Product Description
From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data." There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book. ... Read more

Product Description
The combined study of logic and language goes back at least as far as the Middle Ages. In the last twenty-five years it has gained momentum with the formulation of Montague semantics and Generative Syntax, and the subsequent diversification of research programs.The Handbook of Logic and Language is the first comprehensive survey of the field. The twenty chapters show both sides of the interaction between logic and language: how logical systems are designed and modified in response to linguistic needs, and how mathematical theory arises out of this process and affects subsequent linguistic theory.Contributors: N. Asher, D. Beaver, W. Buszkowski, D. de Jongh, J. E. Fenstad, J. Groenendijk, H. Hendriks, J. Higginbotham, J. Hintikka, T. M. V. Janssen, H. Kamp, E. J. Keenan, J. T. Lønning, E. Martin, M. J. Moortgat, L. S. Moss, R. Muskens, D. Osherson, B. H. Partee, F. J. Pelletier, W. C. Rounds, G. Sandu, J. Seligman, M. Steedman, M. Stokhof, R. H. Thomason, R. Turner, J. van Benthem, J. van Eijck, A. Visser, D. Westerståhl ... Read more

Customer Reviews (1)

A must-have compendium
The title of this book might be slightly misleading, as it suggests the book covers topics both in linguistics and logic. This isn't so, as the introduction to the book explains. The title is a collection of introductory articles (~80 pages each) for a number of topics which are located on the linguistic/logical interface. Therefore, you will find here a selection of important topics from that area: an introduction to categorial type logics, Montague grammar, type theory as applied in linguistics, situation theory, game-theoretical semantics for languages and so on.

The book is a quite exhaustive compendium - no doubt, it is written from a specific viewpoint, so don't expect any articles on contextualism, but it does a really good job of sketching the field as it looked like 12 years ago. This doesn't mean the material is no longer current - on the contrary, most of the mentioned approaches are actively being developed and the Handbook still provides a worthwhile introduction.

A real advantage of this handbook is the choice of authors. Many of the authors are either the creators or very active developers of theories they write about, so their take on the described area is as representative as it can get. The editors did a really good job of putting together a team of authors that created over 1000 pages of quality material. While the Handbook carries a hefty price tag, the material is most certainly worth it. For any person working actively in the field or even for the more specialized graduate students, this is certainly a must-have. ... Read more

Product Description
The explosive progress of logic, since Frege, has produced applications in linguistics, mathematics and computer science. Students and practitioners of any of these fields, and of philosophy, will find this book an excellent reference or introduction. Now expanded to include non-classical logic, logic for the computer, and more. The central concepts are explained as they come into play in informal writing and conversation­­--argument, validity, relevance, and so on. This study guide progresses to concepts such as probability calculus. ... Read more

Customer Reviews (12)

Logic book review
I should have had this as a subject in school. This book is a good and user-friendly primer to Logic. Reasonably priced too, I bought another book for a friend who wanted to borough my personal copy.

The Tool (Your Mind)
To solve the riddle beguiling the world
School your mind in the fine art of logic:
No method besides will conjure the clues.

The cosmos concealed is cut and unfurled
By disciples of proof; earthbound magic
Spies the truth behind the mystical ruse.

Unable to deal with angel or ghost?
Take a leaf from the good book of nature;
The rational choice discarded by most:
Plain wisdom reveals the wonders that are.
Reject the unreal and you'll travel far
Out of the past and into the future!

With Aristotle's labor near to hand,
A powerful tool is yours to command.

-Jate

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. I would even call this book 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 texts 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 consumers 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 a 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.

One of the more interesting chapter covers fallacious arguments. ... Read more

Customer Reviews (1)

A tour of mathematical logic in one sitting
This short book is a delightful overview of the history of mathematical logic. It is written in Ogden's basic English which makes it very clear and accessible. Here and there are passages with stunning and humorous prose.

