Reviews (4)

Excellent logical system.
While there is currently a variety of logical systems about, Lemmon's is well balanced and fairly intuitive. His approach is to limit his formal system to a few simple rules. The advantage is that it makes his meta-logic much easier, and the reader can grasp the whole system very quickly. The downside it that the system becomes cumbersome when trying to prove more difficult problems. To help simplify the longer proofs, Lemmon provides a list of already proven theorems, which one can substitute into the proof. His approach is elegant, and in my view, successful. While the text tends to be dense, his liberal use of examples clarifies many of the finer points. Still, the reader does have to work at it so I cannot recommend this text to beginning logic students. Davis' "Introduction to Logic" is much more straightforward, and much simpler. However, for serious students of logic, with a solid analytical background, or a good foundation in mathematics, this text provides a very good logical system.

jumping right in the pool
I used this book as part of an independent study of logic.It is dense, so unless you are willing to sit down and study itexhaustively or you have an experienced teacher (as I did), start with something lighter.That said, once I gained some knowledge in the area, the book was a pleasure to use, as Lemmon's precise language made it easier to clarify certain points.The largest drawback to this book is that it doesn't have solutions to its exercises, and these methods are not mechanical-you must know or learn how to make intuitive leaps or you will not be able to solve the problems. davewitt@technologist.com

Isbn: 052179434X
Sales Rank: 342743
Subjects:  1. General    2. Logic    3. Mathematics    4. Nonclassical mathematical logi    5. Nonclassical mathematical logic    6. Philosophy    7. Philosophy / General   

Isbn: 089874170X
Sales Rank: 1009841
Subjects:  1. Logic, Symbolic and mathematic    2. Mathematics    3. Philosophy   

Reviews (4)

Very Terse Treatment of a Broad Range of Topics
If you are already familiar with the material, this book is a concise and clear reference, and yes a great buy. But for learning these topics from the beginning, you would be better served by other books that are focused on just a particular topic.

For example, for logic in the context of set theory, I highly recommend Daniel Velleman's How to Prove it.

Incredible Best Buy
This book is without peer in its breadth of coverage of the foundations of mathematics and logic. I have given this book only 4 stars, because its treatment of any given topic
is not classic. It is the total package that astounds.
For a mere $15, you get a challenging undergraduate introduction to all of the following topics. I have written in parentheses the names of authors of more definitive treatments:

Intuitive set theory through the axiom of choice (Halmos)

Natural numbers Æ Integers Æ Rationals Æ Reals (Feferman)

Mathematical logic (Machover, Smullyan)

Metamathetics (Machover, Mendelson)

Introduction to the axiomatic approach

ZF axiomatic set theory (Suppes)

Boolean algebra through Stone's theorem and the completeness of sentential logic (Halmos & Givant)

Algebra (Birkhoff & MacLane's "Algebra")

Stoll's style is quite discursive, far from the terse lemma-theorem-corollary-remark style of so much 20th century mathematics. My only major disappointment is that the formal proof technique set out in chpt. 4 is natural deduction rather than the tableau method or Quine's Main Method.

It is indeed the case that there are no solutions to the exercises, but I do not believe that that is a major flaw.

Reviews (10)

Very good introductory/review logic book
I was took a few logic courses back when completing my bachelors. After several years as with everything else oyur memory becomes stale. I've decided to go to law school so I needed a logic review before taking the LSAT. This book is perfect for that. Clear concise explanations and examples, written very well and doesn't leave you asking questions about the ideas the author is trying to convey to you. I defiitely recomeend this book for the avid knowledge junky or for academic purposes.

Excellent value, well written, a bit old fashioned.
The good news. This book is excellent value for the money, and is the best written Schaum's Outline I have ever read. It is certainly not excessively mathematical, compared to nearly everything that passes for logic nowadays. Schaum's outlines are seldom written by first-raters in their respective fields. This is a clear exception; Varzi is a first rate contemporary philosopher. This book is an excellent example of modern scientific communication.

The bad news. The book's approach to logic is a bit on the old fashioned side. Much of the material on traditional logic could have been omitted. The book shares a flaw that is sadly all too common: trivial propositions take 20-40 lines to prove. The refutation tree or natural deduction machinery of this and other contemporary books is far too ponderous. This book, like all too many books in the philosophical logic tradition, devotes time to topics that leave me cold, such as modal logic. Meanwhile, it slights or omits topics that fascinate me, such as mereology, the isomorphism between truth functors and Boolean algebra, and metatheory. I like probability and inductive logic and feel that these have a great deal to offer to logic and philosophy, but this book only scratches the surface of these topics. The main comsumers of logic nowadays are computer scientists. It is not at all clear that this book would be of any value to them. On the other hand, this is an excellent book for your typical philosophy major.

excellent introduction to the mechanics of logic
This book is an excellent introduction to what I call the
mechanics of logic. If you are interested in metalogic
proofs, like the deduction theorem, then don't look here.
This book teaches the basics of logic. It presents logic
in several different ways: using Aristole's version (strictly
for historical reasons), using Venn diagrams, a Hilbert-style
logic (rules to introduce and remove boolean operators), and
semantic tableaux. Also, it first introduces propositional
logic, then it proceeds to predicate logic. The book has
a peculiar approach that it does not introduce functions (not
predicate functions) until much later.

Isbn: 007911251X
Sales Rank: 1064739
Subjects:  1. Artificial Intelligence    2. Automatic theorem proving    3. Computer Bks - Other Applications    4. Computer Books And Software    5. Computer Programming    6. Miscellaneous Software   

Reviews (20)

Graham Priest's Logic Intro. is well worth the purchase.
Graham Priest's Logic on Oxford Univ. Press I must say is superb.A short introduction that straddles the line between 'keeping to the basics of logic', but not really so.

The latter is strange to say, I must admit, but the point is that Priest touches upon the general basis of formal logics, but does not patronize the reader with cliche examples and content that can be found in several intro. books on logic.Rather, Priest introduces many important and contemporary problems that go on in logic (hence giving the reader a taste of-- not only technical aspects of logical systems-- but the philosophical issues that arise out of logics as well).Although this book does not necessarily go into extreme depth of particular issues, its survey of issues such as tense logic, existential import problems, and so forth are more than satisfactory.

In addition, Priest's style of writing is very clear, organized, and to the point.I must admit, Priest's writing is superb (as is evident in this work, as well as his other books and numerous logic/philosophy articles).In addition, Priest is quite possibly one of the most well-established and well known logicians of our day; so, the buyer should feel assured that he is more than qualified to write this book.

My advice is pick up this book! For the price---its a killer deal!

Also, I would recommend as 'follow-ups' to this book, Priest's Intro. to Non-Classical Logics and Susan Haack's Philosophy of Logics and her other work, Deviant Logics and Fuzzy Logic (in which Haack tries to tackle many philosophical problems that arise in classical/non-classical logics while defending the classical logics position).

Intro to Graham Priest's Logic
For its length and breadth, I'd recommend this little book to most people.I teach a course on Logic, and even I learned a bit from this short introduction.

The worry, however, is that Priest takes this book as an opportunity to push his own non-standard view on formal logic, which is why a better title for this book would be `A short Introduction to Priest's Logic'.

Most immediately evident is that Priest uses many of the chapters as a place to show how an argument for the existence of god.For example, much of the chapter on predicate logic is devoted to showing the fallacy inherent in the cosmological argument for the existence of god.His chapter on decision theory is in part devoted to showing how Pascal's wager goes wrong.

Probably even more subversive is that, in an introductory level logic book, Priest presents his own unorthodox solutions to paradoxes in logic.For example, to solve the problem of self-reference, he presents his own view regarding four valued logics, without even a word explaining that not only is this not the standard view, it's not even a very popular one.He also offers fuzzy logic as a solution of vagueness and sorites paradoxes.

Overall, I thoroughly enjoyed reading this book, and would offer it to any friend interested in a brief introduction to some advanced topics in logic.But I'll be sure to emphasize that much of what he offers for solutions is hardly accepted by mainstream analytic philosophy.Priest took advantage of this chance to write an introductory level text as an opportunity to push his own views, and anyone reading this should be aware of this fact before beginning.

Reviews (8)

Great stuff.
First, this isn't one of Smullyan's popular puzzle books- its a serious mathematics text. Second, don't use this as your first exposure to first-order logic (note the title doesnt say "Introduction to ...")- although logically self-contained, it requires some experience to appreciate what a neat little book this is.

It's not a general mathematical logic text- there is no model theory (beyond basic Skolem-Lowenheim), incompleteness, recursion theory, or set theory. It covers tableaux (this alone is worth the price of the book), Hilbert-style axiomatic systems (briefly), sequent systems, Gentzen's Hauptsatz and Extended Hauptsatz, Craig's and Beth's theorems, and more. But the heart of the book is completeness theorems, their proofs, and closely related material such as compactness and Herbrand-like theorems. Smullyan shows there are two main approaches to completeness (analytic vs. synthetic), breaks each into stages, provides nice abstracted formulations, and usually gives several different proofs of each result. The centerpiece is his "Fundamental Theorem of Quantification Theory", a theorem associating a truth-table tautology with every valid first-order sentence (check out the amazingly slick proof of completeness for the the Hilbert-style system that this provides). Similar constructions such as magic sets are also discussed. All this forms a much more extensive and illuminating look at completeness proofs than I've seen elsewhere.

The first-order logic used in the book has no equality and no function signs. There are few exercises, most of them simple. Smullyan writes clearly and with an appropriate amount of rigor (but its not as polished as his later books). Makes a great supplement to more general-purpose introductory mathematical logic books. If you haven't seen the tableau method yet buy this book immediately. Experienced readers will appreciate the sophisticated coverage of completeness proofs.

An Oddity But a Good-ity. Wait, that's terrible.
The reviewer from Illinois gave a very good characterization of Smullyan's style here:
"Smullyan has divorced logic from its roots: logics are simply recursively-defined sets of sentences and mappings, and that is that. No discussions, ala WvO Quine, on the history or linguistic difficulties of a concept, just definition and proof."
Readers familiar with Smullyan's enormous talent for popular exposition may be expecting the same herein: not so. This is very much for people who have attained what medical professionals call "mathematical maturity" (which is about as difficult to attain as zen, yet perhaps amounts to little more than the ability to read VCR instruction manuals). For example, the very first section is a wiz-bang treatment of trees (not the usual graph-theoretic ones), defined in the abstract/axiomatic fashion.
Of course, people who spend perhaps way too much of their time steeped in math are attracted to treatments of just this sort.
A structural characterization in terms of sets and mappings is much more meaningful, interesting, and aesthetically pleasing to those with these unusual inclinations (compulsions?) than a characterization framed significantly by historical motivation (please understand that I'm speaking roughly here). This is why I gave a positive review. A star was witheld for the selfish reason that I'm not sure I'll find much use for such an odd treatment of model theory, the topic for which I was seeking a more mainstream treatment when I purchased this. Regrets are nonetheless few: time spent reading Smullyan is never a waste.

Reviews (5)

Excellent book, but not for the beginner.
As a beginner in the study of philosophy, I have frequently read that the study of paradoxes is a waste of time, that paradoxes add little to the appreciation of philosophy as a whole.Perhaps that's true.Prof. Sainsbury in his introduction even warns us that the study of paradoxes is said to have led to the premature death of Philetas of Cos back in the old days.

I made the mistake of thinking that as a beginning student of philosophy I would be capable of fully appreciating this book and absorbing its contents.In fact, I am not, and could not.However, I can say without hesitation that it wasn't Professor Sainsbury's fault.He writes very clearly and without affectation, presenting the material as well as anyone could.Perhaps he makes some errors in his analysis of the paradoxes, but others will have to judge that, not I.

In addition to the "fun" of paradoxes, he also relates them to more general problems of philosophy, which I was better able to absorb.For example, in discussing Newcomb's paradox and rational behavior, he has this to say:

"A clear perception of the advantages of being a one-boxer cannot give you a REASON for becoming one - even if that were in your power.Atheists might clearly perceive the comfort to be derived from theism, but this does not give them a REASON for believing that God exists.The light of reason cannot direct one toward what one perceives as irrational.To adopt a position one regards as irrational one needs to rely on something other than reason:drugs, fasting, chanting, dancing, or whatever."

This is one of the better and more succinct descriptions of the relationship between reason and religious belief that I have read, even though I don't completely agree with it.Reason can take one part-way toward a belief in God, even if total belief is ultimately irrational.But at least one understands what Prof. Sainsbury has to say on the subject, and it's a minor point, anyway.

Highly recommended, for those who can handle it.

Knock your mind loose from your brain
Philosophy begins in wonderment. Sometimes it ends there, too.

Good paradoxes aren't just for entertainment (although they _are_ vastly entertaining; check out any of Raymond Smullyan's books for proof of that assertion). Each of them opens a door to all sorts of fascinating issues of tremendous philosophical importance.

Mark Sainsbury's fine introduction, in its heavily revised second edition, is a set of keys to those doors. For example, his discussion of Zeno's famous paradoxes doesn't just inform the lay reader what they are; it explains why they're important even today: because they call into question whether the now-standard mathematical analyses of the paradoxes adequately capture our ordinary understanding of space. That is, the paradoxes can be resolved in the ideal space of mathematicians, but that doesn't _necessarily_ mean they can be resolved in the space in which we really live.

In difficulty, the exposition is about one notch higher than in William Poundstone's _Labyrinths of Reason_, so you may want to read Poundstone first if you're new to this subject altogether. But do get around to this one. It's a solid account, from a more or less "analytic" outlook (though that term probably suffers from all the "vagueness" problems discussed in Sainsbury's second chapter).

Sainsbury will also introduce some topics Poundstone doesn't cover -- notably, and perhaps most interestingly, Graham Priest's "dialethism" -- a logic in which, Priest claims, it's possible for some contradictions to be true[!]. Sainsbury doesn't agree but nevertheless concludes that he doesn't have a knockdown argument against it. (Be aware that Sainsbury's account has been criticized by other philosophers, including Priest. Follow up with Priest's own books if you get interested in this subject.)

Sainsbury also doesn't hesitate to offer his own resolutions of the paradoxes, but he warns the reader not to accept his resolutions blindly. In fact there are several about which I continue to disagree with him (not an unusual phenomenon when the subject is paradoxes), but he's changed my mind on a couple.

Overall, then, this is a well-written and cogently argued presentation, highly recommended to anyone interested in paradoxes and their relevance to philosophy.

Excellent Text for Students and Professors
I am now using this text for a Problem Solving course.

I came across this text as a graduate student some years ago.Indeed, the problems presented in this text literally left me unsafe to drive on more than one occasion.The problems raised are philosophically intoxicating.The author should be commended for his clarity and ability to bring the issues to the forefront of discussion and thought.