A critical appraisal of second-order logic

History and Philosophy of Logic 14 (1):67-86 (1993)
Abstract
Because of its capacity to characterize mathematical concepts and structures?a capacity which first-order languages clearly lack?second-order languages recommend themselves as a convenient framework for much of mathematics, including set theory. This paper is about the credentials of second-order logic:the reasons for it to be considered logic, its relations with set theory, and especially the efficacy with which it performs its role of the underlying logic of set theory
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    References found in this work BETA
    Alonzo Church (1956). Introduction to Mathematical Logic. Princeton, Princeton University Press.
    Alonzo Church (1944). Introduction to Mathematical Logic. London, H. Milford, Oxford University Press.

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