The time span covered begins with Aristotle's syllogistic (ca. 300 BCE) and ends with the theory of recursive functions (which brings us to the 1930's). Among the contributions to this development Nidditch gives special attention to those of Aristotle, Boole, Pierce, Frege, Cantor and Peano. In addition, the influences of Lull, Dalgarno and Wilkins, Descartes, Leibniz, Peacocke (the 18th century one, not the more famous 20th century one), Jevons, Schroeder, Russell, Whitehead, Hilbert and Brouwer and a few more, are recorded.

All of this is compressed into just under 90 (very small) pages. Obviously, this leaves no room for any serious historical scholarship.

In spite of the extremely compressed format the reader can glean surprisingly much about the development of logic, due to the authors choice to present mathematical logic as the outcome of four different themes or projects: the traditional logic of Aristotle, the quest for a 'complete and automatic' language for reasoning or thought, new (19th century) developments in algebra and geometry and their application to logic and, finally, meta-mathemtics.

The main question, and worry, is what group of readers this book is best suited for. Let me begin by stating who it is not for.

If you're seriously interested in mathematical logic what you need is a good textbook on logic, and this is not it.
If you're seriously interested in the history of logic you need something much more substantial, like Kneale and Kneale's 'The Development of Logic', or at least DeLong's 'A Profile of Mathematical Logic'.
For those who are after a non-technical introduction to logic Priest's 'Logic: A Very Short Introduction' is probably a better choice.

But if you are interested in logic, but don't know exactly the nature and extent of your interest (or level of commitment), this might very well be the book for you. It will, in other words, serve as a good introduction to an introduction to logic. All the more so since it is easily finished in one sitting.
If you already have some knowledge of logic, and just want to kick back with a little relaxing logic reading, then, too, Nidditch is your man. ... Read more

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Collected here for the first time, this series of lectures delivered by Lonergan at Boston College in 1957 illustrates a pivotal time in Lonergan's intellectual history, marking both the transition from the faculty psychology still present in his work Insight to intentionality analysis and his initial differentiation of the existential level of consciousness.

The lectures on logic deal with the general character of mathematical logic and its relation to truth, Scholasticism, and Aristotelian logic. Continuing Lonergan's long-standing interest in the foundations of thought, the lectures on existentialism offer a penetrating account of Husserl and his influence. They also deal with Jaspers, Heidegger, Sartre, and Marcel. They offer reflections on such topics as being oneself, dread, horizon, and the existential gap. Perhaps more dramatically than in any other work these papers reveal Lonergan's dual commitment to the rigor of scientific analysis (in the field of mathematical logic) and to the sensitivity of continental philosophies to existential issues.

Bernard Lonergan (1904-1984), a professor of theology, taught at Regis College, Harvard University, andBoston College. An established author known for his Insight and Method in Theology, Lonergan received numerous honorary doctorates, was a Companion of the Order of Canada in 1971 and was named as an original members ofthe International Theological Commission by Pope Paul VI.

Product Description
This book provides an elementary "hands-on" presentationof important mathematical logic topics.Explores topics thatare at the cutting edge of developments in computer science, while preserving the integrity of traditional logic. Stresses several self-contained proofsystems of interest to mathematical logic, some more suitable than others forparticular kinds of questions.For anyone interested in ComputerScience or Mathematics. ... Read more

Customer Reviews (3)

Great as preparation for automated reasoning, not so hot otherwise
In terms of the coverage of logic for mathematics and computer science, the target here is really the area of automated theorem proving. The book is split into two sections:

*) Quantifier-free logics
*) Logic with quantifiers

While the basic coverage of the propositional and predicate calculi is typical of what is done in other logic books, chapter three deals with equational logic and there is some coverage of abstract algebra. In particular, the representation of algebraic structures such as groups and fields. There is also extensive coverage of term rewrite systems (TRSs), which are constructed using replacement rules that resemble those of formal grammars.
If you are looking for a text in a course in basic mathematical logic, in my opinion this one is unsuitable. The extensive coverage of representations of structures including graphs takes you down a path not normally taken in a course in mathematical logic. In terms of computer science, it would have been helpful if more effort were spent in tying the logic into more mainstream areas covered in the computer science major. I also would not consider using this book as a text in a course in computation theory.

