# The Indispensability of Mathematics

# The Indispensability of Mathematics

This chapter discusses Hartry Field's attempt to respond to the indispensability argument by showing how to dispense with mathematics in formulating our best scientific theories. It is pointed out that Field does not want to stop us from using mathematics in our scientific theorizing, but rather, that he wishes to explain the use of mathematics as a ‘theoretical juice extractor’, which allows us to draw out the consequences of our non‐mathematical assumptions. Objections to Field's programme are considered, including objections to the logical assumptions made by his account of applications, and objections to his claim that mathematics can always be dispensed with. While these objections are not conclusive, it is noted that mathematical assumptions may be valuable enough to remain present in even our best formulations of our scientific theories. Hence the book's project, to consider the case for anti‐platonism on the assumption that mathematics is indispensable to empirical science.

*Keywords:*
Hartry Field, indispensability, applications, mathematics, science, juice extractor, conservativeness

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