Una defensa del realismo científico nominalista. Respuesta a Joseph Melia

Nominalistic scientific realism restricts to the field of spatio-temporal entities the belief in the unobservable underpinned by the success of science. This claim requires giving criteria to decouple from the realistic attitude the Platonic entities committed in scientific ontology; entities such as numbers or vector spaces. Hartry Field has been the first to try to settle this requirement from a systematic point of view. His strategy seeks to show that scientific theories can be completely nominalized, namely, reformulated in a language expunged from commitments to mathematical objects. Joseph Melia (1998) has (somewhat harshly) questioned the soundness of this project. In his view, fieldian nominalism: (i) commits us to arbitrary, causally irrelevant objects, (ii) violates the requirement of ontological parsimony and (iii) lacks sufficient resources to remove the reference to fundamental constants such as e and π. This paper provides a response to Melia's objections. First, I reaffirm the nominalistic adequacy of Field's metaphysics. Then I argue that the charge of ontological waste misses an important technical detail involved in the development of this metaphysics. Finally, I outline a technique to recover the reference to irrational magnitudes from a nominalistic point of view.