A logician from holland
I used this book as a course book and I can say that it is quite difficult to follow the book. All the proofs are either intuitive or very shortwithout much explanation or example. So, if you want to take this book as aguide for this field think twice!

gives basics for automated reasoning
I found this book to be an excellent reference for automated reasoning. It covers resolution and unification in great detail. It also covers Knuth-Bendix procedure for equational logic. I used this book as a startingpoint to learning about automated reasoning and logic in AI.

I recommendthis book for anyone who is just beginning to learn about automatedreasoning.

The one suggestion that I have to anyone reading this book isto review your abstract algebrea and set theory. Although this books doesintroduce and cover abstract algebra basics, anohter reference is useful.As for set theory, try Schaum's Outline on Set Theory as an intro or arefresher. ... Read more

Product Description
Linear Logic is a branch of proof theory which provides refined tools for the study of the computational aspects of proofs.These tools include a duality-based categorical semantics, an intrinsic graphical representation of proofs, the introduction of well-behaved non-commutative logical connectives, and the concepts of polarity and focalisation. These various aspects are illustrated here through introductory tutorials as well as more specialised contributions, with a particular emphasis on applications to computer science: denotational semantics, lambda-calculus, logic programming and concurrency theory. The volume is rounded-off by two invited contributions on new topics rooted in recent developments of linear logic. The book derives from a summer school that was the climax of the EU Training and Mobility of Researchers project 'Linear Logic in Computer Science'. It is an excellent introduction to some of the most active research topics in the area. ... Read more

Product Description
Logic: Techniques of Formal Reasoning, 2/e is an introductory volume that teaches students to recognize and construct correct deductions. It takes students through all logical steps--from premise to conclusion--and presents appropriate symbols and terms, while giving examples to clarify principles. Logic, 2/e uses models to establish the invalidity of arguments, and includes exercise sets throughout, ranging from easy to challenging. Solutions are provided to selected exercises, and historical remarks discuss major contributions to the theories covered. ... Read more

Customer Reviews (5)

a great book for demystifying mathematical proof, especially for programmers
I used this book in a course I took in logic at the University of Virginia as an elective in the philosophy department while pursuing my degree in electrical engineering.

I returned to this book in 1994 when I found myself studying math on my own.I was trying to tackle analysis and not satisfied that the proofs I was studying were sound.

This book was a godsend to me.I wanted to see how far it was possible to dispense with any hand waving whatsoever when proving a theorem, and I was deeply distrustful of the typical arguments found in higher math books.

Other books on logic seemed to assume you were comfortable with mathematical proof itself and proceeded to show you how to informally prove theorems about formal systems.You can imagine how little use that was to me.

This book introduced the techniques of formal logic as a game with simple rules that you had to practice, which is a great way to demystify the more complex styles of argument that are commonplace in higher math.The problems grow very slowly and smoothly in complexity through the book, with no enormous gaps that readers have to fill in on their own (a rarity in math books, I think).

If you are a programmer, an exercise I highly recommend is to write a program to validate proofs expressed in the system of the book, as you work your way through it.

After spending six months working through this book, I proceeded to Halmos's "Naive Set Theory", another great book, BTW, that paves the way to understanding higher math.

I can't imagine a better preparation for Halmos's book than KMM's Techniques of Formal Reasoning.

I still use it after 40 years
The first edition of this book was the textbook for my first formal logic course at UCLA in 1967, taught by Donald Kalish. Because of it, I changed my major from Physics to Mathematics with a specialty in Logic and Set Theory. Forty years later, I still pull the book out and do exercises from the later chapters,certain that such mental exercise sharpens my decision-making skills. I highly recommend this book to anyone who wishes to improve their deductive reasoning.

