 The suggested reduction of all mathematics expressible in higher-order logic to the first-order level would be philosophically significant in showing that mathematics is not a study of general concepts, but of structures consisting of particulars (Hintikka 1996: 207). This is not to say that actual mathematics would be best carried out in terms of \(\mathbf{IFL}\), only that it could in principle be so carried out (Hintikka 1996: 205, 2006a: 477). For a critique of Hintikka’s conclusions, see Väänänen (2001), Feferman (2006), and Bazzoni (2015).