Online research in philosophy

What is informal logic, is it ``logic" at all? Main contemporary approaches are briefly presented and critically commented. If the notion of consequence is at the heart of logic, does it make sense to speak about ``informal" consequence? A valid inference is truth preserving, if the premises are true, so is the conclusion. According to Prawitz two further conditions must also be satisfied in the case of classical logical consequence: (i) it is because of the (...) logical form of the sentences involved and not because of their specific content that the inference is truth preserving; (ii) it is necessary that if the premises are true, then so is the conclusion. According to the prevalent criteria of informal logic an argument is cogent if and only if (i) its premises are rationally Acceptable, (ii) its premises are Relevant to its conclusion and (iii) its premises constitute Grounds adequate for accepting the conclusion (the ``ARG" conditions according to Govier). The ARG criteria characterize a certain broad kind of consequence relation. We do not (in general) have truth preservence in cogent arguments but if the premises are acceptable and other criteria are met, then so is the conclusion. We can speak about form in a loose sense and finally, there is rational necessity of the grounding or support relation. So a certain broad notion of logical consequence emerges from this comparison. The norms of ARG are norms of elementary scientific methodology in which argument is seen as embodying reasoning within a process of inquiry or of belief formation in subject areas accessible to every informed intellectual. (shrink)

The Editors express their gratitude and appreciation to the indi-viduals listed below who served as referees for Informal Logic for Volumes 31 (2011) and 32 (2012).

This article challenges the common view that improvements in critical thinking are best pursued by investigations in informal logic. From the perspective of research in psychology and neuroscience, hu-man inference is a process that is multimodal, parallel, and often emo-tional, which makes it unlike the linguistic, serial, and narrowly cog-nitive structure of arguments. At-tempts to improve inferential prac-tice need to consider psychological error tendencies, which are patterns of thinking that are natural for peo-ple but frequently lead to mistakes (...) in judgment. This article discusses two important but neglected error ten-dencies: motivated inference and fear-driven inference. (shrink)

When, if ever, is one justified in accepting the premises of an argument? What is the proper criterion of premise acceptability? Providing a comprehensive theory of premise acceptability, this book answers these questions from an epistemological approach that the author calls "common sense foundationalism". His work will be of interest to specialists in informal logic, critical thinking and argumentation theory as well as to a broader range of philosophers and those teaching rhetoric.

Informal Logic is an introductory guidebook to the basic principles of constructing sound arguments and criticizing bad ones. Non-technical in approach, it is based on 186 examples, which Douglas Walton, a leading authority in the field of informal logic, discusses and evaluates in clear, illustrative detail. Walton explains how errors, fallacies, and other key failures of argument occur. He shows how correct uses of argument are based on sound strategies for reasoned persuasion and critical responses. Among (...) the many subjects covered are: forms of valid argument, defeasible arguments, relevance, appeals to emotion, personal attack, straw man argument, jumping to a conclusion, uses and abuses of expert opinion, problems in drawing conclusions from polls and statistics, loaded terms, equivocation, arguments from analogy, and techniques of posing, replying to, and criticizing questions. This new edition takes into account many new developments in the field of argumentation study that have occurred since 1989, many created by the author. Drawing on these developments, Walton includes and analyzes 36 new topical examples and also brings in recent work on argumentation schemes. Ideally suited for use in courses in informal logic and introduction to philosophy, this book will also be valuable to students of pragmatics, rhetoric, and speech communication. (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)

The issue of the relationship between formal and informal logic depends strongly on how one understands these two designations. While there is very little disagreement about the nature of formal logic, the same is not true regarding informal logic, which is understood in various (often incompatible) ways by various thinkers. After reviewing some of the more prominent conceptions of informal logic, I will present my own, defend it and then show how informal (...) logic, so understood, is complementary to formal logic. (shrink)

Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more nuanced understanding of mathematical proof and discovery may be achieved by paying attention to the aspects of mathematical argumentation which can be captured by informal, rather than formal, logic. Two accounts of argumentation are (...) considered: the pioneering work of Stephen Toulmin [The uses of argument, Cambridge University Press, 1958] and the more recent studies of Douglas Walton, [e.g. The new dialectic: Conversational contexts of argument, University of Toronto Press, 1998]. The focus of both of these approaches has largely been restricted to natural language argumentation. However, Walton’s method in particular provides a fruitful analysis of mathematical proof. He offers a contextual account of argumentational strategies, distinguishing a variety of different types of dialogue in which arguments may occur. This analysis represents many different fallacious or otherwise illicit arguments as the deployment of strategies which are sometimes admissible in contexts in which they are inadmissible. I argue that mathematical proofs are deployed in a greater variety of types of dialogue than has commonly been assumed. I proceed to show that many of the important philosophical and pedagogical problems of mathematical proof arise from a failure to make explicit the type of dialogue in which the proof is introduced. (shrink)

