Like any great book, this one could be a bit, though not too much, better. By far and away the most useful element of Quine's book is his treatment of translating ordinary English into logical schemata. I have never seen such a lucid and effective presentation of the task, and I recommend the book very highly to anybody on that account. His presentation of truth-functional and quantificational schemata are solid are simply excellent. The book, however, is not without its defects of which I should caution prospective buyers about. First, there are many treatments in the book of historical interest, but to a student of first-order logic they may seem to be a bit excessive. His incorporation of Polish notation, while fascinating in its own right, is not in accorance with Quine's drive for efficiency and conciseness. A similar account goes for his treatment of Boolean algebra. It is in that treatment that Quine introduces many ideas indispensible to quantificational logic, yet it is tempting to skip over those chapters when one can sufficiently delve into quantification theory. Secondly, his notation is, as another reviewer points out, unorthodox. It is very effective and in my opinion superior to the conventional formality, but this could be difficult to deal with, and one wonders if Quine should have been more cautious about varying his symbols from the norm. Finally, Quine's treatment of the Completeness Proof and the Lowenheim Theorem, while quite solid in their own right, could be more effective. Quine seems to be keen on applying a constructivist approach to the proof, and spends many pages on definitions and lemmas that can be avoided. One can provide a proof by contradiction in order to sufficiently demonstrate most of his treatment of the matter, as so much of it is spent proving the "law of infinite conjunction," which is really only an 8 step proof. I won't go into the details here, but keep that in mind when studying the chapter. Nevertheless, Quine's work is as entertaining as it is rigorous.
