This is Greg Restall’s website, with news, writings, links, and bite sized updates. For background look below.

Proof Theory and Philosophy

Proof Theory and Philosophy: book manuscript in progress.

This is my next book-length writing project. I am writing a book which aims to do these things:

  1. Be a useable textbook in philosophical logic, accessible to someone who’s done only an intro course in logic, covering at least some model theory and proof theory of propositional logic, and maybe predicate logic.
  2. Be a user-friendly, pedagogically useful and philosophically motivated presentation of cut-elimination, normalisation and conservative extension, both (a) why they’re important to meaning theory and (b) how to actually prove them. (I don’t think there are any books like this available, but I’d be happy to be shown wrong.)
  3. Present the duality between model theory and proof theory in a philosophically illuminating fashion.
  4. Teach both formal philosophical logic in such a way that is not doctrinaire or logically partisan. That is, I will not argue that classical logic, or that intuitionistic logic, or that My Favourite Logic is the One True Logic. (Of course, hearing me say this is not a surprise.)
  5. I am (at this stage, at least) planning to make the book available for download as well as published by an academic publisher.

The first couple of chapters are now available: pdf with hyperlinks, paper-saving 2up pdf. Comments are most welcome at the wiki.


Author: Greg Restall
Status: In Progress

Local file: ptp.pdf (1MB)

Subjects: classical logic meaning non-classical logic proofs quantifiers sequents


I’m Greg Restall, and this is my website. I work in Philosophy at the University of Melbourne. Email: greg at; Post: School of of Philosophy, Anthropology and Social Inquiry, University of Melbourne, Parkville 3010, Australia.

Start at the home page—a summary of the site. The left column is news, archived on the news archive page. The central column contains recent items from the writing page, which lists my publications. These are also categorised by topic. You can follow my links at my account on delicious and occasional short snarky remarks at @consequently on twitter.

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This site is handcoded: I write text in Textmate, and Webby files things in the right place and uploads them to the server. This page was last modified on 2009-01-03 at 11:56PM.


There are two kinds of truths: those of reasoning and those of fact. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contigent and their opposites are possible.
— Gottfried Leibniz Monadology.