Hartry Field has attacked the indispensability argument by arguing that mathematics is in fact dispensable to science. He does this by showing a way to dispense with quantification over mathematical entities in Newtonian gravitation theory. He, thus, advances a kind of fictionalism about mathematics. In this chapter, Field's program is outlined and the prospects for its success are evaluated. An important part of the task of assessing what is required of Field's program involves understanding how we should read the crucial term “indispensable” in Quine's argument.

Hartry Field has attacked the indispensability argument by arguing that mathematics is in fact dispensable to science. He does this by showing a way to dispense with quantification over mathematical entities in Newtonian gravitation theory. He, thus, advances a kind of fictionalism about mathematics. In this chapter, Field's program is outlined and the prospects for its success are evaluated. An important part of the task of assessing what is required of Field's program involves understanding how we should read the crucial term “indispensable” in Quine's argument.