 The point here is that the fact that an existential claim is derivable casts at least some doubt on the purely analytic status of \(\lambda\)-Conversion. The question of how we obtain knowledge of such principles is still an open question in philosophy. It is an important question to address, since Frege’s most insightful definitions are cast using quantifiers ranging over concepts and relations (e.g., the ancestrals of a relation) and it would be useful to have a philosophical explanation of how such entities and the principles which govern them become known to us. In contemporary philosophy, this question is still poignant, since many philosophers do accept that properties and relations of various sorts exist. These entities are the contemporary analogues of Frege’s concepts.