On the synthetic content of implicit definitions

Abstract

This paper addresses the issue of stipulation in three cases of implicit definitions (postulates of scientific terms, systems of axioms and abstraction principles). It argues that the alleged implicit definitions do not have a purely stipulative status. Stipulation of the vehicles of the implicit definitions in question should end up with true postulates. However, those postulates should not be taken to be true only in virtue of stipulation since they have extra commitments. Horwich’s worry emerges in all three kinds of implicit definitions under consideration, since the existence of meanings so that the alleged postulates are true depends on extra requirements that should be fulfilled. Moreover, if Ramseyfication method is applied to the three kinds of implicit definition, they are split up into two components from which the first one is broadly factual while the second one is purely stipulative. The paper argues that their definitional task in each case should be assigned to their second component i.e. their Carnap-conditional.