In Michael Frauchiger (ed.), Themes From Barcan Marcus. Ontos Verlag. pp. 51-74 (2015)
Second-order logic and modal logic are both, separately, major topics of philosophical discussion. Although both have been criticized by Quine and others, increasingly many philosophers find their strictures uncompelling, and regard both branches of logic as valuable resources for the articulation and investigation of significant issues in logical metaphysics and elsewhere. One might therefore expect some combination of the two sorts of logic to constitute a natural and more comprehensive background logic for metaphysics. So it is somewhat surprising to find that philosophical discussion of secondorder modal logic is almost totally absent, despite the pioneering contribution of Barcan.
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