The Barcan formulas and necessary existence: the view from Quarc

Synthese 198 (11):11029-11064 (2020)
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The Modal Predicate Calculus gives rise to issues surrounding the Barcan formulas, their converses, and necessary existence. I examine these issues by means of the Quantified Argument Calculus, a recently developed, powerful formal logic system. Quarc is closer in syntax and logical properties to Natural Language than is the Predicate Calculus, a fact that lends additional interest to this examination, as Quarc might offer a better representation of our modal concepts. The validity of the Barcan formulas and their converses is shown by Quarc to be a result of the specific incorporation of quantification in the Predicate Calculus, and not as reflecting a feature of the interaction of quantification and modality more generally. Necessary existence is shown to follow from the identification, in the Predicate Calculus on its canonical interpretation, of particular quantification, ascription of existence and the ‘there is’ construction, three constructions which are distinguished in both Quarc and Natural Language. The issues surrounding the Barcan formulas, their converses and necessary existence are thus shown to be an artefact of a specific logic system, not an essential feature of our relevant modal concepts or of formal logic.



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The Quantified Argument Calculus.Hanoch Ben-Yami - 2014 - Review of Symbolic Logic 7 (1):120-146.
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Hanoch Ben-Yami
Central European University

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Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
Individuals: An Essay in Descriptive Metaphysics.Peter Frederick Strawson - 1959 - London, England: Routledge. Edited by Wenfang Wang.
The Objects of Thought.Tim Crane - 2013 - Oxford: Oxford University Press.

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