An introductory logic textbook where the central concept is not deduction but search and logical form. (Deduction - logical consequence - drops out as a special case. TIt is meant for a class-based rather than a lecture-based course, and for students with general interests.

I here defend logical atomism. This defense rests on reinterpreting logical atomism as a search for logical forms. This reinterpretation has two parts comprising six chapters. In the first part, I do some historically-driven recovery. In the introduction, I review the literature on Russell's logical atomism. In Chapter 1, I argue that the dominant interpretation of logical atomism is wrong on historical grounds: it accounts for neither the history of logical atomism nor for crucial (...) elements of the logical atomist texts. In Chapter 2, I then use Russell's writings to recover what I argue is the core of logical atomism. I explicate the critical notions and essential ingredients of logical atomism using "Principia Mathematica" as the archetype of logical atomism. I argue that logical atomsts are term busters. The essential ingredient of a logical atomist's term busting practice is a higher-order logic with the power of impredicative comprehension. In Chapter 3, I discuss the widespread view that Wittgenstein held a version of logical atomism. Focusing on his pre-"Tractatus" writings and changes in his earlier views, I argue that Wittgenstein embraced a philosophy of logic incompatible with emulating impredicative comprehension in April 1914. As such, Wittgenstein was a logical atomist, if ever, in October 1913, possibly through April 1914. In the second part, having clarified what logical atomism is, I present a modern logical atomism. In Chapter 4, I develop a philosophy of logic for logical atomism based on the notion of a pure logic. I critically discuss normativity in logic, the epistemology of pure logic, and logical pluralism. In Chapter 5, I propose a formal logic for logical atomism. I argue for the logic of logical atomism being an infinitely-descending and infinitely-ascending simple type theory with impredicative comprehension compatible with a domain empty of particulars. In Chapter 6, I critically discuss what the ontology of logical atomism should be, that is, what the ontology of the logical atomist's logic must be. This includes an ontology of logical concepts and of logical forms as completely-general, necessarily-existing logical facts with no constituents. I conclude by indicating avenues for new work on logical atomism. (shrink)

Derek Turner, Professor of Philosophy, has written an introductory logic textbook that students at Connecticut College, or anywhere, can access for free. The book differs from other standard logic textbooks in its reliance on fun, low-stakes examples involving dinosaurs, a dog and his friends, etc. This work is published in 2020 under a Creative Commons AttributionNonCommercial-NoDerivatives 4.0 International License. You may share this text in any format or medium. You may not use it for commercial purposes. If you share it, (...) you must give appropriate credit. If you remix, transform, add to, or modify the text in any way, you may not then redistribute the modified text. (shrink)

ADVANGEBOOKS - UNDERSTANDING ARGUMENTS: AN INTRODUCTION TO INFORMAL LOGIC, 9E shows readers how to construct arguments in everyday life, using everyday language. In addition, this easy-to-read textbook also devotes three chapters to the formal aspects of logic including forms of argument, as well as propositional, categorical, and quantificational logic. Plus, this edition helps readers apply informal logic to legal, moral, scientific, religious, and philosophical scenarios, too. Important Notice: Media content referenced within the product description or the product text may not (...) be available in the ebook version. (shrink)

Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In addition, this is the only introduction to logic available today that presents (...) all the major forms of proof--trees, natural deduction in all its major variants, axiomatic proofs, and sequent calculus. The book also features numerous exercises, with solutions available on an accompanying website. -/- Logic is the ideal textbook for undergraduates and graduate students seeking a comprehensive and accessible introduction to the subject. -/- Provides an essential introduction to classical logic Emphasizes the how and why of logic Covers both formal and philosophical issues Presents all the major forms of proof--from trees to sequent calculus Features numerous exercises, with solutions available online The ideal textbook for undergraduates and graduate students . (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.

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.