Informal logic is the attempt to develop a logic to assess, analyse and improve ordinary language (or "everyday") reasoning. It intersects with attempts to understand such reasoning from the point of view of philosophy, formal logic, cognitive psychology, and a range of other disciplines. Most of the work in informal logic focuses on the reasoning and argument (in the premise-conclusion sense) one finds in personal exchange, advertising, political debate, legal argument, and the social commentary (...) that characterizes newspapers, television, the World Wide Web and other forms of mass media. (shrink)

Much work in MKM depends on the application of formal logic to mathematics. However, much mathematical knowledge is informal. Luckily, formal logic only represents one tradition in logic, specifically the modeling of inference in terms of logical form. Many inferences cannot be captured in this manner. The study of such inferences is still within the domain of logic, and is sometimes called informal logic. This paper explores some of the benefits informal (...) class='Hi'>logic may have for the management of informal mathematical knowledge. (shrink)

Informal logic offers a radical new perspective on the evaluation of arguments. But little work has been done on how deep concepts in the logical foundations of argument need to be modified in light of such efforts. This paper offers an indication of what might be done by sketching a new approach to the theory of entailment, truth and relevance.

This is an introductory guide to the basic principles of constructing good arguments and criticizing bad ones. It is nontechnical in its approach, and is based on 150 key examples, each discussed and evaluated in clear, illustrative detail. The author explains how errors, fallacies, and other key failures of argument occur. He shows how correct uses of argument are based on sound argument strategies for reasoned persuasion and critical questions for responding. Among the many subjects covered are: techniques of posing, (...) replying to, and criticizing questions, forms of valid argument, relevance, appeals to emotion, personal attack, uses and abuses of expert opinion, problems in deploying statistics, loaded terms, equivocation, and arguments from analogy. (shrink)

In this paper, I present a decision procedure for evaluating arguments expressed in natural language. I think that other instructors of informal logic and critical thinking might find this decision procedure to be a useful addition to their teaching resources.

Argumentation theory underwent a significant development in the Fifties and Sixties: its revival is usually connected to Perelman's criticism of formal logic and the development of informal logic. Interestingly enough it was during this period that Artificial Intelligence was developed, which defended the following thesis (from now on referred to as the AI-thesis): human reasoning can be emulated by machines. The paper suggests a reconstruction of the opposition between formal and informal logic as a move (...) against a premise of an argument for the AI-thesis, and suggests making a distinction between a broad and a narrow notion of algorithm that might be used to reformulate the question as a foundational problem for argumentation theory. (shrink)

The aim of this paper is to adapt Miranda Fricker’s concept of testimonial injustice to cases of what I call “argumentative injustice”: those cases where an arguer’s social identity brings listeners to place too much or little credibility in an argument. My recommendation is to adopt a stance of “metadistrust”—we ought to distrust our inclinations to trust or distrust members of stereotyped groups.

Arguments with what are called "independent" or "convergent" premises are typically diagrammed by using an arrow between each premise and the conclusion. This makes diagramming objections to the reasoning difficult. It also obscures differences in argument structure. I suggest that a single arrow should be used for such arguments and that this is so even in the extreme form of independent premises when the argument is entirely unstructured. I then discuss the diagramming of objections.

However, if we take a more generous view about possibility, then more alternatives present themselves. The best of these may be something that we formerly took to be impossible, and which is better than the best of the earlier possibilities.

We present a compositional semantics for first-order logic with imperfect information that is equivalent to Sevenster and Sandu’s equilibrium semantics (under which the truth value of a sentence in a finite model is equal to the minimax value of its semantic game). Our semantics is a generalization of an earlier semantics developed by the first author that was based on behavioral strategies, rather than mixed strategies.

Hamblin’s Fallacies remains one of the crucial documents in the development of informal logic and argumentation theory. His critique of traditional approaches to the fallacies (what he dubbed ‘The Standard Treatment’) helped to revitalize the study of fallacies. Recently I had occasion to reread Fallacies and came to the conclusion that some of my earlier criticisms (1989, 1990) had missed the real force of what was going on there, that I and others have perhaps not fully appreciated what (...) Hamblin is up to. In this paper, I plan to revisit Fallacies and make manifest its coherence. (shrink)

