Graham Priest has recently argued, in several of his papers and a book manuscript,for a view about nothing according to which nothing is paradoxical in several respects. The focus of the present paper is on three sub-...Graham Priest has recently argued, in several of his papers and a book manuscript,for a view about nothing according to which nothing is paradoxical in several respects. The focus of the present paper is on three sub-claims of his view:(1) that nothing is an object,(w)that nothing is not an object, and(3) that everything grounds for its being on its being different from nothing. The author argues, both philosophically and formally, in this paper that Priest's arguments for the above sub-claims are not persuasive enough. Especially, the author argues that Priest's formal theory of nothing will suffer from a dilemma: either it will allow that there is a paradise of many nothings and therefore embrace an inflated ontology, or it will identify all nothings to be one and the same thing and therefore make everything ground everything in a certain sense.展开更多
C((t))is the formal Laurent series over the field C of complex numbers.It is a henselian valued field,and its valuation ring,denoted by C[[t]],is the formal power series over C.Let K be any model of Th(C((t)))with OK ...C((t))is the formal Laurent series over the field C of complex numbers.It is a henselian valued field,and its valuation ring,denoted by C[[t]],is the formal power series over C.Let K be any model of Th(C((t)))with OK its valuation ring and k its residue field.Then k is algebraically closed and OK is elemenatry equivalent to C[[t]].We first describe the definable subsets of OK,showing that every definable subset X of OK is either res-finite or res-cofinite,i.e.,the residue res(X)of X,is either finite or cofinite in k.Moreover,X is res-finite iff OK\X is res-cofinite.Applying this result,we show that GL(n,OK),the group of invertible n by n matrices over the valuation ring,is stably dominated via the residue map.As a consequence,we conclude that GL(n,OK)is generically stable,generalizing Y.Halevi's result,where K is an algebraically closed valued field.展开更多
基金supported by China’s MOE project of Key Research Institute of Humanities and Social Sciences at Universities (22JJD720021)the project of National Social Science Foundation of China(23BZX123)。
文摘Graham Priest has recently argued, in several of his papers and a book manuscript,for a view about nothing according to which nothing is paradoxical in several respects. The focus of the present paper is on three sub-claims of his view:(1) that nothing is an object,(w)that nothing is not an object, and(3) that everything grounds for its being on its being different from nothing. The author argues, both philosophically and formally, in this paper that Priest's arguments for the above sub-claims are not persuasive enough. Especially, the author argues that Priest's formal theory of nothing will suffer from a dilemma: either it will allow that there is a paradise of many nothings and therefore embrace an inflated ontology, or it will identify all nothings to be one and the same thing and therefore make everything ground everything in a certain sense.
基金supported by The National Social Science Fund of China(Grant No.20CZX050)。
文摘C((t))is the formal Laurent series over the field C of complex numbers.It is a henselian valued field,and its valuation ring,denoted by C[[t]],is the formal power series over C.Let K be any model of Th(C((t)))with OK its valuation ring and k its residue field.Then k is algebraically closed and OK is elemenatry equivalent to C[[t]].We first describe the definable subsets of OK,showing that every definable subset X of OK is either res-finite or res-cofinite,i.e.,the residue res(X)of X,is either finite or cofinite in k.Moreover,X is res-finite iff OK\X is res-cofinite.Applying this result,we show that GL(n,OK),the group of invertible n by n matrices over the valuation ring,is stably dominated via the residue map.As a consequence,we conclude that GL(n,OK)is generically stable,generalizing Y.Halevi's result,where K is an algebraically closed valued field.
