Argues that Americans must improve their understanding of probability and logic.

This book consists of 220 logic problems on which students can practice their beginner's logic skills. At least one solution is provided for each exercise. The point is to provide a vehicle for practice that will not make additional demands on the instructor's time. In addition, Logic Problems, unlike most other "secondary" texts, does not require the additional purchase of a primary text. It includes sentential and predicate arguments, and employs truth tables, formal proofs, conditional proofs and (...) reductio. Contents: The Apparatus; Sentential Problems; Predicate Problems; Sentential Solutions; Predicate Solutions. (shrink)

The species of metaphysical speculation known as ontology is as old as philosophy itself. It is encountered in one form or another in all climes and times. In Western philosophy, it is already cultivated in a fairly sophisticated form in Parmenides: Being is positive and does not admit to the possibility of negation. Being is a plenum, etc. The problem which exercised the mind of Parmenides has lost something of its vitality in our time but it has recognizably survived in (...) such contemporary questions as “Are there negative facts?” At the present day, however, the liveliest issues of ontology revolve round a topic which has a different, if no less celebrated, ancestry. It is the problem of universals which, much discussed by Plato, was taken up and made a principal concern by the scholastics. It is being canvassed again in recent times under the heading of abstract entities. What I wish to investigate is the connection between the metaphysics of abstract entities and the discipline of logic as developed in the modern era. (shrink)

In this concise text, Roy Bhaskar sets out to diagnose, explain and resolve the "problems of philosophy". _Plato Etc._ reviews all the main areas of the subject: the theory of knowledge and philosophy of science; the philosophy of logic and language; the philosophies of space, time and causality; the philosophy of the social and life sciences and of dialectic; ethics, politics and aesthetics; and the history and sociology of philosophy. Among the issues discussed are the problems of induction (...) and universals, the question of relativism, Heidegger’s "scandal of philosophy", the nature of moral truth and the conundrum of free will and determinism. The last two chapters consist of a synoptic account of the development of Western philosophy from the pre-Socratics to poststructuralism. _Plato Etc._ seeks to revindicate the philosophical project, and to demonstrate that the author’s "dialectical critical realism" has the categorical power to remedy the problem fields of philosophy. The book serves both as a critical introduction to philosophy and as an invaluable resource for the scholar. (shrink)

What is mathematics; Symbolic logic; A reviw of number and notation; Further review topics; Introduction to proofs; Direct proof I; Direct Proog II; Indirect proof; Analogy abnd geometric proof.

In addition to a somewhat detailed exposition of certain portions of what may be called the book-work of formal logic, the following pages contain a number of problems worked out in detail and unsolved problems, by means of which the student may test his command over logical processes. In the expository portions of Parts I, II, and III, dealing respectively with terms, propositions, and syllogisms, the traditional lines are in the main followed, though with certain modifications; e.g., in the (...) systematisation of immediate inferences, and in several points of detail in connexion with the syllogism. For purposes of illustration Euler's diagrams are employed to a greater extent than is usual in English manuals. In Part IV, which contains a generalisation of logical processes in their application to complex inferences, a somewhat new departure is taken. So far as I am aware this part constitutes the first systematic attempt that has been made to deal with formal reasonings of the most complicated character without the aid of mathematical or other symbols of operation, and without abandoning the ordinary non-equational or predicative form of proposition. This attempt has on the whole met with greater success than I had anticipated; and I believe that the methods formulated will be found to be both as easy and as effective as the symbolical methods of Boole and his followers. The book concludes with a general and sure method of solution of what Professor Jevons called the inverse problem, and which he himself seemed to regard as soluble only by a series of guesses. (shrink)

It is a paradox, whose importance familiarity fails to diminish, that the most highly developed and useful scientific theories are ostensibly expressed in terms of objects never encountered in experience. The line traced by a draughtsman, no matter how accurate, is seen beneath the microscope as a kind of corrugated trench, far removed from the ideal line of pure geometry. And the “point-planet” of astronomy, the “perfect gas” of thermodynamics, or the “pure species” of genetics are equally remote from exact (...) realization. Indeed the unintelligibility at the atomic or sub-atomic level of the notion of a rigidly demarcated boundary shows that such objects not merely are not but could not be encountered. While the mathematician constructs a theory in terms of “perfect” objects, the experimental scientist observes objects of which the properties demanded by theory are and can, in the very nature of measurement, be only approximately true. As Duhem remarks, mathematical deduction is not useful to the physicist if interpreted rigorously. It is necessary to know that its validity is unaltered when the premise and conclusion are only “approximately true.” But the indeterminacy thus introduced, it is necessary to add in criticism, will invalidate the deduction unless the permissible limits of variation are specified. To do so, however, replaces the original mathematical deduction by a more complicated mathematical theory in respect of whose interpretation the same problem arises, and whose exact nature is in any case unknown. (shrink)