The "textbook explosion" in recent years in the field of logic has frequently been deplored on the grounds that it has resulted in a proliferation of repetitious and sometimes antiquated material. A sober evaluation of this volume, unfortunately, supports this thesis. Despite the subtitle, the bulk of the material in this book wasn't "modern" two centuries ago. Why should 196 pages of a 355 page text be devoted to such topics as "Logic and Psychology," "Types of Statements in Logical (...) English," "The Syllogism," "Translation into Logical English," and "Informal Fallacies"? Philosophic issues are often obscured by the unmanageable clutter of syllogistic form, squares of opposition, sorites, and other baggage. Moreover, why should an entire appendix be devoted to a "block diagram" of a machine which computes the logical relationship between any two sentences? Especially when it is known that no such machine is possible. There is material of genuine philosophical interest in this book and there is a rather desultory treatment of elementary symbolic logic by means of a confused set of natural deduction rules.—H. P. K. (shrink)

This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Part I, Logic Sets, and Numbers, shows how mathematical logic is used (...) to develop the number structures of classical mathematics. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of (...) Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (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.

The notion of logical form and its applications are at the heart of some of the classical problems in philosophical logic and are the focus of Peter Long’s investigations in the three essays that comprise this volume. In the first, major, essay the concern is with the notion of logical form as it applies to arguments involving hypotethical statements, for example ‘If today is Wednesday then tomorrow is Thursday; today is Wednesday: therefore tomorrow is Thursday.’ Whilst (...) such an argument is cited by logical textbooks as a paradigm of one that is ‘formally valid’, it is not hard to show that the conjunction forming a hypothetical statement is not a logical constant, in which case the argument form If p then q; p: therefore q is not a logical form. But, then, how can logic claim to be the science of formal inference? The author resolves this difficulty by drawing a fundamental distinction within the notion of the form under which an argument is valid. With this distinction it becomes possible for the first time to determine the status of any formally valid argument involving hypotheticals, whether as premises or conclusion or both. The second and third essays take up the notion of logical form as it applies to such simple propositions as ‘This sheet is white’ and ‘London is north of Paris.’ When we speak of the first as giving expression to the relation of relations’s relating to its terms, what is in question is a formal relation and we call it such because the relation is expressed through these propositions having the respective forms Fa and Fab. It is shown that the confusion of formal relations with relations proper explains the assimilation of facts to complexes and is that the root of the theory of universals. _Peter Long_ has taught at the University of Leeds and University College London, and is a past Fellow of Trinity College, Cambridge. (shrink)

On Friday the 1st and Saturday the 2nd of December 1995, the Sonderforschungsbereich 340 held a workshop entitled Syntax and Semantics of Partial Wh-Movement. This volume contains most of the papers presented there.1 One of the leading ideas underlying the workshop was that detailed investigation of the partial wh-movement construction provides an excellent test ground for checking assumptions about the syntax/semantics interface.

Two arguments favoring propositionalist accounts of attitude sentences are being revisited: the Church-Langford translation argument and Thomason's argument against quotational theories of indirect discourse. None of them proves to be decisive, thus leaving the option of searching for a developed quotational alternative. Such an alternative is found in an interpreted logical form theory of attitude ascription. The theory differentiates elegantly among different attitudes but it fails to account for logical dependencies among them. It is argued, however, that (...) the concept of logical consequence does not well apply to dependencies among belief sentences and that the requirement to account for logical relations among such sentences should be relaxed. (shrink)

Introduction 1.1 GOALS This book is devoted to an in-depth investigation of some of the properties of Logical Form (LF). In particular, the primary aim of ...

In §12 of his 1837 magnum opus, the Wissenschaftslehre, Bolzano remarks that “In the new logic textbooks one reads almost constantly that ‘in logic one must consider not the material of thought but the mere form of thought, for which reason logic deserves the title of a purely formal science’” (WL §12, 46).1 The sentence Bolzano quotes is his own summary of others’ philosophical views; he goes on to cite Jakob, Hoffbauer, Metz, and Krug as examples of thinkers who (...) held that logic abstracts from the matter of thought and considers only its form. Although Bolzano does not mention Kant by name here, Kant does of course hold that “pure general logic”, what Bolzano would consider logic in the traditional sense (the theory of propositions, representations, inferences, etc.), is formal. As Kant remarks in the Introduction to the 2nd edition of Kritik der reinen Vernunft , (pure general) logic is “justified in abstracting – is indeed obliged to abstract – from all objects of cognition and all of their differences; and in logic, therefore, the understanding has to do with nothing further than itself and its own form” (KrV, Bix).2. (shrink)

