Proof Theory

Abstract
At the turn of the nineteenth century, mathematics exhibited a style of argumentation that was more explicitly computational than is common today. Over the course of the century, the introduction of abstract algebraic methods helped unify developments in analysis, number theory, geometry, and the theory of equations; and work by mathematicians like Dedekind, Cantor, and Hilbert towards the end of the century introduced set-theoretic language and infinitary methods that served to downplay or suppress computational content. This shift in emphasis away from calculation gave rise to concerns as to whether such methods were meaningful, or appropriate to mathematics. The discovery of paradoxes stemming from overly naive use of set-theoretic language and methods led to even more pressing concerns as to whether the modern methods were even consistent. This led to heated debates in the early twentieth century and what is sometimes called the “crisis of foundations.” In lectures presented in 1922, David Hilbert launched his Beweistheorie, or Proof Theory, which aimed to justify the use of modern methods and settle the problem of foundations once and for all. This, Hilbert argued, could be achieved as follows
Keywords No keywords specified (fix it)
Categories (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: 10,612
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA

No citations found.

Similar books and articles
Richard Zach, Hilbert's Program. Stanford Encyclopedia of Philosophy.
Panu Raatikainen (2001). Exploring Randomness. Notices of the AMS 48 (9):992-6.
Wilfried Sieg (1999). Hilbert's Programs: 1917-1922. Bulletin of Symbolic Logic 5 (1):1-44.
Rüdiger Thiele (1997). Über die Variationsrechnung in Hilberts Werken zur Analysis. NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 5 (1):23-42.
Analytics

Monthly downloads

Added to index

2010-10-16

Total downloads

24 ( #70,447 of 1,098,412 )

Recent downloads (6 months)

1 ( #285,057 of 1,098,412 )

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.