Putnam, peano, and the Malin génie: Could we possibly bewrong about elementary number-theory? [Book Review]

Abstract
This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following (along with Saul Kripke's ‘scepticalsolution’), Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable (even if imaginary) set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective (recognition-transcendent) truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others.
Keywords anti-realism  logic  mathematics  objectivity  Platonism  realism  scepticism  thought-experiments  truth  verificationism
Categories (categorize this paper)
DOI 10.1023/A:1022477922265
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
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 28,840
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Internal Realism, Truth and Understanding.Gordon Steinhoff - 1986 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:352 - 363.
Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics.Solomon Feferman - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:442 - 455.
Putnam, Realism and Truth.Janet Folina - 1995 - Synthese 103 (2):141--52.
Putnam on Realism, Reference and Truth: The Problem with Quantum Mechanics.Christopher Norris - 2001 - International Studies in the Philosophy of Science 15 (1):65 – 91.
Putnam's Model-Theoretic Argument(S). A Detailed Reconstruction.Jürgen Dümont - 1999 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 30 (2):341-364.

Monthly downloads

Added to index

2009-01-28

Total downloads

21 ( #239,666 of 2,177,988 )

Recent downloads (6 months)

1 ( #317,698 of 2,177,988 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums