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856.4.0.u: http://critica.filosoficas.unam.mx/index.php/critica/article/view/910/878

100.1.#.a: Fernández, Ángel Nepomuceno

524.#.#.a: Fernández, Ángel Nepomuceno (1993). Logicist Notions in Philosophy of Mathematics. Crítica. Revista Hispanoamericana de Filosofía; Vol 25 No 75, 1993; 85-103. Recuperado de https://repositorio.unam.mx/contenidos/4115452

245.1.0.a: Logicist Notions in Philosophy of Mathematics

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

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520.3.#.a: The point of view according to which logic has priority over mathematics has been maintained by some philosophers and mathematicians in two senses: a strong view and a weak view. Both of them are logicist: The first one regards mathematics as reducible to logic. The second one considers that the essence of mathematics can be known by researching the logical consequences of a certain system of postulates or axioms; thus, the underlying logic (whatever the mathematical theory might be) is crucial for this sort of studies. Some logicist concepts are interesting in philosophy of mathematics. So it is necessary to study the state of being in use of each point of view. In fact, the weak view has prevailed. To show that, we settle down how logicist statements have been influenced by Gödel’s theorem, though that goes against formalist philosophy. Afterwards, we present a formal system for second order logic; treatment of nominalization is enclosed, and every Frege’s law is proved to be a theorem. Finally, a short balance is made. The point of view according to which logic has priority over mathematics has been maintained by some philosophers and mathematicians in two senses: a strong view and a weak view. Both of them are logicist: The first one regards mathematics as reducible to logic. The second one considers that the essence of mathematics can be known by researching the logical consequences of a certain system of postulates or axioms; thus, the underlying logic (whatever the mathematical theory might be) is crucial for this sort of studies. Some logicist concepts are interesting in philosophy of mathematics. So it is necessary to study the state of being in use of each point of view. In fact, the weak view has prevailed. To show that, we settle down how logicist statements have been influenced by Gödel’s theorem, though that goes against formalist philosophy. Afterwards, we present a formal system for second order logic; treatment of nominalization is enclosed, and every Frege’s law is proved to be a theorem. Finally, a short balance is made.

773.1.#.t: Crítica. Revista Hispanoamericana de Filosofía; Vol 25 No 75 (1993); 85-103

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

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310.#.#.a: Cuatrimestral

300.#.#.a: Páginas: 85-103

264.#.1.b: Instituto de Investigaciones Filosóficas, UNAM

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

doi: https://doi.org/10.22201/iifs.18704905e.1993.910

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245.1.0.b: Nociones logicistas en filosofía de la matemática

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Artículo

Logicist Notions in Philosophy of Mathematics

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). Logicist Notions in Philosophy of Mathematics. Crítica. Revista Hispanoamericana de Filosofía; Vol 25 No 75, 1993; 85-103. Recuperado de https://repositorio.unam.mx/contenidos/4115452

Descripción del recurso

Autor(es)
Fernández, Ángel Nepomuceno
Tipo
Artículo de Investigación
Área del conocimiento
Artes y Humanidades
Título
Logicist Notions in Philosophy of Mathematics
Fecha
2019-01-07
Resumen
The point of view according to which logic has priority over mathematics has been maintained by some philosophers and mathematicians in two senses: a strong view and a weak view. Both of them are logicist: The first one regards mathematics as reducible to logic. The second one considers that the essence of mathematics can be known by researching the logical consequences of a certain system of postulates or axioms; thus, the underlying logic (whatever the mathematical theory might be) is crucial for this sort of studies. Some logicist concepts are interesting in philosophy of mathematics. So it is necessary to study the state of being in use of each point of view. In fact, the weak view has prevailed. To show that, we settle down how logicist statements have been influenced by Gödel’s theorem, though that goes against formalist philosophy. Afterwards, we present a formal system for second order logic; treatment of nominalization is enclosed, and every Frege’s law is proved to be a theorem. Finally, a short balance is made. The point of view according to which logic has priority over mathematics has been maintained by some philosophers and mathematicians in two senses: a strong view and a weak view. Both of them are logicist: The first one regards mathematics as reducible to logic. The second one considers that the essence of mathematics can be known by researching the logical consequences of a certain system of postulates or axioms; thus, the underlying logic (whatever the mathematical theory might be) is crucial for this sort of studies. Some logicist concepts are interesting in philosophy of mathematics. So it is necessary to study the state of being in use of each point of view. In fact, the weak view has prevailed. To show that, we settle down how logicist statements have been influenced by Gödel’s theorem, though that goes against formalist philosophy. Afterwards, we present a formal system for second order logic; treatment of nominalization is enclosed, and every Frege’s law is proved to be a theorem. Finally, a short balance is made.
Idioma
spa
ISSN
ISSN electrónico: 1870-4905; ISSN impreso: 0011-1503

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