The Logic Manual Paperback – 17 Oct 2010
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About the Author
Volker Halbach is Reader and CUF Lecturer in Philosophy at the University of Oxford
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Top Customer Reviews
If you want an introduction to logic, then this one is good.
Most Helpful Customer Reviews on Amazon.com (beta)
Having access to the on line materials is certainly a plus with this one, and I highly recommend it as a second or third read for those new to philosophical logic.
Mainly the text proved a disappointment. In my experience, what gets people hooked on logic is the puzzles---simple-looking questions which, sometimes after hours of struggle, illuminate some deep pattern or symmetry. The aim of this text, though, seems mainly to be to inculcate extremely 'correct' notations and definitions. The exercises (including the supplementary online exercises) are generally trivial applications of the formalism. My students also complained that the book's exposition lacked motivation.
The Gentzen-style approach to natural deduction is great for metatheory, but awkward for actually building proofs. So why are the exercises on natural deduction just routine proof constructions? Why not include, for example, questions about admissibility of inference rules?
Tarski-style semantics is already notationally awkward, but the author's choices make this worse. For example, instead of $M\models \phi$ we get $|\phi|_M=1$. The notation for the value of a variable $x$ under an assignment $\beta$ is $|x|^\beta_M$, even though it is simply the value of the function $\beta$ and so could be written $\beta(x)$. Altogether the discussion of semantics looks like a thicket of brambles. And after building up the formalism the author forgoes stimulating students with puzzles which could make the formalism seem worthwhile in the first place, for example regarding definability. Instead the semantic exercises are just routine verifications that the machine clicks forward properly.
So all in all, this book presents logic as a ritualistic or even priestly discipline where the main thing is to be notationally correct. It doesn't stimulate the creative thinking which makes logic fun.
Some examples of introductory books which (notwithstanding their own pros and cons) do convey the pleasure of puzzling include Barwise et al's *Language Proof and Logic*, Goldfarb's *Deductive Logic*, and Smullyan's *Logical Labyrinths*. Sadly, none of those exudes the philosophical purity of Halbach. But, better to start with puzzles---let precision arise as needed.