Proof Theory and Philosophy: book manuscript in progress.
You are welcome to download and read this document. I especially welcome feedback on it. As it is not yet published in final form, if you want to cite the paper, please check with me first. Thanks.
This is my next book-length writing project. I am writing a book which aims to do these things:
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.
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.)
Present the duality between model theory and proof theory in a philosophically illuminating fashion.
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.)
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 here: pdf with hyperlinks.
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