It is shown that the logical theory of belief statements must be prepared to take into account relationships among statements which are subtler and more delicate than is requisite in other contexts. It is necessary here to draw distinctions (of a modal and semantical character) which the standard assertory logic can ignore with impunity. This is due to the fact that it is entirely possible to be in ignorance of various logical relationships (eg., entailment, equivalence, etc.) that in fact (...) obtain among believed statements, and so, for example to believe the premisses of a valid deductive argument, and yet disbelieve the conclusion which follows from them. The implications of such difficulties for the logic of belief statements are examined. (shrink)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

A philosophical argument in ordinary language is made the basis for a series of deductive logic exercises. Problems of translating the reasoning and alternative symbolizations are discussed to help guide students toward accurate charitable formalizations. Finally, the inference is critically evaluated in light of its deductive validity.

Logical Forms explains both the detailed problems involved in finding logical forms and also the theoretical underpinnings of philosophical logic. In this revised edition, exercises are integrated throughout the book. The result is a genuinely interactive introduction which engages the reader in developing the argument. Each chapter concludes with updated notes to guide further reading.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators. It starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantic and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. (...) A specialist can use the book as a source of references. Results and methods of many directions in propositional modal logic, from completeness and duality to algorithmic problems, are collected and systematically presented in one volume. (shrink)

One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers (...) explore the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information. (shrink)

This book is intended to serve as an advanced text and reference work on modal logic, a subject of growing importance which has applications to philosophy and linguistics. Although it is based mainly on research which I carried out during the years 1969-1973, it also includes some related results obtained by other workers in the field. Parts 0, 1 and 2, can be used as the basis of a one year graduate course in modal logic. The material which (...) they contain has been taught in such courses at Stanford since 1970. The remaining parts of the book contain more than enough material for a second course in modal logic. The exercises supplement the text and are usually difficult. I wish to thank Stanford University and Bar-Han University for making it possible for me to continue and finish this work, and A. Ungar for correcting the typescript. Bar-Ilan University, Israel Dov M. GABBA Y PART 0 AN INTRODUCTION TO GENERAL INTENSIONAL LOGICS CHAPTER 0 CONSEQUENCE RELATIONS Motivation We introduce the notions of a consequence relation and of a semantics. We show that every consequence relation is complete for a canonical semantics. We define the notion of one semantics being Dian in another and study the basic properties of this notion. The concepts of this chapter are generalizations of the various notions of logical system and possible world semantics found in the literature. (shrink)