Most Excellent Logic Text
Logic: Techniques of Formal Reasoning, 2nd Edition, by Donald Kalish, Richard Montague, and Gary Mar 1980 (1964)

I was originally introduced to the 1964 edition of Kalish and Montague's Logic: Techniques of Formal Reasoning in early 1970. As an undergraduate taking elementary logic for the first time, needless to say I found the demands of sentential and predicate calculus and theorem-proving in general to be daunting and not a little painful. It was many years later after receiving advanced degrees and teaching logic courses myself, along with researching some of the theoretical horizons in artificial intelligence, that I turned back to this most precious of textbooks. Finding that a second edition had been published, I eagerly bought a copy and set out to re-prove all those theorems.

Sharpening one's logic skills can be a struggle, but it is one well worth undergoing especially with the demands for reasoned discipline imposed by Kalish, Montague, and Mar.Every so often, I go back to this text to prove the theorems once again (though I occasionally skip over a few in the first three chapters). I've found just a few suggestions I would make to the authors, if they were still around, or to whoever may edit it in the future. These pertain only to the first 5 chapters.

The transition from the 125 theorems of the sentential calculus to those of the predicate calculus is a bit rough-going. Almost immediately, one is expected to engage in abbreviated theorem-proving which certainly assumes a command of all those theorems that came before. It would seem that a few more exercises would help students acquire more familiarity with those theorems and with abbreviated proofs. Moreover, one is introduced to more complex inference rules, such as separation of cases, for which few exercises have prepared one, at least up to that point. These may be minor quibbles, but they can cause a lot of confusion, especially to students introduced to logic for the first time.

Additionally, well into Chapter III, it is possible to construct a proof of one of the advanced theorems with the use of hypothetical syllogism. In theorem T235 (corresponding to the Aristotelian syllogism Barbara), one can derive two pure hypothetical statements permitting the application of hypothetical syllogism (the law of transitivity) to deduce a third. Yet neither hypothetical syllogism as a specific rule of inference nor the concept of transitivity has been introduced in previous pages. In fact, hypothetical syllogism as such (including explanations of pure and mixed syllogisms) is never introduced, though principles of syllogism are. The law of transitivity is not introduced until late in Chapter V. Of course, one can derive them, but this can cause confusion for a beginner.

I highly recommend this text over all others that are commonly used in basic undergraduate or even graduate courses. Though Logic: Techniques of Formal Reasoning is more demanding than, say, any of the Copi books, those demands result in more disciplined reasoning, proofs, and a broader understanding of logic and its relation to mathematics.

Myrna L. Estep, Ph.D.

Best Textbook
With some saddness, I noted the death of Dr Kalish this month.As an undergrad at UCLA during the mid 60's, I was fortunate to take Dr Kalish's class in Symbolic Logic.Over the years, I realized that his course usingthis textbook was the most valuable class I took, either as an undergrad ora graduate student.The text offers disciplined procedural logic thatclarifies thought processes.At various times, I worked as a mathematicalprogrammer in several higher level languages without ever taking a formalcourse in any of them.I attribute my success in this area to theTechniques of Formal Reasoning.

