Against the Unrestricted Applicability of Disjunction Elimination

Rerum Causae 9 (2):92-111 (2017)
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Abstract

In this paper, I argue that the disjunction elimination rule presupposes the principle that a true disjunction contains at least one true disjunct. However, in some contexts such as supervaluationism or quantum logic, we have good reasons to reject this principle. Hence, disjunction elimination is restricted in at least one respect: it is not applicable to disjunctions for which this principle does not hold. The insight that disjunction elimination presupposes the principle that a true disjunction contains at least one true disjunct is applied to two arguments which argue for this very principle. I show that these arguments are rule-circular since they rest on disjunction elimination. I claim that rule-circularity better explains why the arguments fail than the explanations provided by Rumfitt (2015), which, for instance, rely on controversial principles about truth.

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Marcel Jahn
Humboldt University, Berlin

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References found in this work

The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge: Harvard University Press.
Truth and other enigmas.Michael Dummett - 1978 - Cambridge: Harvard University Press.
Vagueness.Timothy Williamson - 1994 - British Journal for the Philosophy of Science 46 (4):589-601.
The Connectives.Lloyd Humberstone - 2011 - MIT Press. Edited by Lloyd Humberstone.
Theories of Vagueness.Rosanna Keefe - 2000 - New York: Cambridge University Press.

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