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100.1.#.a: Fernández, Ángel Nepomuceno

524.#.#.a: Fernández, Ángel Nepomuceno (1993). Sistemas de cálculo como formas de Logicismo. Crítica. Revista Hispanoamericana de Filosofía; Vol 25 No 73, 1993; 15-35. Recuperado de https://repositorio.unam.mx/contenidos/4115356

245.1.0.a: Sistemas de cálculo como formas de Logicismo

502.#.#.c: Universidad Nacional Autónoma de México

561.1.#.a: Instituto de Investigaciones Filosóficas, UNAM

264.#.0.c: 1993

264.#.1.c: 2019-01-07

506.1.#.a: La titularidad de los derechos patrimoniales de esta obra pertenece a las instituciones editoras. Su uso se rige por una licencia Creative Commons BY-NC-ND 4.0 Internacional, https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.es, fecha de asignación de la licencia 2019-01-07, para un uso diferente consultar al responsable jurídico del repositorio por medio del correo electrónico alberto@filosoficas.unam.mx

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520.3.#.a: The logicism may be regarded like a fossil stone that has not utility nowadays. In this sense, logicism took care of the research about the foundations of mathematics but apparently its task arrived at its end many years ago because of sorne results that were eetablished during the century. However it is not wholly right. Understanding logicism as an attempt to reduce classical mathematics to logic means we can distinguish: 1) the idea according to which mathematic is logic in sorne way, and 2) a metaphysical program of research to: a) define mathematical notions as logical notions, and b) show that the mathematical theorems are logical theorems. The failure (if so) concerned to 2), since 1) was assumed by many logicians. Recovering logicism is not easy and there may be several ways. One of them is the one followed by N.B. Cocchiarella whose systems (there are more than one) represent a form of logicism (Frege"s or Russell"s form). From those systems -though a bit changed from my own point of view- we can define a modal calcule that may have application in computer science, what would not be a stale work. From a common language we take in account two systems in order to show that Cocchiarella"s modified system is as powerful deductively as that of Church modified functional second order calcule. We can obtain new systems that represent form of logicism and are more powerful than that of Church enlarging Cochiarella"s modified system. These new systems, that becomes modal systems provided that one adds appropiate modal tools (then they may be used in computer science), may be useful to study logicism itself (as historical philosophy of logic and mathematics). The logicism may be regarded like a fossil stone that has not utility nowadays. In this sense, logicism took care of the research about the foundations of mathematics but apparently its task arrived at its end many years ago because of sorne results that were eetablished during the century. However it is not wholly right. Understanding logicism as an attempt to reduce classical mathematics to logic means we can distinguish: 1) the idea according to which mathematic is logic in sorne way, and 2) a metaphysical program of research to: a) define mathematical notions as logical notions, and b) show that the mathematical theorems are logical theorems. The failure (if so) concerned to 2), since 1) was assumed by many logicians. Recovering logicism is not easy and there may be several ways. One of them is the one followed by N.B. Cocchiarella whose systems (there are more than one) represent a form of logicism (Frege"s or Russell"s form). From those systems -though a bit changed from my own point of view- we can define a modal calcule that may have application in computer science, what would not be a stale work. From a common language we take in account two systems in order to show that Cocchiarella"s modified system is as powerful deductively as that of Church modified functional second order calcule. We can obtain new systems that represent form of logicism and are more powerful than that of Church enlarging Cochiarella"s modified system. These new systems, that becomes modal systems provided that one adds appropiate modal tools (then they may be used in computer science), may be useful to study logicism itself (as historical philosophy of logic and mathematics).

773.1.#.t: Crítica. Revista Hispanoamericana de Filosofía; Vol 25 No 73 (1993); 15-35

773.1.#.o: http://critica.filosoficas.unam.mx/index.php/critica

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758.#.#.1: http://critica.filosoficas.unam.mx/index.php/critica

doi: https://doi.org/10.22201/iifs.18704905e.1993.876

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Artículo

Sistemas de cálculo como formas de Logicismo

Fernández, Ángel Nepomuceno

Instituto de Investigaciones Filosóficas, UNAM, publicado en Crítica. Revista Hispanoamericana de Filosofía, y cosechado de Revistas UNAM

Licencia de uso

Procedencia del contenido

Cita

Fernández, Ángel Nepomuceno (1993). Sistemas de cálculo como formas de Logicismo. Crítica. Revista Hispanoamericana de Filosofía; Vol 25 No 73, 1993; 15-35. Recuperado de https://repositorio.unam.mx/contenidos/4115356

Descripción del recurso

Autor(es)
Fernández, Ángel Nepomuceno
Tipo
Artículo de Investigación
Área del conocimiento
Artes y Humanidades
Título
Sistemas de cálculo como formas de Logicismo
Fecha
2019-01-07
Resumen
The logicism may be regarded like a fossil stone that has not utility nowadays. In this sense, logicism took care of the research about the foundations of mathematics but apparently its task arrived at its end many years ago because of sorne results that were eetablished during the century. However it is not wholly right. Understanding logicism as an attempt to reduce classical mathematics to logic means we can distinguish: 1) the idea according to which mathematic is logic in sorne way, and 2) a metaphysical program of research to: a) define mathematical notions as logical notions, and b) show that the mathematical theorems are logical theorems. The failure (if so) concerned to 2), since 1) was assumed by many logicians. Recovering logicism is not easy and there may be several ways. One of them is the one followed by N.B. Cocchiarella whose systems (there are more than one) represent a form of logicism (Frege"s or Russell"s form). From those systems -though a bit changed from my own point of view- we can define a modal calcule that may have application in computer science, what would not be a stale work. From a common language we take in account two systems in order to show that Cocchiarella"s modified system is as powerful deductively as that of Church modified functional second order calcule. We can obtain new systems that represent form of logicism and are more powerful than that of Church enlarging Cochiarella"s modified system. These new systems, that becomes modal systems provided that one adds appropiate modal tools (then they may be used in computer science), may be useful to study logicism itself (as historical philosophy of logic and mathematics). The logicism may be regarded like a fossil stone that has not utility nowadays. In this sense, logicism took care of the research about the foundations of mathematics but apparently its task arrived at its end many years ago because of sorne results that were eetablished during the century. However it is not wholly right. Understanding logicism as an attempt to reduce classical mathematics to logic means we can distinguish: 1) the idea according to which mathematic is logic in sorne way, and 2) a metaphysical program of research to: a) define mathematical notions as logical notions, and b) show that the mathematical theorems are logical theorems. The failure (if so) concerned to 2), since 1) was assumed by many logicians. Recovering logicism is not easy and there may be several ways. One of them is the one followed by N.B. Cocchiarella whose systems (there are more than one) represent a form of logicism (Frege"s or Russell"s form). From those systems -though a bit changed from my own point of view- we can define a modal calcule that may have application in computer science, what would not be a stale work. From a common language we take in account two systems in order to show that Cocchiarella"s modified system is as powerful deductively as that of Church modified functional second order calcule. We can obtain new systems that represent form of logicism and are more powerful than that of Church enlarging Cochiarella"s modified system. These new systems, that becomes modal systems provided that one adds appropiate modal tools (then they may be used in computer science), may be useful to study logicism itself (as historical philosophy of logic and mathematics).
Idioma
spa
ISSN
ISSN electrónico: 1870-4905; ISSN impreso: 0011-1503

Enlaces