IntroductionA quick glance at the opening paragraphs in many of the classic logic textbooks reveals a common view: Logical methods highlight the reasoning patterns of a single agent engaged in some form of mathematical thinking.A sampling from my bookshelf: Shoenfield’s Mathematical Logic: “Logic is the study of reasoning; and mathematical logic is the study of the type of reasoning done by mathematicians”; Enderton’s A Mathematical Introduction of Logic: “Symbolic logic is a mathematical model of deductive thought”; and Chiswell (...) and Hodges Mathematical Logic: “In this course we shall study some ways of proving statements.” However, this traditional view of the “subject matter” of logic is expanding. There is a growing literature using phrases such as “rational interaction” or “information flow” to describe its subject matter while still employing traditional logical methods. The clearest example of this can be found in the work of Johan van Benthem and others on l .. (shrink)

The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems. The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, (...) and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory. It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions. (shrink)

Logical form and logical analysis as the search for it have been introduced during the development of logic and analytical philosophy and are still widely considered as key tools or methods for the solution of philosophical puzzles. It is instructive to have a look at a criticism of these presupositions and I present Wittgenstein as the author who provides such a criticism. I present a development of his view of logical form which went from the (...) thesis of the ineffability of logical form to the denial of the meaningfulness of the notion of logical form as such. This refusal is linked to Wittgenstein’s abandonment of the idea of the language of pure experience. The method of philosophical therapies is presented as an alternative to logical analysis and this methodology is linked with Wittgenstein’s consideration of game and family resemblance. (shrink)

Robyn Carston and I share a general methodological position which I call ‘Truth-Conditional Pragmatics' (TCP). TCP is the view that the effects of context on truth-conditional content need not be traceable to the linguistic material in the uttered sentence. Some effects of context on truth-conditional content are due to the linguistic material (e.g. to context-sensitive words or morphemes which trigger the search for contextual values), but others result from ‘free' pragmatic processes. Free pragmatic processes take place not because the linguistic (...) material demands it, but because the utterance's content is not faithfully or wholly encoded in the uttered sentence, whose meaning requires adjustment or elaboration in order to determine an admissible content for the speaker's utterance. To make room for these processes, I will argue, we need to distinguish the logical form of an utterance, in the standard sense, and its modified logical form, affected by free pragmatic processes. This distinction will be elaborated and I will show that it can be interpreted in three different ways. (shrink)

The concept of legal gap is tackled from a number of logical perspectives and semantic methods. After presenting our own goal (Section 1), a first introduction into legal logic refers to Bobbio’s works and his formalization of legal statements (Sections 2 and 3). Then Woleński’s contribution to the area is taken into account through his reference to the distinction between two juridical systems (viz. Common Law vs Civil Law) and the notion of conditional norms (Section 4). The notion of (...) reason is also highlighted in the case of Raz’s legal logic, thereby leading to a future connection with von Wright’s logic of truth and an analogy made with an anti-realist reading of truth-values and norms (Section 5). Our personal contribution is introduced through a reflection on how logic should deal with the logical form of norms (Section 6), before entering a number of crucial definitions and distinctions for the concepts of norm, legal statement, and promulgation (Section 7). The final point is a proposed semantics for legal statements, which is both many-valued and gap-friendly (Section 8). A distinction between a number of requirements for permission and forbiddance leads to a set of non-classical juridical systems in which non-permission and forbiddance are not equivalent with each other any more; this does justice to Woleński’s former distinction between Common Law and Civil Law, also leading ultimately to a non-classical square of legal oppositions in which several legal operators may collapse into other ones (Section 9). (shrink)

