Gödel, Tarski and the Lure of Natural Language

Download or read book Gödel, Tarski and the Lure of Natural Language written by Juliette Kennedy and published by Cambridge University Press. This book was released on 2020-12-17 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.