Kalish
If taught by the right person, this book will reveal all of the issues of contemporary logic. It is best supplemented on first reading with Schuman's "logic" guide. As Kalish was influenced by Russell, I found theTheorems in the Principia matched perfectly those found in this book. Thelatest edition of this book is much improved, in my opinion. It offers moreguidance to understanding how to solve problems, and offers a great manyuseful hints and tips. Kalish is/was (?) the Chair of the department ofUCLA. He is a modern master and authority on this subject. In my opinion,if you wish to spend time on understanding the strengths ofcontemporarysymbolic logic, there is no better book to buy. ... Read more

Product Description
This volume is an accessible introduction to the subject of many-valued and fuzzy logic suitable for use in relevant advanced undergraduate and graduate courses. The text opens with a discussion of the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented.For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. ... Read more

Customer Reviews (1)

lucid and excellent overview
Merrie Bergmann's work is extremely readable and lucid on a difficult and convoluted topic. Bergmann was responsible for the lucid semantic sections of Bergmann, Moor, and Nelson's The Logic Book. IMHO this is by far the best introductory symbolic logic text available. Bergmann has a real talent for presenting formal logical ideas of a most advanced sort in an accessible manner. Bergman's treatment is highly up to date. She is both formally proficient and philosophically astute. Despite her philosophical ability she had to move from the Philosophy Department at Dartmouth to the Computer Science department at Smith, hardly a salary demotion, but the partial loss to the phlosophy profession of a highly insightful and illuminating thinker.

Her major focus is on the use of many-valued and fuzzy logics to deal with vagueness. She understands a fuzzy logic as an infinite valued logic, rather than a probabilistic logic that assigns a probability weight to propositions. One cannot do better than this work on this topic ... Read more

Product Description
This is an introductory textbook on probability and induction written by one of the world's foremost philosophers of science.The book has been designed to offer maximal accessibility to the widest range of students (not only those majoring in philosophy) and assumes no formal training in elementary symbolic logic.It offers a comprehensive course covering all basic definitions of induction and probability, and considers such topics as decision theory, Bayesianism, frequency ideas, and the philosophical problem of induction.The key features of the book are:* A lively and vigorous prose style* Lucid and systematic organization and presentation of the ideas* Many practical applications* A rich supply of exercises drawing on examples from such fields as psychology, ecology, economics, bioethics, engineering, and political science* Numerous brief historical accounts of how fundamental ideas of probability and induction developed.* A full bibliography of further readingAlthough designed primarily for courses in philosophy, the book could certainly be read and enjoyed by those in the social sciences (particularly psychology, economics, political science and sociology) or medical sciences such as epidemiology seeking a reader-friendly account of the basic ideas of probability and induction.Ian Hacking is University Professor, University of Toronto. He is Fellow of the Royal Society of Canada, Fellow of the British Academy, and Fellow of the American Academy of Arts and Sciences. he is author of many books including five previous books with Cambridge (The Logic of Statistical Inference, Why Does Language Matter to Philosophy?, The Emergence of Probability, Representing and Intervening, and The Taming of Chance). ... Read more

Customer Reviews (9)

recommended!
The author gives admirable attention to clarity for the topics discussed in this book. As an introductory text, it's not reasonable to expect completeness for the more complex topics addressed. I highly recommend this book to anyone looking for an introduction to probability and inductive logic.

Connecting The Dots
This book clearly explains ideas in logic and in statistics/probability courses I have taken, and includes several insights new to me. It contains several real world exercises and answers. For me it's hard to put down. Every minute spent going through it has been very much worth it.

Best text on logic and philosophy of probability
Maybe 1/3 of a college course in probability and statistics consists of a rapid trip, in math language, through basic conceptual ideas such as the interpretation of "probability", Bayes rule, significance tests and confidence intervals.This book, aimed at students of philosophy, treats this material and the associated math much more slowly and carefully -- relating probability to logic and philosophy, not just to math.For instance it has clear discussions of the principle of maximizing expected utility;the frequentist/Bayes philosophies and the coherence ideas emphasized by Bayesian apologists; the logic of significance tests and confidence intervals.Concepts are illustrated by creative selection of hypothetical story examples -- much more interesting than the usual math textbooks full of X's and Y's. The final 20 pages are a rather big jump toward technical philosophy -- arguing that both Bayesian and frequentist philosophies comprise "evasions" rather than "solutions" of "the problem of induction".