Although conceived as a textbook, this extraordinary work contains a great deal of material which is either completely new or which has not appeared before in book form. It is intended as an upperlevel text for those with some familiarity with the subject already. After the introduction, there is a long chapter on formal systems which contains new material on algorithms and the theory of definition; epitheory of formal systems is then discussed, followed by an elegant algebraic treatment of (...) logic. Curry then formulates systems for negation and implication in the next two chapters, follows them by quantification theory, and ends with a sketch of modal logic. What distinguishes this from other logic texts which try to cover about the same ground is this: Curry exercises virtually exquisite care in his analysis of some of the more difficult points, variables and substitution, for example, that others often tend to gloss over. Each chapter has a section dealing with supplementary but related topics so as to give the reader some idea where the subject goes. There is an enormous bibliography and hundreds of references, including historical ones; these also increase its scholarly value. The author takes an informal semantical viewpoint about logic—trying to treat meaning as well as form as essential to logic. This view and a pellucid style make things move freely in the most difficult spots; only Curry's occasionally peculiar terminology might be confusing.—P. J. M. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. We study a new class of NP search problems, those which can be proved total using standard combinatorial reasoning based on approximate counting. Our model for this kind of reasoning is the bounded arithmetic theory [math] of [E. Jeřábek, Approximate counting by hashing in bounded arithmetic, J. Symb. Log. 74(3) (2009) 829–860]. In particular, the Ramsey and weak pigeonhole search problems lie in the new class. We give a purely computational (...) characterization of this class and show that, relative to an oracle, it does not contain the problem CPLS, a strengthening of PLS. As CPLS is provably total in the theory [math], this shows that [math] does not prove every [math] sentence which is provable in bounded arithmetic. This answers the question posed in [S. Buss, L. A. Kołodziejczyk and N. Thapen, Fragments of approximate counting, J. Symb. Log. 79(2) (2014) 496–525] and represents some progress in the program of separating the levels of the bounded arithmetic hierarchy by low-complexity sentences. Our main technical tool is an extension of the “fixing lemma” from [P. Pudlák and N. Thapen, Random resolution refutations, Comput. Complexity, 28(2) (2019) 185–239], a form of switching lemma, which we use to show that a random partial oracle from a certain distribution will, with high probability, determine an entire computation of a [math] oracle machine. The introduction to the paper is intended to make the statements and context of the results accessible to someone unfamiliar with NP search problems or with bounded arithmetic. (shrink)

The topics of structural proof theory and logic programming have influenced each other for more than three decades. Proof theory has contributed the notion of sequent calculus, linear logic, and higher-order quantification. Logic programming has introduced new normal forms of proofs and forced the examination of logic-based approaches to the treatment of bindings. As a result, proof theory has responded by developing an approach to proof search based on focused proof systems in which introduction rules are organized into two alternating (...) phases of rule application. Since the logic programming community can generate many examples and many design goals, the close connections with proof theory have helped to keep proof theory relevant to the general topic of computational logic. (shrink)

How does science work? Does it tell us what the world is "really" like? What makes it different from other ways of understanding the universe? In Theory and Reality , Peter Godfrey-Smith addresses these questions by taking the reader on a grand tour of one hundred years of debate about science. The result is a completely accessible introduction to the main themes of the philosophy of science. Intended for undergraduates and general readers with no prior background in philosophy, Theory and (...) Reality covers logical positivism the problems of induction and confirmation Karl Popper's theory of science Thomas Kuhn and "scientific revolutions" the views of Imre Lakatos, Larry Laudan, and Paul Feyerabend and challenges to the field from sociology of science, feminism, and science studies. The book then looks in more detail at some specific problems and theories, including scientific realism, the theory-ladeness of observation, scientific explanation, and Bayesianism. Finally, Godfrey-Smith defends a form of philosophical naturalism as the best way to solve the main problems in the field. Throughout the text he points out connections between philosophical debates and wider discussions about science in recent decades, such as the infamous "science wars." Examples and asides engage the beginning student a glossary of terms explains key concepts and suggestions for further reading are included at the end of each chapter. However, this is a textbook that doesn't feel like a textbook because it captures the historical drama of changes in how science has been conceived over the last one hundred years. Like no other text in this field, Theory and Reality combines a survey of recent history of the philosophy of science with current key debates in language that any beginning scholar or critical reader can follow. (shrink)

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an (...) up-to-date and reliable guide essential for the student. (shrink)

This is the first introductory textbook on non-classical propositional logics.

Important philosophical volume by foremost architectural conceptualist emphasizes organic design, interrelated study of all arts. He provides introductory, retrospective, and prospective analysis, explores the creative instinct, organic order, form and vitality, form and time, form and logic, form and function, the dogmatic, mechanized, and the creative mind, and more.

This unique book provides a gentle introduction to an increasingly important type of formal logic called CLAUSAL FORM LOGIC (CFL). Having evolved out of human reasoning, CFL represents the ideal to which all computer-based systems must approximate. Most present day computational logic systems are based on it, including the well-know artificial intelligence language PROLOG.

