David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 16 (2):244-255 (2008)
Paul Benacerraf's argument from multiple reductions consists of a general argument against realism about the natural numbers (the view that numbers are objects), and a limited argument against reductionism about them (the view that numbers are identical with prima facie distinct entities). There is a widely recognized and severe difficulty with the former argument, but no comparably recognized such difficulty with the latter. Even so, reductionism in mathematics continues to thrive. In this paper I develop a difficulty for Benacerraf's argument against reductionism that is of comparable severity to the now widely recognized difficulty with his general argument against realism. Thanks to Kit Fine, Hartry Field, Jeff Sebo, Ted Sider, Stephen Schiffer, and anonymous referees at Philosophia Mathematica for helpful comments on earlier versions of this paper. Thanks to Aron Edidin for many helpful discussions of the problems that inspired it. CiteULike Connotea Del.icio.us What's this?
|Keywords||No keywords specified (fix it)|
|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
Paul Benacerraf (1996). Recantation or Any Old W-Sequence Would Do After All. Philosophia Mathematica 4 (2):184-189.
John Bickle (1992). Multiple Realizability and Psychophysical Reduction. Behavior and Philosophy 20 (1):47-58.
Sven Walter (2002). Need Multiple Realizability Deter the Identity-Theorist? Grazer Philosophische Studien 65 (1):51-75.
Julie Zahle (2003). The Individualism-Holism Debate on Intertheoretic Reduction and the Argument From Multiple Realization. Philosophy of the Social Sciences 33 (1):77-99.
Caj Strandberg (2004). In Defence of the Open Question Argument. Journal of Ethics 8 (2):179-196.
John Bickle (1995). Connectionism, Reduction, and Multiple Realizability. Behavior and Philosophy 23 (2):29-39.
Paul Draper, Kai Draper & Joel Pust (2007). Probabilistic Arguments for Multiple Universes. Pacific Philosophical Quarterly 88 (3):288–307.
Jaegwon Kim (1992). Multiple Realization and the Metaphysics of Reduction. Philosophy and Phenomenological Research 52 (1):1-26.
Ned Block (2008). Anti-Reductionism Slaps Back. Noûs 31 (s11):107-132.
Elliott Sober (1999). The Multiple Realizability Argument Against Reductionism. Philosophy of Science 66 (4):542-564.
Added to index2009-01-28
Total downloads90 ( #13,106 of 1,098,979 )
Recent downloads (6 months)2 ( #175,054 of 1,098,979 )
How can I increase my downloads?