Work · Analytic Philosophy
A Functional Calculus of First Order Based on Strict Implication
The first published system of quantified modal logic – containing the formula later named after her.
Introduction
Ruth C. Barcan published this short technical paper in the Journal of Symbolic Logic in 1946, the year she completed her doctorate at Yale. It adds quantifiers (“for all x”, “there is an x”) to C. I. Lewis’s system S2 of strict implication – a logic in which one statement strictly implies another only if it is impossible for the first to be true and the second false – and so presents the first published formal system of quantified modal logic (Carnap’s “Modalities and Quantification” appeared in the same volume of the journal a few months later). Among its theorems is what became known as the Barcan formula: if it is possible that something is F, then there is something that is possibly F (◇∃xFx → ∃x◇Fx). Its consequences for whether merely possible things exist are still debated.
More works by Ruth Barcan Marcus
Sources: Wikidata
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