Comments on predicative logic

Journal of Philosophical Logic 35 (1):1 - 8 (2006)
Abstract
We show how to interpret intuitionistic propositional logic into a predicative second-order intuitionistic propositional system having only the conditional and the universal second-order quantifier. We comment on this fact. We argue that it supports the legitimacy of using classical logic in a predicative setting, even though the philosophical cast of predicativism is nonrealistic. We also note that the absence of disjunction and existential quantifications allows one to have a process of normalization of proofs that avoids the use of "commuting conversions."
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