Metalogic: An Introduction to the Metatheory of Standard First Order Logic

by Geoffrey Hunter

This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically truth-functional) first order logic. Included is a complete proof, accessible to non-mathematicians, of the undecidability of first order logic, the most important fact about logic to emerge from the work of the last half-century.

Hunter explains concepts of mathematics and set theory along the way for the benefit of non-mathematicians. He also provides ample exercises with comprehensive answers.

Genres: Logic, Mathematics, Philosophy, Nonfiction

288 pages, Paperback

First published January 28, 1971

Reviews

[Dave Bufano · Rating 5 out of 5]

This can be a hard book to find. What's amazing is that a book with this title can be fun to read. I'm re-reading it now. It's even more fun if you're reading Kuhn's "Structure of Scientific Revolutions" at the same time. I don't know what happens if you eat only broccoli and tofu over the same period of time.

[Erik · Rating 5 out of 5]

A genuine beauty of a logic book. Clear and reader friendly. At least that's what I thought. Apparently the students hated it. The notation is beastly, but what can you do? Tough completeness proof for predicate logic.

[Nathan Ormond · Rating 3 out of 5]

The first half of this book was brilliant. Walked me through all of the basics of Cantors set theory and metalogic etc... then the second half came and some jumps were made to the point that it was just like pages of proofs like Russell and Whiteheads Principia and then Godels proof - maybe I was too lazy and didnt have the time to patiently sit through them but these were pretty useless for me when I wanted more of a high level overview of the concepts of metalogic than a demonstration of specific proofs. If the book had continued on like the first half it would've got 5 stars from me but the second half was pretty bad in places hence only the 3 ...

[John · Rating 3 out of 5]

Easy to read, hard to understand. Could be wrong, but doesn't seem to have much utility. Seems to be proofs for things taken for granted in Intro.

[Lulu]

Logic

[Erin]

I can't rate this mostly because I only understood about a third of it.
Oops.