Conservativeness and Eliminability for Anti-Realistic Definitions. Towards a Global View of the Meaning of Logical Constants

According to the Polish logician S. Leśniewski, definitions give the whole meaning of the symbol they define and nothing more if, and only if, they respect two criteria: conservativeness and eliminability. These criteria were formulated in a way that suits realistic definitions. In this paper we will see in what way these two criteria should be reformulated if we want them to fit anti-realistic definitions (of logical constants). We will then show the consequences that these reformulations involve in the framework of the sequent calculus. Finally, in the light of the previous results, we will analyse the case of anti-realistic definitions for the modal operator box