Martin presents fifteen previously unpublished essays which he wrote before 1973. Despite several references to his earlier books such as Truth and Denotation, these essays will be intelligible to those who have not yet read anything by R. M. Martin as long as you can master long formulations in the notation of a formal first-order language. Indeed, these essays can serve as an introduction to the work of Martin. The first three essays present Martin's metaphysical system. Essays 4, 5, and (...) 6 amplify his system by showing how a wide variety of sentences can have their logical form represented in the formal language which displays Martin's ontology. In the remaining nine essays he critically evaluates positions of other philosophers such as Hiz, Carnap, Quine, Fitch, Chisholm, Popper, Sellars, Heyting, Lorenzen, and Putnam, from the perspective of his system. Because his systematic approach unifies all of the papers and because he uses technical terms in the development of his system, it is regrettable that the book offers no index. (shrink)

Introduction to Logic is a proven textbook that has been honed through the collaborative efforts of many scholars over the last five decades. Its scrupulous attention to detail and precision in exposition and explanation is matched by the greatest accuracy in all associated detail. In addition, it continues to capture student interest through its personalized human setting and current examples. The 14th Edition of Introduction to Logic, written by Copi, Cohen & McMahon, is dedicated to the many thousands of students (...) and their teachers - at hundreds of universities in the United States and around the world - who have used its fundamental methods and techniques of correct reasoning in their everyday lives. (shrink)

An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.

Subtitled "Ideas and Arguments from Plato to Sartre," this volume is intended, as are many others, to serve both as a textbook for introductory courses in philosophy and as an introduction to philosophic thinking. One of its goals, and one admirably achieved, is to provide some hearing both to all the very greatest figures in the history of western philosophy and to some major opposing traditions. No one can read the volume and fail to grasp something of the content and (...) spirit in the work of such men as Plato, Aristotle, Aquinas, Descartes, Hume, Kant, Wittgenstein and others. What makes Flew's work creative and original is a combination of factors. First of all, he combines in a very stimulating and integral way two methods commonly adopted in works of this kind, namely representative selections from original sources and expository and critical commentary. Almost one half of the work consists of material taken from the primary sources, but these selections are not set off in large chunks interspersed with commentary. Rather they are worked into the text to illustrate the thrust of the arguments and ideas involved, and thus we find Hobbes' militant manifesto of metaphysical materialism confronting the Eleatic Stranger's argument for the existence of "certain incorporeal Forms which are objects of the mind" in The Sophist, Hume's views on finality contrasted with the argument developed by Aquinas in his fifth way, and Frege's polemic against confusing the logical with the psychological set opposite the arguments of Locke concerning the meaning of human understanding. In addition, in offering his own critical comment Flew deliberately seeks to set forth his own conclusions even in areas that have been and are controversial. Thus the work is by no means an impersonal account but conveys something of the enthusiasm and excitement that the author experiences in trying to forge sound arguments and assess the soundness of arguments advanced by others--and this, for Flew, is the principal work of the philosopher. One could argue over many of the nuances that Flew's way of proceeding gives to the meaning of the philosophies discussed, but this in no way detracts from the value of this stimulating and exceptionally informative introduction.--W. E. M. (shrink)

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs (...) of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. (shrink)

Brief yet also comprehensive, Think with Socrates: An Introduction to Critical Thinking uses the methods, ideas, and life of Socrates as a model for critical thinking. It offers a more philosophical, historical, and accessible introduction than longer textbooks while still addressing all of the key topics in logic and argumentation. Applying critical thinking to the Internet, mass media, advertising, personal experience, expert authority, the evaluation of sources, writing argumentative essays, and forming a worldview, Think with Socrates resonates with today's students (...) and teaches them how to apply their skills to the real world. At the same time, it also covers the ancient intellectual roots and history of the field, placing critical thinking in its larger context to help students appreciate its perennial value. Author Paul Herrick incorporates original sources from newspapers, a variety of media, and philosophical writing, along with engaging "interludes" featuring selections from Plato's dialogues. A Companion Website at www.oup.com/us/herrick offers resources for students and instructors. (shrink)

A Logical Introduction to Probability and Induction starts with elementary logic and uses it as basis for a philosophical discussion of probability and induction. Throughout the book results are carefully proved using the inference rules introduced at the beginning. The textbook is suitable for undergraduate courses in philosophy and logic.

