Abstract

ALVARADO MARAMBIO, JOSÉ TOMÁS. Second-Order Barcan Formulas and Transcendent Universals. Ideas y Valores [online]. 2013, vol.62, n.152, pp.111-131. ISSN 0120-0062.

ABSTRACT It has been pointed out that the Barcan Formula -BF- and the Converse Barcan Formula -CBF- seem to be valid for higher-order modal quantificational logic. If quantifiers are construed as ranging over properties, the validity of BF and CBF seems to entail the existence of transcendent universals that do not require instantiation in order to exist in a possible world. The paper discusses this argument given that semantics, in which validity results follow from one another, do not require that the "intensions" assigned to higher- order variables be instantiated in a possible world in order for the intension to exist in such a world. In a modified, more neutral semantics, higher-order BF and CBF are no longer valid. The paper also argues that even if higher-order BF and CBF were valid, no substantive metaphysical results would be obtained, since different forms of nominalism and theories of tropes would accept them.

Keywords : Barcan Formula; Converse Barcan Formula; transcendent universals.

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