 Among philosophical issues that have been addressed in connection with IF logic are the reconstruction of mathematical reasoning on the first-order level (Hintikka 1996, 1997), definability of a self-applied truth predicate (Hintikka 1991, 1996, 2001; Sandu 1998), truth and axiomatic set theory (Hintikka 1996, 2004a), and insights into the nature of negation (Hintikka 1991, 1996, 2002; Hintikka &amp; Sandu 1989; Sandu 1994). These issues will be discussed in Sections 4 and 5.