Putnam, peano, and the Malin génie: Could we possibly bewrong about elementary number-theory? [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal for General Philosophy of Science 33 (2):289-321 (2002)
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)|
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
David Liggins (2008). Quine, Putnam, and the 'Quine-Putnam' Indispensability Argument. Erkenntnis 68 (1):113 - 127.
Charles Sayward (2003). Does Scientific Realism Entail Mathematical Realism? Facta Philosophica 5:173-182.
Christopher Norris (2001). Putnam on Realism, Reference and Truth: The Problem with Quantum Mechanics. International Studies in the Philosophy of Science 15 (1):65 – 91.
Christopher Norris (2002). Hilary Putnam: Realism, Reason, and the Uses of Uncertainty. Distributed in the U.S. By Palgrave.
Janet Folina (1995). Putnam, Realism and Truth. Synthese 103 (2):141--52.
Philip Hugly & Charles Sayward (2006). Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic. rodopi.
Susan Vineberg (1996). Confirmation and the Indispensability of Mathematics to Science. Philosophy of Science 63 (3):263.
Solomon Feferman (1992). Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:442 - 455.
Gordon Steinhoff (1986). Internal Realism, Truth and Understanding. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:352 - 363.
Jürgen Dümont (1999). Putnam's Model-Theoretic Argument(S). A Detailed Reconstruction. Journal for General Philosophy of Science 30 (2):341-364.
Added to index2009-01-28
Total downloads17 ( #105,475 of 1,167,998 )
Recent downloads (6 months)1 ( #140,193 of 1,167,998 )
How can I increase my downloads?