On Evans's Vague Object from Set Theoretic Viewpoint

@article{citeulike:2963055, abstract = {Abstract\ \ 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.}, author = {Yatabe, Shunsuke and Inaoka, Hiroyuki}, citeulike-article-id = {2963055}, doi = {10.1007/s10992-005-9022-7}, journal = {Journal of Philosophical Logic}, keywords = {philosophy, print, set-theory, vaguness}, number = {4}, pages = {423--434}, posted-at = {2008-07-04 09:48:03}, priority = {2}, title = {On Evans's Vague Object from Set Theoretic Viewpoint}, url = {http://dx.doi.org/10.1007/s10992-005-9022-7}, volume = {35}, year = {2006} }

TY - JOUR ID - citeulike:2963055 L3 - citeulike-article-id:2963055 N2 - Abstract  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. IS - 4 JF - Journal of Philosophical Logic EP - 434 TI - On Evans's Vague Object from Set Theoretic Viewpoint VL - 35 SP - 423 KW - philosophy KW - print KW - set-theory KW - vaguness AU - Yatabe, Shunsuke AU - Inaoka, Hiroyuki PY - 2006//28/ UR - http://dx.doi.org/10.1007/s10992-005-9022-7 ER -