Featuring an exceptionally clear writing style and a wealth of real-world examples and exercises, Logic, Second Edition, shows how logic relates to everyday life, demonstrating its applications in such areas as the workplace, media and entertainment, politics, science and technology, student life, and elsewhere.Thoroughly revised and expanded in this second edition, the text now features 2600 exercises, more than 1000 of them new; three new chapters on legal arguments, moral arguments, and analyzing a long essay; enhanced pedagogy; and (...) much more.FEATURES* 2600 exercises--more than 1000 of them new--breathe new life into logic* Real-world examples help bring logic down to earth for students* A unique, extended explanation or model of the answer to the first question of each "Check Your Understanding" section shows students what is expected of their answers* An additional 25% of the exercises are answered at the back of the book* "Profiles in Logic" provide short sketches of logicians, philosophers, mathematicians, and others associated with logic* "Logic Challenge" problems present puzzles and paradoxes that end each chapter on a fun note* Additional pedagogical elements--marginal definitions, key terms, a glossary, reference boxes, and bulleted chapter summaries--make the material even more accessible* Detailed guides help students learn to create "truth tables" and Venn diagramsSUPPORT PACKAGEAn Instructor's Manual with Computerized Test Bank on CD includes: Solutions to all exercises in the book, enhanced by explanations and answers that elucidate the details of the correct answersKey Terms and a summary for each chapterA customizable Computerized Test Bank--with multiple-choice, true/false, and fill-in-the-blank questions--that allows instructors to give exams or homework problems that can be auto-gradedA traditional "pencil-and-paper" Test Bank and answer key containing the same questions as the Computerized Test BankPowerPoint-based lecture outlinesThe Instructor's Manual with Computerized Test Bank and the traditional Test Bank are also available in printed format.A Companion Website offers:Instructor Resources :A downloadable version of the Instructor's Manual PowerPoint-based lecture outlinesStudent Resources:Brief chapter summariesInteractive Flash Cards with key terms and definitionsWeb links and other media resourcesPractice quizzes with answers and explanations The Learning Management System Cartridges include, in a fully downloadable format:Instructor's Manual and Computerized Test Bank Student material from the companion websiteThe Perfect Text for Your Course... No Matter How You Teach ItYour course is unique; you have your own teaching philosophy and style. Whether you teach traditional Introduction to Logic, Critical Thinking/Informal Logic, or Formal Logic, Baronett: Logic, Second Edition, can be tailored to fulfill your course needs.We'll make it easy for you; choose one of our Alternate Editions or build the book you want, chapter by chapter.Option 1. Author Stan Baronett has suggested four Alternate Editions that may work for you. Each Alternate Edition comes in full color, with answers to problems, a full glossary, and an index. The books are in stock and available for ordering. Please see the ISBN information below.Logic: Concise EditionChapters 1, 3, 4, 5, 6, 7, 8Order using ISBN: 978-0-19-994129-2Logic: An Emphasis on Critical Thinking and Informal LogicChapters 1, 2, 3, 4, 10, 11, 12, 13 A-E, 14, 15Order using ISBN: 978-0-19-994128-5Logic: An Emphasis on Formal LogicChapters 1, 5, 6, 7, 8, 9Order using ISBN: 978-0-19-994126-1Logic: With Diagramming used in Chapter 4. Informal FallaciesFull textOrder using ISBN: 978-0-19-997081-0Option 2. Create your own customized textbook by choosing the specific chapters that you need for your course. Please contact your Oxford University Press Sales Representative or call 800.280.0280 for details. (shrink)

Epistemic logic has grown from its philosophical beginnings to find diverse applications in computer science, and as a means of reasoning about the knowledge and belief of agents. This book provides a broad introduction to the subject, along with many exercises and their solutions. The authors begin by presenting the necessary apparatus from mathematics and logic, including Kripke semantics and the well-known modal logics K, T, S4 and S5. Then they turn to applications in the context of distributed (...) systems and artificial intelligence. These include the notions of common knowledge, distributed knowledge, explicit and implicit belief, the interplays between knowledge and time, and knowledge and action, as well as a graded (or numerical) variant of the epistemic operators. The authors also discuss extensively the problem of logical omniscience. They cover Halpern & Moses' theory of honest formulas, and they make a digression into the realm of nonmonotonic reasoning and preferential entailment. They discuss Moore's autoepistemic logic, together with Levesque's related logic of "all I know". Furthermore, they show how one can base default and counterfactual reasoning on epistemic logic. Graduate students in philosophy or in computer science, especially those with an interest in AI, will find this book useful. (shrink)

This is a contribution to construction of a research roadmap for future cognitive systems, including intelligent robots, in the context of the euCognition network, and UKCRC Grand Challenge 5: Architecture of Brain and Mind. -/- A meeting on the euCognition roadmap project was held at Munich Airport on 11th Jan 2007. This document was in part a response to discussions at that meeting. An explanation of why specifying requirements is a hard problem, and why it needs to be done, along (...) with some suggestions for making progress, can be found in this presentation: http://www.cs.bham.ac.uk/research/projects/cosy/papers/#pr0701 "What's a Research Roadmap For? Why do we need one? How can we produce one?" Working on that presentation made me realise that certain deceptively familiar words and phrases frequently used in this context (e.g. "robust". "flexible", "autonomous") appear not to need explanation because everyone understands them, whereas in fact they have obscure semantics that needs to be elucidated. Only then can we understand what the implications are for research targets. In particular, they need explanation and analysis if they are to be used to specify requirements and research goals, especially for publicly funded projects. -/- First draft analyses are presented here. In the long term I would like to expand and clarify those analyses, and to provide many different examples to illustrate the points made. This will probably have to be a collaborative research activity. (shrink)

