Application Without Mapping Jeffrey Ketland September 26, 2020 Abstract According to “mapping accounts” of applied mathematics (Bueno & Colyvan (2011), Pincock (2012), Bueno & French (2018)), the application of mathematics “establish[es] a mapping from the empirical set up to a convenient mathematical structure” (Bueno & Colyvan (2011): 353), and this mapping “embed[s] certain features of the empirical world into a mathematical structure” (Bueno & Colyvan (2011): 352). Do all examples of applied mathematics proceed by invoking this sort of represen- tational mapping from an assumed target structure to a representing pure structure? I give some examples of applied mathematics which proceed without invoking such a mapping. These proceed, instead, using comprehension or set-existence axioms. Contents 1 Mapping Accounts of Applied Mathematics 1 2 Applications Without Mappings 5 3 Conclusion 13 Appendices 14 A Königsberg Formalization 14 1 Mapping Accounts of Applied Mathematics 1.1 Core Ideas of “Mapping Accounts” of Applied Mathematics Hartry Field stated, in the preface to his monograph Field (1980) defending nominalism, that the question “ what sort of account is possible of how mathematics is applied to the physical world? ” is “the really fundamental one” for the philosophy of mathematics (Field (1980): vii). 1