English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The standard treatment of sets and definable classes in first-orderZermelo-Fraenkel set theory accords in many respects with the Fregeanfoundational framework, such as the distinction between objects and concepts.Nevertheless, in set theory we may define an explicit association of definableclasses 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 Fregeanabstraction generally. Because these extension and abstraction operators aredefinable, they provide a deflationary account of Fregean abstraction, oneexpressible in and reducible to set theory -- every assertion in the languageof set theory allowing the extension and abstraction operators $\varepsilon F$,$\# G$, $\alpha H$ is equivalent to an assertion not using them. The analysisthus sidesteps Russell's argument, which is revealed not as a refutation ofBasic Law~V as such, but rather as a version of Tarski's theorem on thenondefinability of truth, showing that the proto-truth-predicate "$x$ fallsunder the concept of which $y$ is the extension" is not expressible.

Fregean abstraction in Zermelo-Fraenkel set theory: a deflationary account