The field of modern logic is too extensive to be worked through by open cast mining. To open it up, we need to sink shafts and construct adits. This is the method of most text books: a systematic exposition of a number of main topics, supplemented by exercises to teach skill in the appurtenant techniques, lays a secure foundation for subsequent dis cussion of selected questions. Compared with this, the present treatment is more like a network of exploratory drillings (...) to show that it would be worthwhile to start mining operations, or to work the existing shafts and adits, as the case may be. Within this metaphor we may also describe the inherent weakness of this conception: once a cavity is pierced, the duct's capacity will in general not be sufficient to carry away the discovered riches. But whether we are concerned with a new or an already worked mine - at any rate, the experience should stimulate us into either reviving an existing system of shafts or even, in particularly fortunate cases, designing a new ap proach. (shrink)

Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses 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. (...) The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems. (shrink)

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ (...) iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, (...) and they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

Logical Forms explains both the detailed problems involved in finding logical forms and also the theoretical underpinnings of philosophical logic. In this revised edition, exercises are integrated throughout the book. The result is a genuinely interactive introduction which engages the reader in developing the argument. Each chapter concludes with updated notes to guide further reading.

It seems to be a humdrum fact of human agency that we act on intentions or decisions that we have made at an earlier time. At breakfast, you look at the Taco Hut menu online and decide that later today you’ll have one of their avocado burritos for lunch. You’re at your desk and you hear the church bells ring the noon hour. You get up, walk to Taco Hut, and order the burrito as planned. As mundane as this sort (...) of scenario might seem to be, philosophers have raised a problem in understanding it. If you are simply abiding by this morning’s decision, how are you acting autonomously? Your earlier self seems to be calling the shots; if you are just acting accordingly, without thinking through it or in some other way trying to ensure that the past decision conforms to your present standpoint, it is not clear how this amounts to an exercise of your present autonomous agency. It seems, rather, that your earlier self has succeeded in slaving you to her own purposes. She was the one who wanted (intended, judged it to be good, etc.) to have an avocado burrito. In simply following through, your current self seems to be just an automaton performing the commands left behind by your former self. Of course, you might not allow yourself to be shackled by your earlier self. You might refuse to follow anything but your own present judgments: you will only go to Taco Hut if this is what you judge you should do right now, and once at Taco Hut you will only eat the avocado burrito if that is what you want to eat once there. But if this is the way you generally operate, this seems to block your ability to make effective future-directed decisions. The puzzle, then, is one of explaining how the future self can do the bidding of her past self without losing her autonomy. We call this “the Problem of Diachronic Autonomy.” Philosophers raising this problem take it to show that there must be reasons or rational requirements to follow-through with our past decisions. According to these philosophers, we can only make sense of our diachronic autonomy if our past decisions put rational pressure on us to follow through. We argue that there is no Problem of Diachronic Autonomy. There is, in other words, no puzzling situation that needs explaining. Consequently, there is no need coming from this purported puzzle to think that our future-directed decisions generate reasons or rational requirements to follow through. The correct view of our diachronic autonomy is the “naïve” one: the “future self” can do the bidding of the “past self” without giving up its autonomy because, very simply, the past self is the same agent as the future self. I am acting autonomously when I get the avocado burrito, because I was the one who decided to get the burrito. I am acting on my own freely-formed decision. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Readymades, Monochromes, Etc.:Nominalism and the Paradox of ModernismJ. M. Bernstein (bio)If Schopenhauer's thesis of art as an image of the world once over bears a kernel of truth, then it does so only insofar as this second world is composed out of elements that have been transposed out of the empirical world in accord with Jewish descriptions of the messianic order as an order just like the habitual order (...) but changed in the slightest degree.—T. W. Adorno, Aesthetic TheoryAdorno's philosophy as a whole, and his aesthetic theory in particular, is irrevocably bound to the tradition and achievements of high modernism. Although Adorno himself did not recognize American Abstract Expression as the apotheosis of high modernism in painting, that judgment now hardly seems contentious.1 And that raises a problem: it is the problem of R. Mutt, again, the problem of the porcelain urinal called Fountain, which was refused admittance to the Society of Independent Artists' Exhibition in April 1917 in spite of the Society's proclaimed democratic slogan "No jury, no prizes"—the work whose life or after-life begins with the beautiful photograph of it by Stieglitz set against the background of Marsden Hartley's The Warriors and that appeared shortly thereafter in the new avant-garde journal The Blind Man. Whatever the immediate repercussions of Fountain, there can be little doubt that much of what is most vital in art in the second half of this century is unthinkable without it; Duchamp's readymade offers an exemplary alternative to the tradition of high modernist painting that has continued to be generative. For a modernist like Adorno, for whom authentic art is that which best rises to the demands and necessities of artistic materials, for whom internal consistency and rigor would appear to be everything, for whom, finally, aesthetic form is the "objective organization within each artwork of what appears as bindingly eloquent" [AT 143; emphasis mine], Duchamp's gesture of simply naming or claiming artistic status for an ordinary bathroom fixture must be anathema. In this respect, Adorno's aesthetic theory would seem to be in the same predicament as Clement Greenberg's modernism: inextricably bound to a tradition that history has left behind. And while the option of refuting the claim of Fountain is certainly possible, and should not be too quickly suppressed (there is something in the claim that will forever be skeptically self-defeating), nonetheless there does appear to be an exemplariness to Fountain that exceeds the narrow provocation of Duchamp's nominalist gesture; something in the readymade, in fact, seems (art historically? aesthetically? conceptually?) irresistible. If so, then modernist [End Page 83] formalism must either find a way of accommodating the readymade without departing from its internal logic or find its claim to our attention forfeited.After laying out the bold outlines of Adorno's formalism, the remainder of this essay will seek to uncover an account of the readymade in the context of what I will eventually call "the paradox of modernism" in order to locate in what way the readymade can be accommodated to a defense of Adorno's late modernism. For the purposes of this argument, I am going to assume that the best overall defense of Duchamp's gesture, which makes it foundational for the understanding of modern art, is that offered by Thierry de Duve in his Kant after Duchamp. My elaboration of Adorno's late modernism will hence proceed, in part, through a charting of some of the fault lines in de Duve's Duchamp. My contention shall be that the generativity of Fountain as readymade not only belongs within modernism, but is only intelligible within a wholly modernist and formalist frame of reference.Adorno's Formalism and the Material MotiveAdorno opens the section of Aesthetic Theory entitled "Coherence and Meaning" with the drastic sounding thesis that "Although artworks are neither conceptual nor judgmental, they are logical" [AT 136]. He continues:In them nothing would be enigmatic if their immanent logicality did not accommodate discursive thought, which criteria they nevertheless regularly disappoint. They most resemble the form of a syllogism and its prototype in empirical thought. That in the temporal... (shrink)

A comprehensive introduction to formal logic, Logic and Philosophy: A Modern Introduction is a rigorous yet accessible text, appropriate for students encountering the subject for the first time. Abundant, carefully crafted exercise sets accompanied by a clear, engaging exposition build to an exploration of sentential logic, first-order predicate logic, the theory of descriptions, identity, relations, set theory, modal logic, and Aristotelian logic. And as its title suggests, Logic and Philosophy is devoted not only (...) to logic but also to the philosophical debates that led to the development of the field. Much new material has been added for the 13th edition. An introduction to set theory and its relationship to logic and mathematics, including philosophical issues, is now part of Chapter 13. Chapter 15 is an introduction to modal logic and Kripke semantics, concluding with a discussion of philosophical problems with any logical accommodation of modalities. Instructors who do not wish to present proof methods will find chapters on truth trees for both sentential and first-order logic, and a presentation of trees for modal logic. Special features of this text include presentations of the history of logic, alternatives to traditional methods of conditional and indirect proof, and a discussion of semantic problems with universal and existential instantiations. Throughout, the authors are sensitive to philosophical issues that arise from the relationship between ordinary language, symbolic logic, and justifications for the syntax and semantics of the various symbolic languages. Discussions range from the justification of the truth table for the sentential rendering of if... then statements to semantic and syntactic paradoxes, including some troubling paradoxes that arise in ordinary language (e.g., the so-called hangman or surprise quiz paradox). Logic and Philosophy includes ample material for a one-semester or two-semester course and provides a thorough preparation for more advanced logic courses. (shrink)

Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study (...) the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery. We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics. The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources. The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well. Key Features: Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science Written by internationally leading researchers in the field of pure and applied logic Combines mathematical theory of modal logic and applications in artificial intelligence and computer science Numerous open problems for further research Well illustrated with pictures and tables. (shrink)

