A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices

Philosophia Mathematica 15 (3):291-320 (2007)

Abstract
In a recent article, Azzouni has argued in favor of a version of formalism according to which ordinary mathematical proofs indicate mechanically checkable derivations. This is taken to account for the quasi-universal agreement among mathematicians on the validity of their proofs. Here, the author subjects these claims to a critical examination, recalls the technical details about formalization and mechanical checking of proofs, and illustrates the main argument with aanalysis of examples. In the author's view, much of mathematical reasoning presents genuine meaning-dependent mathematical characteristics that cannot be captured by formal calculi. ‘…there is a conflict between mathematical practice and the formalist doctrine.’ [Kreisel, 1969, p. 39]
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/nkm023
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 42,401
Through your library

References found in this work BETA

The Seas of Language.Michael Dummett - 1993 - Oxford University Press.
Proofs and Refutations.Imre Lakatos - 1980 - Noûs 14 (3):474-478.
Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
Introduction to Metamathematics.Stephen Cole Kleene - 1968 - Journal of Symbolic Logic 33 (2):290-291.

View all 31 references / Add more references

Citations of this work BETA

Proofs, Pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
Why Do Informal Proofs Conform to Formal Norms?Jody Azzouni - 2009 - Foundations of Science 14 (1-2):9-26.

View all 20 citations / Add more citations

Similar books and articles

Proofs, Pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
Proofs and Arguments: The Special Case of Mathematics.Jean Paul Van Bendegem - 2005 - Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.
The Surveyability of Long Proofs.Edwin Coleman - 2009 - Foundations of Science 14 (1-2):27-43.
Why Do Mathematicians Re-Prove Theorems?John W. Dawson Jr - 2006 - Philosophia Mathematica 14 (3):269-286.
Why Do We Believe Theorems?Andrzej Pelc - 2009 - Philosophia Mathematica 17 (1):84-94.
Towards a Theory of Mathematical Argument.Ian J. Dove - 2009 - Foundations of Science 14 (1-2):136-152.

Analytics

Added to PP index
2009-01-28

Total views
82 ( #96,102 of 2,255,308 )

Recent downloads (6 months)
5 ( #374,821 of 2,255,308 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature