On Evans's vague object from set theoretic viewpoint

Journal of Philosophical Logic 35 (4):423 - 434 (2006)
Gareth Evans proved that if two objects are indeterminately equal then they are different in reality. He insisted that this contradicts the assumption that there can be vague objects. However we show the consistency between Evans's proof and the existence of vague objects within classical logic. We formalize Evans's proof in a set theory without the axiom of extensionality, and we define a set to be vague if it violates extensionality with respect to some other set. There exist models of set theory where the axiom of extensionality does not hold, so this shows that there can be vague objects
Keywords axiom of extensionality  classical logic  extensionality  set theory  vague object  vagueness
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References found in this work BETA
George Boolos (1971). The Iterative Conception of Set. Journal of Philosophy 68 (8):215-231.
Michael Dummett (1975). Wang's Paradox. Synthese 30 (3-4):201--32.

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