Friends, welcome to the first page of Logic in India. It is for Indian students prepared for first paper entitled Principles of Logic in Diploma-in-Reasoning course of Department of Philosophy, Kurukshetra University, Kurukshetra, where I taught four years. It is also beneficial for graduate students who have elementary logic course in their syllabus. Basically I used both printed books and internet sources to prepare it. You can find the course syllabus in my post “Philosophy is Nothing without (...) Logic” at The Positive Philosophy page and also in the side links of this page. This is only a draft, kindly send your suggestions and ideas to dr.sirswal@gmail.com or niyamak.drs@gmail.com, I shall be highly thankful to you. A short list of reference books are mentioned below of the Table of Contents and reference sites are linked with this page. This page introduces the basic conceptions of formal logic, informal logic and also Symbolic logic. (shrink)

HOW WE THINK PART ONE: THE PROBLEM OF TRAINING THOUGHT CHAPTER ONE WHAT IS THOUGHT? § i. Varied Senses of the Term No words are oftener on our lips than ...

According to a prevalent view among philosophers formal logic is the philosopher’s main tool to assess the validity of arguments, i.e. the philosopher’s ars iudicandi. By drawing on a famous dispute between Russell and Strawson over the validity of a certain kind of argument – of arguments whose premises feature definite descriptions – this paper casts doubt on the accuracy of the ars iudicandi conception. Rather than settling the question whether the contentious arguments are valid or not, Russell and (...) Strawson, upon discussing the proper logical analysis of definite descriptions, merely contrast converse informal validity assessments rendered explicit by nonequivalent logical for-malizations. (shrink)

The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic (...) logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. Key Features - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic -Useful bibliographies in every chapter - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter. (shrink)

Information-based epistemology maintains that ‘being informed’ is an independent cognitive state that cannot be reduced to knowledge or to belief, and the modal logic KTB has been proposed as a model. But what distinguishes the KTB analysis of ‘being informed’, the Brouwersche schema (B), is precisely its downfall, for no logic of information should include (B) and, more generally, no epistemic logic should include (B), either.

The Handbook of the Logic of Argument and Inference is an authoritative reference work in a single volume, designed for the attention of senior undergraduates, graduate students and researchers in all the leading research areas concerned with the logic of practical argument and inference. After an introductory chapter, the role of standard logics is surveyed in two chapters. These chapters can serve as a mini-course for interested readers, in deductive and inductive logic, or as a refresher. Then (...) follow two chapters of criticism; one the internal critique and the other the empirical critique. The first deals with objections to standard logics (as theories of argument and inference) arising from the research programme in philosophical logic. The second canvasses criticisms arising from work in cognitive and experimental psychology. The next five chapters deal with developments in dialogue logic, interrogative logic, informal logic, probability logic and artificial intelligence. The last chapter surveys formal approaches to practical reasoning and anticipates possible future developments. Taken as a whole the Handbook is a single-volume indication of the present state of the logic of argument and inference at its conceptual and theoretical best. Future editions will periodically incorporate significant new developments. (shrink)

The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic (...) logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. Key Features - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic -Useful bibliographies in every chapter - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter. (shrink)

Janusz Czelakowski Elements of Formal Action Theory 1. Elementary Action Systems 1.1 Introductory Remarks. In contemporary literature one may distinguish ...

The main tool of the arithmetization and logization of analysis in the history of nineteenth century mathematics was an informal logic of quantifiers in the guise of the “epsilon–delta” technique. Mathematicians slowly worked out the problems encountered in using it, but logicians from Frege on did not understand it let alone formalize it, and instead used an unnecessarily poor logic of quantifiers, viz. the traditional, first-order logic. This logic does not e.g. allow the definition and (...) study of mathematicians’ uniformity concepts important in analysis. Mathematicians’ stronger logic was rediscovered around 1990 as the form of independence-friendly logic which hence is not a new logic nor a further development of ordinary first-order logic but a richer version of it. (shrink)