For a textbook, rather than bedtime reading, on this material it is hard to imagine a better treatment.My only criticism -- perhaps a criticism of analytic philosophy in general -- is that it seems more concerned with teaching the reader how to critique other people's arguments that with teaching them how to say anything constructive about the real world.

First Rate Introductory Text
This is a first rate introductory text prepared by a well known philosopher and expert on the logic and history of probability & statistics.The approach is disarmingly simple.Hacking avoids complicated math and proofs and teaches via the intuitive appeals to the underlying logic of these topics.Hacking begins with an intuitively based discussion of basic features of probability theory, expectation, Bayes rule, and decision analysis.This is followed by a particularly good exposition of the different senses of probability; belief-Bayesian and frequentist.Hacking shows how both approaches can be used fruitfully and rigorously in even mundane problems.These sections are followed by very nice chapters on the underlying logic of normal distributions, statistical hypothesis testing, and confidence intervals.This is the diametrical opposite of the cookbook approach used often in many statistics books and provides very nice understanding of key features of statistical methods.I never appreciated the strength of the confidence interval approach before reading this book.Hacking concludes with some concise but thoughtful chapters on the philosophical implications of these ideas, particularly as applied to the classic problem of induction.The quality of writing is excellent and the book features a large number of good examples and problems to work through.Strongly recommended to individuals who want to learn more about the basis of statistical methods.

Especially good on Bayesianism and Frequentism
(FOUR AND A HALF STARS)
This is more an intro to the PHILOSOPHY of probability and inductive logic than an intro to the MATHEMATICS of probability of inductive logic, although some of the basic mathematical ideas are covered (which is useful if you're gonna discuss the philosophy). Do not get this book if you're just looking for a typical mathematical intro to statistics.But DO get this book if you want to know about the foundations of Bayesianism or are interested in the Frequentists vs. Bayesian debate.It is the best intro out there on the Frequentists/Bayesians issue, and it is extremely helpful for someone who is trying to get a handle on Bayesian reasoning.Also, those who are more into the mathematical aspects of probability could find this book useful in giving them a wider perspective on the subject.On the whole, it's clearly written and fun to read, although it is not an "easy" book.A basic knowledge of probability theory and some initial grasp of induction are good to have before reading this.But overall, it's highly recommended for those who want to know about the conceptual underpinnings of probability/induction in general, and Bayesian and Frequentism specifically.
... Read more

Product Description
Domains are mathematical structures for information and approximation; they combine order-theoretic, logical, and topological ideas and provide a natural framework for modelling and reasoning about computation. The theory of domains has proved to be a useful tool for programming languages and other areas of computer science, and for applications in mathematics.
Included in this proceedings volume are selected papers of original research presented at the 2nd International Symposium on Domain Theory in Chengdu, China. With authors from France, Germany, Great Britain, Ireland, Mexico, and China, the papers cover the latest research in these sub-areas: domains and computation, topology and convergence, domains, lattices, and continuity, and representations of domains as event and logical structures.
Researchers and students in theoretical computer science should find this a valuable source of reference. The survey papers at the beginning should be of particular interest to those who wish to gain an understanding of some general ideas and techniques in this area. ... Read more

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All current issues in HOL theorem proving and formal verification of hardware and software systems are addressed. Among the HOL theorem proving systems evaluated are Coq, HOL, Isabelle, and PVS. Softcover. ... Read more

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The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition.

This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction.

This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.

