Gödel, Tarski and the Lure of Natural Language

Introduces an original approach to foundations of mathematics, departing from Gödel and Tarski and spanning many different areas of logic.

In this book Juliette Kennedy presents an original perspective on foundations of mathematics. Departing from Gödel and Tarski's work, the treatment is historically, logically and set-theoretically rich, and topics such as naturalism and foundations receive their due, but now with an entirely new twist.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, Juliette Kennedy considers what roles the concepts of 'entanglement' and 'formalism freeness' play in a range of logical settings, from computability and set theory to model theory and second order logic, to logicality, developing an entirely original philosophy of mathematics along the way. The treatment is historically, logically and set-theoretically rich, and topics such as naturalism and foundations receive their due, but now with a new twist.