A critical appraisal of second-order logic

History and Philosophy of Logic 14 (1):67-86 (1993)
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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DOI 10.1080/01445349308837210
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Stewart Shapiro (2005). Sets and Abstracts – Discussion. Philosophical Studies 122 (3):315-332.

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