 If indeed problems related to the idea of all subsets are avoided in \(\mathbf{EIFL}\) (Hintikka 1997), it offers a way of defending a certain form logicism. Unlike in historical logicism, the idea is not to consider logic as an axiom system on the same level as mathematical axiom systems (Hintikka 1996:  183),[83]  and to attempt to reduce mathematics to logic. Rather, Hintikka (1996: 184) proposes to ask: (a) Can the crucial mathematical concepts be defined in logical terms? (b) Can the modes of semantically valid logical inferences used in mathematics be expressed in logical terms? The idea is not to concentrate on deductive rules of logic: no complete set of deductive rules exist anyway for \(\mathbf{IFL}\). Because the status of higher-order logic is potentially dubious – due to the problems associated with the notion of powerset – a positive solution to questions (a) and (b) calls for a first-order logic more powerful than \(\mathbf{FO}\). 