Product Description
This book contains 21 essays by leading authorities on aspects of contemporary logic, ranging from foundations of set theory to applications of logic in computing and in the theory of fields. In computer science and mathematics, this gap between foundations and applications is small, as illustrated by essays on the proof theory of non-classical logics, lambda calculus, relating logic programs to inductive definition, and definability in Lindenbaum algebras. Other chapters discuss how to apply model theory to field theory, complex geometry and groups, and how to recover from its automorphism group. ... Read more

Product Description
In this volume, Lambek and Scott reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory.In Part I, they show that typed lambda-calculi, a formulation of higher-order logic, and cartesian closed categories, are essentially the same.Part II demonstrates that another formulation of higher-order logic, (intuitionistic) type theories, is closely related to topos theory.Part III is devoted to recursive functions.Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained.Detailed historical references are provided throughout, and each section concludeds with a set of exercises. ... Read more

Customer Reviews (1)

This is definitely Higher!
I was looking for a book for my girlfriend this Christmas and stumbled upon this one.At first I thought it would be too light but was I ever mistaken!!This book is so high that it would make Jack Kerouac dizzy.It begins with a treatment of basic category theory and ccc's and then goes on to present toposes and intuitionistic type theory.The authors take care to annotate their turnstile with the set of free variables (Hah!I bet you thought I had no idea what this book was about!) so that they can deal with empty types in a reasonable way.The treatment of presheaf models is very lucid and the discussion of internal languages and lambda-calculi is excellent.In fact many papers of Koymans are just exercises from this book worked out.The book is slightly out of date, no treatment of linear logic or symmetric monoidal-closed categories.Overall this book is highly recommended for the beginner and expert alike. ... Read more

Product Description
This textbook provides a first introduction to mathematical logic which is closely attuned to the applications of logic in computer science. In it the authors emphasize the notion that deduction is a form of computation. Whilst all the traditionals subjects of logic are covered thoroughly: syntax, semantics, completeness, and compactness; much of the book deals with less traditional topics such as resolution theorme proving, logic programming and non-classical logics - modal and intuitionistic - which are becoming increasingly important in computer science. No previous exposure to logic is assumed and so this will be suitable for upper level undergraduates or beginning graduate students in computer science or mathematics. From reveiws of the first edition: "... must surely rank as one of the most fruitful textbooks introduced into computer science ... We strongly suggest it as a textbook ... " SIGACT News ... Read more

Customer Reviews (2)

It is of great help for undergraduate computer science students
I am currently an undergraduate computer science student, and as such, I say that this book was of great help to me in understanding both the basics and more advanced features of logic. I can't say anything about the very advanced parts of the book but if the writing style is the same as in the first 2 chapters, then it should be a great book for both undergraduate and graduate students.

good logic introduction to computer science students
This book is very carefully written to take care of its computer science and mathematics audience. The writing style is concise, yet unlike some other logic books, this one is far less dense and the content can easily be followed by an advanced undergraduate student (also, of course, by graduatestudents).

The book contains a relatively balanced coverage on logic.The six sections include Propositional Logic, Predicate Logic, PROLOG,Modal Logic, Intuitionistic Logic and Elements of Set Theory. There is alsoa concise appendix on the history of logic development.

I especiallylike the authors' careful treatment on the logics in PROLOG. Also, theauthors have taken very good care in preparing the manuscript and my wholeclass can only find about ten typos after spending a whole semester usingthis book.

Indeed, this book can easily be re-titled to be "WhatEvery Computer Scientists Should Know About Logic".

Highlyrecommended. ... Read more

Product Description
Hyperarithmetic theory is the first step beyond classical recursion theory. It is the primary source of ideas and examples in higher recursion theory. It is also a crossroad for several areas of mathematical logic: in set theory it is an initial segment of Godel's L; in model theory, the least admissible set after ; in descriptive set theory, the setting for effective arguments. In this book, hyperarithmetic theory is developed at length and used to lift classical recursion theory from integers to recursive ordinals (metarecursion). Two further liftings are then made, first ordinals ( -recursion) and then to sets (E-recursion). Techniques such as finite and infinite injury, forcing and fine structure and extended and combined Dynamic and syntactical methods are contrasted. Several notions of reducibility and computation are compared. Post's problem is answere affirmatively in all three settings. This long-awaited volume of the -series will be a "Must" for all working in the field. ... Read more