This article surveys recent literature by Parsons, McGee, Shapiro and others on the
significance of categoricity arguments in the philosophy of mathematics. After discussing …

Major shifts in the field of model theory in the twentieth century have seen the development
of new tools, methods, and motivations for mathematicians and philosophers. In this book …

Second-order logic has a subtle role in the philosophy of mathematics. It is stronger than first
order logic in that it incorporates “for all properties” into the syntax, while first order logic can …

This Element addresses the viability of categoricity arguments in philosophy by focusing with
some care on the specific conclusions that a sampling of prominent figures have attempted …

The following bare-bones story introduces the idea of a cumulative hierarchy of pure
sets:'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any …

The previous Part I of the paper (https://dx. doi. org/10.2139/ssrn. 4243201) discusses the
option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an …

This paper focuses on the categoricity of arithmetic and determinacy of arithmetical truth.
Several 'internal'categoricity results have been discussed in the recent literature. Against the …

Informally speaking, the categoricity of an axiom system means that its non‐logical symbols
have only one possible interpretation that renders the axioms true. Although non …

Reflection principles are of central interest in the development of axiomatic theories.
Whereas they are independent statements they appear to have a specific epistemological …

On a very natural conception of sets, every set has an absolute complement. The ordinary
cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining …