¿Qué está mal?

Aviso: Antes de informar sobre un error con la descarga, por favor, prueba el enlace directo: What is Mathematics: Gödel's Theorem and Around

Cargando...

Debes iniciar sesión para hacer esto.

What is Mathematics: Gödel's Theorem and Around

What is Mathematics: Gödel's Theorem and Around

What is Mathematics: Gödel's Theorem and Around

Puntuación: ---- | 0 votos
| Enviando voto
| ¡Votado!
|

Detalles del libro:

pos
Global
pos
Categoría
Año:2013
Editor:Autoedición
Páginas:238 páginas
Idioma:inglés
Desde:17/03/2015
Tamaño:1.05 MB
Licencia:Pendiente de revisión

Contenido:

I define mathematical theories as stable self-contained (autonomous?) systems of reasoning, and formal theories - as mathematical models of such systems. Working with stable self-contained models mathematicians have developed their ability to draw a maximum of conclusions from a minimum of premises. This is why mathematical modeling is so efficient (my solution to the problem of "The Incomprehensible Effectiveness of Mathematics in the Natural Sciences" - as put by Eugene Wigner).

For me, Goedel's results are the crucial evidence that stable self-contained systems of reasoning cannot be perfect (just because they are stable and self-contained). Such systems are either non-universal (i.e. they cannot express the notion of natural numbers: 0, 1, 2, 3, 4, ...), or they are universal, yet then they run inevitably either into contradictions, or into unsolvable problems.

For humans, Platonist thinking is the best way of working with imagined structures. (Another version of this thesis was proposed in 1991 by Keith Devlin on p. 67 of his Logic and Information.) Thus, a correct philosophical position of a mathematician should be: a) Platonism - on working days - when I'm doing mathematics (otherwise, my "doing" will be inefficient), b) Formalism - on weekends - when I'm thinking "about" mathematics (otherwise, I will end up in mysticism). (The initial version of this aphorism was proposed in 1979 by Reuben Hersh (picture) on p. 32 of his Some proposals for reviving the philosophy of mathematics.)

Categorías:

Etiquetas:

Cargando comentarios...

Escaneando listas...

El libro en números

Posición global

posición en categorías

en catálogo desde

17/03/2015

puntuación

Nothing yet...

votos

Nothing yet...

'LIKES' sociales

Nothing yet...

Visitas

Descargas

Esto puede tardar un momento

Interés

Segmentación por países

Esto puede tardar un momento

Páginas de entrada

Segmentación por sitios web

evolución

Esto puede tardar un momento

Cargando...