This is my next book-length writing project. I am writing a book which aims to do these things:
Be a useable introduction to philosophical logic, accessible to someone who’s done only an introductory course in logic, covering at least some model theory and proof theory of propositional logic, and maybe a little bit of 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 semantics and (b) how to actually prove them. (I don’t think there are any books like this currently available, but I’d be happy to be shown wrong.)
Present the duality between model theory and proof theory in a philosophically illuminating and clear fashion.
And then apply these results to issues concerning meaning, epistemology and metaphysics, including issues of logical consequence and rationality, the problem of absolute generality, and the status of modality.
Are you interested in getting a look at the draft? The best way to do that is to come to this symposium
in Buenos Aires in July 2018, where we’ll be discussing it.
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