materias:
Matemática
Paradojas
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/159183
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-159183
record_format dspace
spelling I19-R120-10915-1591832023-10-21T04:06:30Z http://sedici.unlp.edu.ar/handle/10915/159183 The examination paradox and formal prediction : Notas de Matemáticas, 6 Bosch, Jorge Eduardo 1969 2023-10-20T17:44:30Z en Matemática Paradojas In treating paradoxes which are formulated in common language, one is sometimes tempted to go too far, by making a mathematical model that demonstrates in a correct way the fundamental assertion of the paradox or its negation. But this is not always relevant, because in several cases the point is to find a logical formulation of the non formal reasoning given by the paradox, and to show -as exactly as possible- where it is incorrect or paradoxical. For example, we do not say anything relevant to the paradox of Achilles and the tortoise by defining a certain mathematical series and thus demonstrating that Achilles reaches the tortoise in a finite time: the point here is to follow step by step Zeno's argument and to show where it is logically wrong. Perhaps in doing it we are led to make more rigorous or more explicit Zeno's argument, but in any case the logical devices employed must respect the "spirit" of the original reasoning. I emphasize this by saying that the informal reasoning is a substantial part of the paradox itself. Material digitalizado en SEDICI gracias a la colaboración de la Biblioteca del Departamento de Matemática de la Facultad de Ciencias Exactas (UNLP). Facultad de Ciencias Exactas Publicacion seriada Publicacion seriada http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Paradojas
spellingShingle Matemática
Paradojas
Bosch, Jorge Eduardo
The examination paradox and formal prediction : Notas de Matemáticas, 6
topic_facet Matemática
Paradojas
description In treating paradoxes which are formulated in common language, one is sometimes tempted to go too far, by making a mathematical model that demonstrates in a correct way the fundamental assertion of the paradox or its negation. But this is not always relevant, because in several cases the point is to find a logical formulation of the non formal reasoning given by the paradox, and to show -as exactly as possible- where it is incorrect or paradoxical. For example, we do not say anything relevant to the paradox of Achilles and the tortoise by defining a certain mathematical series and thus demonstrating that Achilles reaches the tortoise in a finite time: the point here is to follow step by step Zeno's argument and to show where it is logically wrong. Perhaps in doing it we are led to make more rigorous or more explicit Zeno's argument, but in any case the logical devices employed must respect the "spirit" of the original reasoning. I emphasize this by saying that the informal reasoning is a substantial part of the paradox itself.
format Publicacion seriada
Publicacion seriada
author Bosch, Jorge Eduardo
author_facet Bosch, Jorge Eduardo
author_sort Bosch, Jorge Eduardo
title The examination paradox and formal prediction : Notas de Matemáticas, 6
title_short The examination paradox and formal prediction : Notas de Matemáticas, 6
title_full The examination paradox and formal prediction : Notas de Matemáticas, 6
title_fullStr The examination paradox and formal prediction : Notas de Matemáticas, 6
title_full_unstemmed The examination paradox and formal prediction : Notas de Matemáticas, 6
title_sort examination paradox and formal prediction : notas de matemáticas, 6
publishDate 1969
url http://sedici.unlp.edu.ar/handle/10915/159183
work_keys_str_mv AT boschjorgeeduardo theexaminationparadoxandformalpredictionnotasdematematicas6
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