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Introduction to Mathematical Logic by Alonzo Church Average Customer Review: Paperback (28 October, 1996) list price: $49.95 -- our price: $37.88 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (3)
In the introduction to the book the author defines the terms and concepts he will use in the book, with a discussion of proper names, constants and variables, functions, and sentences. He adopts the Fregian point of view that sentences are names of a particular kind. His discussion of this is rather vague however, for he does not give enough clarification of the difference between an "assertive" use of a sentence and its "non-assertive" use. Readers will have to do further reading on Frege in order to understand this distinction more clearly, but essentially what Church is saying here is that sentences are names with truth values. The existential and universal quantifiers are introduced as well. And here the author also introduces the concepts of object language and metalanguage, along with a discussion of the axiomatic method. The author distinguishes between informal and formal axiomatic methods. The modern notions of syntax and semantics are given a nice treatment here, and the di scussion is more in-depth than one might get in more modern texts on mathematical logic. Chapter 1 is a detailed overview of propositional logic, being the usual formal system with three symbols, one constant, an infinite number of variables, rules on how to form well-formed formulas, and the rules of inference. The deduction theorem is proved in detail along with a discussion of the decision problem for propositional logic, with the famous truth tables due to W. Quine introduced here. The notions of consistency and completeness are briefly discussed. The discussion of the propositional calculus is continued in the next chapter where a new system of propositional calculus is obtained by dropping the constants from the first one and adding another symbol (negation). The two systems are shown to be equivalent to each other using a particular well-formed formula in the second one to replace the constant in the first. Other systems of propositional calculus are also introduced here, using the idea of primitive connectives such as disjunction, along with various rules of inference. Church also outlines an interesting propositional calculus due to J.G.P.Nicod, which assumes only one primitive connective, one axiom, and only one rule of inference (besides substitution). The author also introduces partial systems of propositional calculus, with the goal of showing just what must be added to these systems to obtain the full propositional calculus. He discusses the highly interesting and thought-provoking intuitionistic propositional calculus, due to A. Heyting, which is a formalization of the famous mathematical intuitionism of L.E.J. Brouwer. The system he discusses is a variant of Heyting's and he gives references to the positive solution of the decision problem for this system. The author ends the chapter with a brief discussion of how to construct a propositional calculus by employing axiom schemata. The author then moves on to what he has termed functional calculi of first order beginning in the next chapter. Called predicate calculi in today's parlance, the author first defines the pure functional calculus of first order, and shows that the theorems of the propositional calculus also follow when considered as part of this system. Free and bound variables are defined, and Church proves explicitly the consistency of this system, and the deduction theorem. The important construction of a prenex normal form of a well-formed formula is discussed, and the author shows that every well-formed formula of the functional calculus is equivalent to some well-formed formula in prenex normal form. In chapter 4, the author gives an alternative formulation of pure functional calculus of first order, wherein rules of substitution are used and axiom schemata are replaced by instances, making the number of axioms finite. The Skolem normal form of a well-formed formula is defined, which sets up a discussion of satisfiability and validity. The author then proves the Godel completeness theorem, which states that every valid well-formed formula is a theorem. This is followed by a very well written discussion of the Skolem-Lowenheim theorem, and an overview of the decision problem in functional (predicate) calculus. In the last chapter of the book the author considers functional (predicate) calculi of second order, which is distinguished from the first order case by allowing the variables to range over what its predicates and subjects represent. In second-order functional calculus, propositional and predicate variables can have bound occurrences. The author discusses the elimination problem and consistency for second-order predicate calculus, and gives a proof of the (Henkin) completeness theorem. A fairly detailed discussion of a logical system for elementary number theory is given, but the treatment involves notation that is somewhat clumsy and the discussion is difficult to follow. ... Read more Isbn: 0691029067 |
$37.88 |
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Basic Proof Theory (Cambridge Tracts in Theoretical Computer Science) by A. S. Troelstra, H. Schwichtenberg, C. J. van Rijsbergen, S. Abramsky, P. H. Aczel, J. W. de Bakker, Y. Gurevich, J. V. Tucker, Anne S. Troelstra Average Customer Review: Paperback (27 July, 2000) list price: $34.99 -- our price: $34.99 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (2)
It's absolutely no fun to read at all, but it is resolutely Bourbakist in its avoidance of "proprioprecocity"; you will learn nothing that will impress others from reading this book, but you will also learn that intellectual techniques and ideas you thought were "cutting-edge" should be disquoted.And although the deflation of "minimalist" accounts of truth awaits an ill-tempered model theorist able to write competent English, this book contains contains a future of sorts for analytic thought; circling around the issues raised by computational complexity, as manifested in thought and action. If this future be unappealing (as you might reasonably think), perhaps analysis as a mode of thought should be somewhat "deprivileged", such that our description of acceptably orderly cognition is brought more into line with the wanton reasoning practices of "natural consciousness".But at any rate: here is a bar, here raise. ... Read more Isbn: 0521779111 |
$34.99 |
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Modal Logic by Patrick Blackburn, Maarten de Rijke, Yde Venema, C. J. van Rijsbergen, S. Abramsky, P. H. Aczel, J. W. de Bakker, Y. Gurevich, J. V. Tucker Average Customer Review: Paperback (15 November, 2002) list price: $60.59 -- our price: $39.97 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (4)
At the time of writing this, I do not know how this book compares to other introductions to the field of Modal Logic. Moreover, as a student of Yde Venema and of Maarten de Rijke (two of the authors), I am perhaps slightly biased. Nevertheless, I would recommend this book to anyone who wants to seriously delve into the world of Modal Logic.
Isbn: 0521527147 |
$39.97 |
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Logic, Semantics, Metamathematics by Alfred Tarski Average Customer Review: Paperback (01 January, 1981) list price: $29.95 -- our price: $29.95 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (1)
Isbn: 091514476X |
$29.95 |
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Non-standard Analysis by Abraham Robinson Paperback (08 January, 1996) list price: $39.95 -- our price: $32.14 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Isbn: 0691044902 |
$32.14 |
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From the bourgeois to the proletarian revolution by Otto Rühle Unknown Binding (1974) US | Canada | United Kingdom | Germany | France Isbn: 095026346X |
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Grundrisse : Foundations of the Critique of Political Economy (Penguin Classics) by KarlMarx, MartinNicolaus Average Customer Review: Paperback (07 November, 1993) list price: $20.00 -- our price: $13.60 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (4)
Also, Grundrisse starts in a different place from Capital.Thereis a reason for this, and a good discussion of this can be found in thewriting of Raya Dunayevskaya and a counter discussion can be found in RomanRosdolsky.The choice to eventually shelve the organization of theGrundrisse for the organization of Capital flows in part from the changesin the intervening years, most notably the U.S. Civil War. Real lifeconstantly shaped Marx's thinking, hardly fitting the representation wecommonly get of him from ideologues and capital's priests (economists).Asa result, Grundrisse also has serious limitations in its understanding ofthe logic of capital.Basing the entire understanding of Marxism andcapital on Grundrisse leads to the kind of mistakes made by ItalianAutononmist Marxism, esp. Antonio Negri, who find themselves engaged in avery subjectivist understanding of capitalism.A useful, but sympathetic,antidote can be found in Werner Bonefeld and John Holloway's writings. ... Read more Isbn: 0140445757 |
$13.60 |
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Sheaves in Geometry and Logic : A First Introduction to Topos Theory (Universitext) by Saunders MacLane, Ieke Moerdijk Average Customer Review: Paperback (27 October, 1994) list price: $69.95 -- our price: $59.83 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (2)
Isbn: 0387977104 |
$59.83 |
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The Limits of Abstraction by Kit Fine Hardcover (01 November, 2002) list price: $35.00 -- our price: $35.00 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Isbn: 0199246181 |
$35.00 |
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Gender Trouble (Tenth Anniversary Edition) by Judith Butler Average Customer Review: Paperback (September, 1999) list price: $22.95 -- our price: $15.61 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Editorial Review In a new introduction to the 10th-anniversary edition of Gender Trouble--among the two or three most influential books (and by far the most popular) in the field of gender studies--Judith Butler explains the complicated critical response to her groundbreaking arguments and the ways her ideas have evolved as a result. Nevertheless, she has resisted the urge to revise what has become a feminist classic (as well as an elegant defense of drag, given Butler's emphasis on the performative nature of gender). The book was produced, according to Butler, "as part of the cultural life of a collective struggle that has had, and will continue to have, some success in increasing the possibilities for a livable life for those who live, or try to live, on the sexual margins." An attack on the essentialism of French feminist theory and its basis in structuralist anthropology, Gender Trouble expands to address the cultural prejudices at play in genetic studies of sex determination, as well as the uses of gender parody, and also provides a critical genealogy of the naturalization of sex. A primer in gender studies--and sexy reading for college cafés. --Regina Marler ... Read more Reviews (21)
Isbn: 0415924995 |
$15.61 |
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Subjects of Desire by Judith Butler Average Customer Review: Paperback (15 June, 1999) list price: $23.00 -- our price: $23.00 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (1)
Isbn: 0231064519 |
$23.00 |
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An Introduction to Substructural Logics by Greg Restall Paperback (February, 2000) list price: $34.95 -- our price: $34.95 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Isbn: 041521534X |
$34.95 |
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A Shorter Model Theory by Wilfrid Hodges Average Customer Review: Paperback (10 April, 1997) list price: $48.00 -- our price: $48.00 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (4)
Personally, I would have liked to see the following topics at leastmentioned: higher-order languages, typed languages, ultraproducts, gametheory. Nevertheless, this book is still the best and clearest textbook formodel theory.
Isbn: 0521587131 |
$48.00 |
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Phenomenology of Spirit (Galaxy Books) by G. W. F. Hegel, A.V. Miller Average Customer Review: Paperback (01 February, 1979) list price: $18.95 -- our price: $12.89 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (34)
Isbn: 0198245971 |
$12.89 |
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Accursed Share, Vol. 1: Consumption by Georges Bataille, Robert Hurley Average Customer Review: Paperback (26 March, 1991) list price: $16.00 -- our price: $10.88 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (2)
Isbn: 0942299116 |
$10.88 |
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Nietzsche: Writings from the Late Notebooks (Cambridge Texts in the History of Philosophy) by Friedrich Nietzsche, Rüdiger Bittner, Karl Ameriks, Desmond M. Clarke, Kate Sturge Average Customer Review: Paperback (20 February, 2003) list price: $18.99 -- our price: $18.99 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (1)
Isbn: 0521008875 |
$18.99 |
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The Order of Things : An Archaeology of Human Sciences by MICHEL FOUCAULT Average Customer Review: Paperback (29 March, 1994) list price: $14.00 -- our price: $11.20 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (11)
This book started its life under the French title "les mots e les choses", things and words. In the introduction Foucault tries to provide the reader with both an explanation and a road map for this archaeological expedition. He explains that this book should be seen as an attempt towards describing the evolution of representation of the world in thoughts/words over the last 5 centuries. Not a small task, and not an easy one for that matter. It is unfortunate that Foucault did not follow the approach that he chose in DP. In that book he chose one central leitmotiv, the spread of discipline from the military throughout an increasingly complex society, and could leave the "main road" at many instances without the risk of the reader getting lost. This book dearly misses such a backbone. Even worse: whenever Foucault seems to suggest one, he willfully/deviously/confusingly immediately takes an unannounced turn. For example in the introduction he goes in detail about the representation of the world in a language of words. O.K. you think, that sets us on a track of a history of the world with Kant at a critical juncture. Yet in the first chapter we suddenly get a cold shower of a completely chaotic and overwrought description of a Velasquez painting, that has been done much better using less than 10% of the number of words, and is at complete odds with the goals set in the introduction. Next Foucault visits Cervantes' masterpiece. He describes Don Q. as representing man before arrival of the stage of distinction between things and their representations. Cute of course, but wasn't Cervantes fictitious book meant as a comedy. On top of that, one cannot help but consider Cervantes own representation of the first part of DQ in the second a much clearer exploration of the subject of representation than Foucault's. However, inspired by Don Q., Mickey F. chooses his own collection of windmills and goes on a quest that has way more in common with a self-gratulatory/-exploratory/-gratifying acid trip, than the archaeological quest that he promised. Purposely mentioning Kant as the gatekeeper between to eras, but wasting disproportionate amounts of words on some often obscure lesser gods, Foucault could not have done a better job in helping a well-intentioned reader to get lost in this onanistic swamp. As such, finishing this book became an increasingly aggravating and futile struggle. In despite of all his cunning and virtuosity, it is just a clear impression of blind vanity that remains. Too bad, Michel. A brain -certainly such a good one, as you had- is a terrible thing to waste. ... Read more Isbn: 0679753354 |
$11.20 |
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Embodiments of Mind by Warren S. McCulloch Paperback (13 May, 1988) list price: $32.95 -- our price: $32.95 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Isbn: 0262631148 |
$32.95 |
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The Metastases of Enjoyment: Six Essays on Woman and Causality (Wo Es War) by Slavoj Zizek Paperback (01 December, 1994) list price: $19.00 -- our price: $19.00 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Isbn: 086091688X |
$19.00 |
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The Essential Average Customer Review: Audio CD (30 June, 1989) list price: $14.98 -- our price: $14.98 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Editorial Review Rhythm and noise duke it out for the listener's attention on Little Richard's classic Specialty records. The future reverend chants and screams his often surreal--they used to call it "nonsensical"--tales of life ("Tutti Frutti"), love ("Jenny Jenny"), and rock ("Ready Teddy") over pounding piano, thumping drums, and one of the greatest horn presences (both ensemble and solo) in the history of 20th-century music. this disc makes his case better than the written word ever could, though. --Rickey Wright ... Read more Reviews (15)
Asin: B000000QL0 |
$14.98 |
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