What Finitism Could Not Be (Lo que el finitismo no podría ser)

Crítica 35 (103):43 - 68 (2003)
Abstract
In his paper "Finitism" (1981), W.W. Tait maintains that the chief difficulty for everyone who wishes to understand Hilbert's conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argues that all finitist reasoning is essentially primitive recursive. In this paper, we attempt to show that his thesis "The finitist functions are precisely the primitive recursive functions" is disputable and that another, likewise defended by him, is untenable. The second thesis is that the finitist theorems are precisely the universal closures of the equations that can be proved in PRA. /// En su articulo "Finitism" (1981), W.W. Tait sostiene que la dificultad principal para quien quiere comprender la concepción hilbertiana de la matemática finitista es ésta: especificar el sentido de la demostrabilidad de enunciados generales sobre los números naturales sin presuponer totalidades infinitas. Además, Tait argumenta que todo razonamiento finitista es esencialmente primitivo recursivo. En este artículo tratamos de mostrar que su tesis "Las funciones finitistas son precisamente las funciones primitivas recursivas" es discutible y que otra, también defendida por él, resulta insostenible. La segunda tesis es que los teoremas finitistas son precisamente las clausuras universales de las ecuaciones que pueden demostrarse en PRA.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index Translate to english
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,360
External links
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA
    Similar books and articles
    W. W. Tait (2010). Gödel on Intuition and on Hilbert's Finitism. In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
    Vitali Tselishchev (2008). Intuition and Reality of Signs. Proceedings of the Xxii World Congress of Philosophy 41:57-63.
    J. P. Bendegem (2012). A Defense of Strict Finitism. Constructivist Foundations 7 (2):141-149.
    Ofra Magidor (2007). Strict Finitism Refuted? Proceedings of the Aristotelian Society 107 (1pt3):403-411.
    Manuel Comesaña (2001). ¿Tiene Derecho a Existir la Filosofía de la Ciencia? The Proceedings of the Twentieth World Congress of Philosophy 2001:151-157.
    Analytics

    Monthly downloads

    Added to index

    2011-05-29

    Total downloads

    23 ( #63,369 of 1,088,883 )

    Recent downloads (6 months)

    2 ( #42,739 of 1,088,883 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.