Godel, Tarski and the Lure of Natural Language

Is mathematics ''entangled'' with its various formalisations? Or are the central concepts of mathematics largely insensitive to formalisation, or ''formalism free''? What is the semantic point of view and how is it implemented in foundational practice? Does a given semantic framework always have an implicit syntax? Inspired by what she calls the ''natural language moves'' of Gödel and Tarski, Juli...