Linked bibliography for the SEP article " Indispensability Arguments in the Philosophy of Mathematics" by Mark Colyvan

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Although the indispensability argument is to be found in many places in Quine's writings (including 1976; 1980a; 1980b; 1981a; 1981c), the locus classicus is Putnam's short monograph Philosophy of Logic (included as a chapter of the second edition of the third volume of his collected papers (Putnam, 1979b)). See also Putnam (1979a) and the introduction of Field (1989) which has an excellent outline of the argument. Colyvan (2001) is a sustained defence of the argument.

See Chihara (1973), and Field (1980; 1989) for attacks on the second premise and Colyvan (1999b; 2001), Lyon and Colyvan (2008), Maddy (1990), Malament (1982), Resnik (1985), Shapiro (1983) and Urquhart (1990) for criticisms of Field's program. For a fairly comprehensive look at nominalist strategies in the philosophy of mathematics (including a good discussion of Field's program), see Burgess and Rosen (1997), while Feferman (1993) questions the amount of mathematics required for empirical science. See Azzouni (1997; 2004; 2012), Balaguer (1996b; 1998), Bueno (2012), Leng (2002; 2010; 2012), Liggins (2012), Maddy (1992; 1995; 1997), Melia (2000; 2002), Peressini (1997), Pincock (2004), Sober (1993), Vineberg (1996) and Yablo (1998; 2005; 2012) for attacks on the first premise. Baker (2001; 2005), Colyvan (1998; 1999a; 2001; 2002; 2007; 2010; 2012), Hellman (1999) and Resnik (1995a; 1997) reply to some of these objections.

For variants of the Quinean indispensability argument see Maddy (1992) and Resnik (1995a).

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