Basic Proof Theory

Rating:
Summary: You Call Yourselves Analytic Philosophers?
Review: That this book is not yet a foundational text in American graduate programs for analytic philosophy (or mathematics or computer science, for that matter) says something about an intellectual boundary those disciplines do not want to openly cross. Troelstra and Schwichtenberg, two hardened proof theorists with a mathematical conception of the issues involved in proof theory, cover nearly all of that subdiscipline's 70-year history in this affordable volume; and while it's not the clearest book ever written on the subject, it's a damn sight less obfuscatory than the Springer and North-Holland "monographs" (perhaps) available on the topic.

It's absolutely no fun to read at all, but it is resolutely Bourbakist in its avoidance of "proprioprecocity"; you will learn nothing that will impress others from reading this book, but you will also learn that intellectual techniques and ideas you thought were "cutting-edge" should be disquoted. And although the deflation of "minimalist" accounts of truth awaits an ill-tempered model theorist able to write competent English, this book contains contains a future of sorts for analytic thought; circling around the issues raised by computational complexity, as manifested in thought and action.

If this future be unappealing (as you might reasonably think), perhaps analysis as a mode of thought should be somewhat "deprivileged", such that our description of acceptably orderly cognition is brought more into line with the wanton reasoning practices of "natural consciousness". But at any rate: here is a bar, here raise.