Philosophy of logic is a fundamental part of philosophical study, and one which is increasingly recognized as being immensely important in relation to many issues in metaphysics, metametaphysics, epistemology, philosophy of mathematics, and philosophy of language. This textbook provides a comprehensive and accessible introduction to topics including the objectivity of logical inference rules and its relevance in discussions of epistemological relativism, the revived interest in logical pluralism, the question of logic's metaphysical neutrality, and the demarcation between logic and (...) mathematics. Chapters in the book cover the state of the art in contemporary philosophy of logic, and allow students to understand the philosophical relevance of these debates without having to contend with complex technical arguments. This will be a major new resource for students working on logic, as well as for readers seeking a better understanding of philosophy of logic in its wider context. (shrink)

This textbook, oriented toward non-majors in philosophy, aims to provide an understanding not merely of forms of valid and invalid inference but also of the cognitive situation, of the methods of successful "problem-solving thought" and of the role of language therein. Great emphasis is thus placed on semiotics, which is integrated with the material from methodology and logic by considerations from general theory of knowledge. The whole presentation is marked by innovations, both pedagogical and theoretical. Most of the material of (...) the usual course in elementary formal logic is crowded into the last part. The author has attempted, with some success, to develop a reformed "traditional" approach to logic in the light of the recent technical advances in semiotic and symbolic logic, without reducing it to a narrow and fragmentary formal exposition of these sciences. --L. K. B. (shrink)

Jerónimo Pardo's analysis of the problems raised by some popular trinitarian paralogisms is studied in this paper. The purpose is to show how the notions employed by the theologians in order to solve theological problems were introduced into a textbook on logic to deal with some genuinely logical problems. First, the problem, common to all logical approaches, of achieving a fine-grained analysis of the logical form of syllogistical inferences. Second, the problem, typical of the terminist approach (...) to logic, of guaranteeing that Latin is an adequate vehicle for logical analysis. (shrink)

Mathematical Logic: An Introduction is a textbook that uses mathematical tools to investigate mathematics itself. In particular, the concepts of proof and truth are examined. The book presents the fundamental topics in mathematical logic and presents clear and complete proofs throughout the text. Such proofs are used to develop the language of propositional logic and the language of first-order logic, including the notion of a formal deduction. The text also covers Tarski’s definition of truth and the computability concept. It also (...) provides coherent proofs of Godel’s completeness and incompleteness theorems. Moreover, the text was written with the student in mind and thus, it provides an accessible introduction to mathematical logic. In particular, the text explicitly shows the reader how to prove the basic theorems and presents detailed proofs throughout the book. Most undergraduate books on mathematical logic are written for a reader who is well-versed in logical notation and mathematical proof. This textbook is written to attract a wider audience, including students who are not yet experts in the art of mathematical proof. (shrink)

This book is a consideration of Hegel’s view on logic and basic logical concepts such as truth, form, validity, and contradiction, and aims to assess this view’s relevance for contemporary philosophical logic. The literature on Hegel’s logic is fairly rich. The attention to contemporary philosophical logic places the present research closer to those works interested in the link between Hegel’s thought and analytical philosophy, Koch 2014, Brandom 2014, 1-15, Pippin 2016, Moyar 2017, Quante & Mooren 2018 among others). (...) In this context, one particularity of this book consists in focusing on something that has been generally underrated in the literature: the idea that, for Hegel as well as for Aristotle and many other authors, logic is the study of the forms of truth, i.e. the forms that our thought can assume in searching for truth. In this light, Hegel’s thinking about logic is a fundamental reference point for anyone interested in a philosophical foundation of logic. (shrink)

Propositional logic -- Propositions and arguments -- Connectives and argument forms -- Truth tables -- Trees -- Vagueness and bivalence -- Conditionality -- Natural deduction -- Predicate logic -- Predicates, names, and quantifiers -- Models for predicate logic -- Trees for predicate logic -- Identity and functions -- Definite descriptions -- Some things do not exist -- What is a predicate? -- What is logic?

