论文标题
Zermelo-Fraenkel集理论中的Fregean抽象理论：通缩帐户
Fregean abstraction in Zermelo-Fraenkel set theory: a deflationary account
论文作者
论文摘要
一阶Zermelo-fraenkel集合中的集合和可定义类别的标准处理在许多方面都与Fregean基础框架（例如对象和概念之间的区别）。然而，在集合理论中，我们可以将可定义类的明确关联与集合对象$ f \ mapsto \ varepsilon f $以这种方式，我将证明是将弗雷格的《基本法》视为ZF定理方案，Russell notwith。类似的分析也适用于康托尔原理和弗雷格的抽象。 Because these extension and abstraction operators are definable, they provide a deflationary account of Fregean abstraction, one expressible in and reducible to set theory -- every assertion in the language of set theory allowing the extension and abstraction operators $\varepsilon F$, $\# G$, $αH$ is equivalent to an assertion not using them.因此，该分析避开了罗素的论点，这并不是作为基本定律的反驳，而是作为Tarski定理的一种关于真理的不可固定性的版本，表明proto-truth-predicate“ $ x $” $ x $跌倒在其中$ y $的概念下，并不是表达的。
The standard treatment of sets and definable classes in first-order Zermelo-Fraenkel set theory accords in many respects with the Fregean foundational framework, such as the distinction between objects and concepts. Nevertheless, in set theory we may define an explicit association of definable classes with set objects $F\mapsto\varepsilon F$ in such a way, I shall prove, to realize Frege's Basic Law V as a ZF theorem scheme, Russell notwithstanding. A similar analysis applies to the Cantor-Hume principle and to Fregean abstraction generally. Because these extension and abstraction operators are definable, they provide a deflationary account of Fregean abstraction, one expressible in and reducible to set theory -- every assertion in the language of set theory allowing the extension and abstraction operators $\varepsilon F$, $\# G$, $αH$ is equivalent to an assertion not using them. The analysis thus sidesteps Russell's argument, which is revealed not as a refutation of Basic Law~V as such, but rather as a version of Tarski's theorem on the nondefinability of truth, showing that the proto-truth-predicate "$x$ falls under the concept of which $y$ is the extension" is not expressible.
