The article is dedicated to the argument against the Existence Requirement provided by Takashi Yagisawa. We argue that the core of Yagisawa s argument – the Strong Iterability – cannot be inferred from the idea of contingent apriori (Kripke), and is incompatible with the idea of @-transform (Plantinga). Thus, these ideas, contrary to Yagisawa, cannot serve as a methodological basis of the Strong Iterability. We also argue that the Strong Iterability is incompatible with the Constituent Principle. Finally, we show that the concept of world-indexed properties (the argument of Yagisawa relies on the idea of world-indexed properties) is inconsistent, and even if the defender of Strong Iterability can resist this objection, the Strong Iterability must be given up.
Existence requirement; World-indexed properties; Contingent apriori; Necessity, @-transform