Introduction Combinatory logic deals with a class of formal systems designed for studying certain primitive ways in which functions can be combined to form ...

This is an introductory 2001 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 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 this book are a (...) lively and vigorous prose style; lucid and systematic organization and presentation of 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; and a full bibliography of further reading. (shrink)

Semantics is a bridge discipline between linguistics and philosophy; but linguistics student are rarely able to reach that bridge, let alone cross it to inspect and assess the activity on the other side. Professor Kempson's textbook seeks particularly to encourage such exchanges. She deals with the standard linguistic topics like componential analysis, semantic universals and the syntax-semantics controversy. But she also provides for students with no training in philosophy or logic an introduction to such central topics in the philosophy of (...) language as logical form, truth, speech acts, analyticity, entailment and presupposition. The exposition throughout is deliberately argumentative rather than descriptive, introducing the student step by step to the major problems in theoretical semantics. Special emphasis is placed on the need to consider individual arguments within the overall perspective of semantics as an integral part of general linguistic theory. Written primarily as a textbook for undergraduates and graduates in linguistics departments, this book will also be useful to undergraduates in philosophy and in psychology where linguistics is a part of their course. (shrink)

This is a comprehensive introduction to the fundamentals of logic (both formal logic and critical reasoning), with exceptionally clear yet conversational explanations and a multitude of engaging examples and exercises. Herrick's examples are on-point and fun, often bringing in real-life situations and popular culture. And more so than other logic textbooks, Introduction to Logic brings in the history of philosophy and logic through interesting boxes/sidebars and discussions, showing logic's relation to philosophy.

TO THE LOGICAL INVESTIGATIONS A DRAFT OF A PREFACE TO THE LOGICAL INVESTIGATIONS ( 1913) Edited by EUGEN FINK Translated with Introductions by PHILIP J. BOSSERT and CURTIS H. PETERS • MARTINUS NIJHOFF THE HAGUE 1975 © I975 by Martinus Nijhoff. The Hague. Netherlands All rights reserved. including the right to translate or to reproduce this book or parts thereof in any form ISBN-I3: 978-90-247-1711-8 e-ISBN-I3: 978-94-010-1655-1 DOl: 10. 1007/978-94-010-1655-1 TO HERBERT SPIEGELBERG ESTEEMED SCHOLAR, MENTOR, FRIEND ACKNOWLEDGEMENTS (...) We would like to express our thanks to H. L. Van Breda, director of the Husserl-Archiv (Louvain), for his approval and encouragement of this project, and to Professor Dr. Gerhart Husserl, Professor Dr. Eugen Fink and the editors of Tijdschrift voor Philosophie for their permission to undertake it. We also owe a debt of appreciation to Dr. Karl Schuhmann of the Catholic University of Louvain and to Dr. Elmar Holenstein, Dr. Edi Marbach and Mr. Rudolf Bernet of the Husserl-Archiv (Louvain) for their help in reading the original manuscripts and for putting their excellent knowledge of the Husserl "Nachlass" preserved at the Archives at our disposal. We especially wish to thank Professor Herbert Spiegelberg whose careful and critical reading of our manuscript at an earlier stage resulted in numerous suggestions for its improvement; and, last but not least, our wives, Jane and Pam, for their help in preparing the typescripts. TABLE OF CONTENTS Translator's Introductions XI I. HISTORICAL INTRODUCTION XI II. THEMATIC INTRODUCTION XX III. (shrink)

The reductive, as opposed to deductive, view of logic is the form of logic that is, perhaps, most widely employed in practical reasoning. In particular, it is the basis of logic programming. Here, building on the idea of uniform proof in reductive logic, we give a treatment of logic programming for BI, the logic of bunched implications, giving both operational and denotational semantics, together with soundness and completeness theorems, all couched in terms of the resource interpretation of BI’s semantics. (...) We use this set-up as a basis for exploring how coalgebraic semantics can, in contrast to the basic denotational semantics, be used to describe the concrete operational choices that are an essential part of proof-search. The overall aim, toward which this paper can be seen as an initial step, is to develop a uniform, generic, mathematical framework for understanding the relationship between the deductive structure of logics and the control structures of the corresponding reductive paradigm. (shrink)

This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.