非个体与准集合理论（英文）

Non-individuals and Quasi-set Theory

由法兰奇与克鲁兹所提出的准集合理论是目前对非个体的形式化理论中最有前途的一个。它的目标在于对非个体的汇聚这个直觉性概念提出一个形式化的说明,但同时保持其一或多的有限基数性。在准集合理论中,外延等同的概念是以一个限制性的方式加以定义的,该定义排除了被意图当作是非个体的事物。然而,由于该理论的语言中每一个基本语式都是明确二值的,因而我们可以得到这样的一个二元自反关系:该关系的等价集中的所有个体都能够彼此互换而不至于改变任何语式的真假值。因而,任何一对事物间的等同关系可以轻易地在准集合理论中加以定义。从语义层面来说,准集合理论并没有将该语言的语词解释成为非个体,而我们也不容易看出这样的一种解释如何可能被建立起来。

.Quasi-set theory by S.French and D.Krause(2006)has been so far the most promising attempt of a formal theory of non-individuals.It aims to provide a formal elucidation of the intuitive notion of ensembles of non-individuals which nevertheless have finite cardinalities of one or greater.In quasi-set theory,extensional identity is defined with a limited scope to exclude objects that are intended to be non-individuals.However,since every elementary formula of its language is sharply bivalent,a binary relation is obtained which is reflexive and in which members of its equivalence classes are substitutable for each other salva veritate in all formulas.Hence identity of any pair of objects is readily defined in quasi-set theory.On a semantic level,quasi-set theory does not provide an interpretation of its language terms as non-individuals that has explanatory power,and it is not easy to see how such an interpretation can be set up.