Synthese 137 (1-2):141 - 156 (2003)

It is shown that David Hilbert's formalistic approach to axiomaticis accompanied by a certain pragmatism that is compatible with aphilosophical, or, so to say, external foundation of mathematics.Hilbert's foundational programme can thus be seen as areconciliation of Pragmatism and Apriorism. This interpretation iselaborated by discussing two recent positions in the philosophy ofmathematics which are or can be related to Hilbert's axiomaticalprogramme and his formalism. In a first step it is argued that thepragmatism of Hilbert's axiomatic contradicts the opinion thatHilbert style axiomatical systems are closed systems, a reproachposed by Carlo Cellucci. In the second section the question isdiscussed whether Hilbert's pragmatism in foundational issuescomes close to an a-philosophical ``naturalism in mathematics'' assuggested by Penelope Maddy. The answer is ``no'', because forHilbert philosophy had its specific tasks in the general projectto found mathematics. This is illuminated in the concludingsection giving further evidence for Hilbert's foundationalapriorism by discussing his ``axiom of the existence of mind'' andrelating it to the ``one and only axiom'' of the German algebraistof logic, Ernst Schröder, postulating the inherence of signs onthe paper.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1026235118657
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 54,646
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Ontology and Mathematical Practice.Jessica Carter - 2004 - Philosophia Mathematica 12 (3):244-267.
Book Reviews. [REVIEW][author unknown] - 2004 - International Studies in the Philosophy of Science 18 (2-3):231-239.

Add more citations

Similar books and articles

Hilberts Logik. Von der Axiomatik zur Beweistheorie.Volker Peckhaus - 1995 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 3 (1):65-86.
Hilbert's Program Then and Now.Richard Zach - 2007 - In Dale Jacquette (ed.), Philosophy of Logic. Amsterdam: North Holland. pp. 411–447.
Aspekte der frege–hilbert-korrespondenz.Kai F. Wehmeier - 1997 - History and Philosophy of Logic 18 (4):201-209.


Added to PP index

Total views
69 ( #140,524 of 2,386,121 )

Recent downloads (6 months)
5 ( #160,208 of 2,386,121 )

How can I increase my downloads?


My notes