Classical logic yields counterintuitive results for numerous propositional argument forms. The usual alternatives (modal logic, relevance logic, etc.) generate counterintuitive results of their own. The counterintuitive results create problems—especially pedagogical problems—for informal logicians who wish to use formal logic to analyze ordinary argumentation. This paper presents a system, PL– (propositional logic minus the funny business), based on the idea that paradigmatic valid argument forms arise from justificatory or explanatory discourse. PL– avoids the pedagogical difficulties without (...) sacrificing insight into argument. (shrink)

An entertaining series of logic problems and puzzles of increasing difficulty, and all relating important mathematical and logical concepts, includes mind-benders, paradoxes, metapuzzles, number exercises, and a mathematical novel.

Experience in thesis and peer reviewing revealed that most authors have much difficulty in presenting the structural supports of their study. This becomes evident in both their oral and written scientific reports in which little congruency or lack of it is frequently observed between title of the study, general objective (aim), and the hypothesis. Likewise, confusion is usually present when distinguishing purpose from objective when presenting the research problem. In order to aid in approaching the mentioned difficulties an exercise termed (...) Trivium is proposed and explained. This term that designated the main subjects in scholar formation during medieval times, is used to designate the effective coupling of the above three structural elements (title, objective, hypothesis) that, properly used, confer epistemological basis to their scientific reports. Likewise, in order to reinforce this exercise a Quadrivium is recommended in which a fourth structural element is added, i.e., a premise, as the theoretical basis that precisely indicates the purpose of the study and provides immediate support to the hypothesis. Examples to illustrate these exercises are provided. Abiding by this logic may significantly aid science students and some open-minded researchers in adequately constructing their scientific reports, while avoiding frustrating experiences due to uncomfortable observations by peers on their manuscripts. (shrink)

How Logic Works is an introductory logic textbook that is different by design. Rather than teaching elementary symbolic logic as an abstract or rote mathematical exercise divorced from ordinary thinking, Hans Halvorson presents it as the skill of clear and rigorous reasoning, which is essential in all fields and walks of life, from the sciences to the humanities—anywhere that making good arguments, and spotting bad ones, is critical to success. Instead of teaching how to apply algorithms using (...) “truth trees,” as in the vast majority of logic textbooks, How Logic Works builds on and reinforces the innate human skills of making and evaluating arguments. It does this by introducing the methods of natural deduction, an approach that teaches students not only how to carry out a proof and solve a problem but also what the principles of valid reasoning are and how they can be applied to any subject. The book also allows students to transition smoothly to more advanced topics in logic by teaching them general techniques that apply to more complicated scenarios, such as how to formulate theories about specific subject matter. How Logic Works shows that formal logic—far from being only for mathematicians or a diversion from the really deep questions of philosophy and human life—is the best account we have of what it means to be rational. By teaching logic in a way that makes students aware of how they already use it, the book will help them to become even better thinkers. A concise, readable, and user-friendly introduction to elementary symbolic logic that primarily uses natural deduction rather than algorithmic “truth trees” Draws on more than two decades’ experience teaching introductory logic to undergraduates Provides a stepping stone to more advanced topics. (shrink)

Many texts on logic are written with a mathematical emphasis, and focus primarily on the development of a formal apparatus and associated techniques. In other, more philosophical texts, the topic is often presented as an indulgent collection of musings on issues for which technical solutions have long since been devised. What has been missing until now is an attempt to unite the motives underlying both approaches. Paul Hoyningen-Huene’s Formal Logic seeks to find a balance between the necessity of (...) formal considerations and the importance of full reflection and explanation about the seemingly arbitrary steps that occasionally confound even the most serious student of logic. Alex Levine’s artful translation conveys both the content and style of the German edition. Filled with examples, exercises, and a straightforward look at some of the most common problems in teaching the subject, this work is eminently suitable for the classroom. (shrink)

Applied Logic presents logic as a relevant tool for interpreting arguments, not simply as an abstract discipline such as mathematics or physics. Through English-language arguments that are debated today—health care, economic problems, AIDS, and so on—the author strives to give students an appreciation of logic's applicability. An appendix provides answers to selected exercises. Applied Logic and the Instructor's Manual will be of great value to those teaching elementary logic.