This volume provides analyses of the logic-reality relationship from different approaches and perspectives. The point of convergence lies in the exploration of the connections between reality – social, natural or ideal – and logical structures employed in describing or discovering it. Moreover, the book connects logical theory with more concrete issues of rationality, normativity and understanding, thus pointing to a wide range of potential applications. -/- -/- The papers collected in this volume address cutting-edge topics in contemporary discussions amongst (...) specialists. Some essays focus on the role of indispensability considerations in the justification of logical competence, and the wide range of challenges within the philosophy of mathematics. Others present advances in dynamic logical analysis such as extension of game semantics to non-logical part of vocabulary and development of models of contractive speech act. -/- Table of Contents: Introduction: Majda Trobok, Nenad Miščević and Berislav Žarnić.- I. Logical and Mathematical Structures.- Life on the Ship of Neurath: Mathematics in the Philosophy of Mathematics: Stewart Shapiro.- Applied Mathemathics in the Sciences: Dale Jacquette.- The Philosophical Impact of the Löwenheim-Skolem Theorem: Miloš Arsenijević.- Debating (Neo)logicism: Frege and the neo-Fregeans: Majda Trobok.- II. Epistemology and Logic.- Informal Logic and Informal Consequence: Danilo Šuster.- Logical Consequence and Rationality: Nenad Smokrović.- Logic, Indispensability and Aposteriority: Nenad Miščević.- III . Dynamic Logical Models of Meaning.- Extended Game-Theoretical Semantics: Manuel Rebuschi.- Dynamic Logic of Propositional Commitments: Tomoyuki Yamada.- Is Unsaying Polite?: Berislav Žarnić.- IV Logical Methods in Ontological and Linguistic Analyses.- Towards a Formal Account of Identity Criteria: Massimiliano Carrara and Silvia Gaio.- A Mereology for the Change of Parts: Pierdaniele Giaretta and Giuseppe Spolaore.- Russell versus Frege: Imre Rusza.- Goodman’s OnlyWorld: Vladan Djordjević.-. (shrink)

The lack of a theory of relevance in the current state of the art of informal logic has often been considered regrettable, a gap that must be filled before the Relevance-Sufficiency-Acceptability model can be considered complete. I wish to challenge this view. A theory of relevance is neither desirable nor possible. Informal logic can get by perfectly well, and has been doing so far, with relevance judgments that are by nature unanalysable and intuitive. Criticism of theories (...) of relevance, for example in Woods (1992), is deflated. (shrink)

Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational (...) models with infinitely many agents, PAL-K_omega, as well as standard extensions thereof, e.g., PAL-T_omega, PAL-S4_omega, and PAL-S5_omega. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL. (shrink)

Safe Safety arguments are key components in a safety case. Too often, safety arguments are constructed without proper reasoning. To address this, we argue that informal logic argument schemes have important roles to play in safety argument construction and reviewing process. Ten commonly used reasoning schemes in computer system safety domain are proposed. The role of informal logic dialogue games in computer system safety arguments reviewing is also discussed and the intended work in this area is (...) proposed. It is anticipated that this work will contribute toward the development of computer system safety arguments, and help to move forward the interplay between research in informal logic and research in computer system safety engineering. (shrink)

Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I (...) also describe some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem. (shrink)

Logic With Trees is a new and original introduction to modern formal logic. It contains discussions on philosophical issues such as truth, conditionals and modal logic, presenting the formal material with clarity, and preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and exercises guide beginners through the book, with answers to selected exercises enabling readers to check their progress. Logic With Trees equips students with: a complete and clear account of the truth-tree (...) system for first order logic; the importance of logic and its relevance to many different disciplines; the skills to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic; the ability to contest claims that "ordinary" reasoning is well represented by formal first order logic. (shrink)

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives (...) outlines of two arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two different proof systems with respect to the semantics is proven (Theorems 2.11. and 2.15.), as well as a normal form theorem (Theorem 3.23.), an elimination theorem for the actuality operator (Corollary 3.27.), and the decidability of the logic (Corollary 3.28.). (shrink)

Rabern and Rabern (Analysis 68:105–112 2 ) and Uzquiano (Analysis 70:39–44 4 ) have each presented increasingly harder versions of ‘the hardest logic puzzle ever’ (Boolos The Harvard Review of Philosophy 6:62–65 1 ), and each has provided a two-question solution to his predecessor’s puzzle. But Uzquiano’s puzzle is different from the original and different from Rabern and Rabern’s in at least one important respect: it cannot be solved in less than three questions. In this paper we solve Uzquiano’s (...) puzzle in three questions and show why there is no solution in two. Finally, to cement a tradition, we introduce a puzzle of our own. (shrink)

I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...

Logic brings elementary logic out of the academic darkness into the light of day. Paul Tomassi makes logic fully accessible for anyone trying to come to grips with the complexities of this challenging subject. This book is written in a patient and user-friendly way which makes both the nature and value of formal logic crystal clear. This textbook proceeds from a frank, informal introduction to fundamental logical notions to a system of formal logic rooted (...) in the best of our natural deductive reasoning in daily life. The book includes plenty of exercise to put the students' reading to test, summay boxes of key points, a glossary and many illustrations. This book will be useful to any student who needs a patient and comprehensible introduction to what otherwise can be a daunting subject. (shrink)

We shall introduce in this paper a language whose formulas will be interpreted by games of imperfect information. Such games will be defined in the same way as the games for first-order formulas except that the players do not have complete information of the earlier course of the game. Some simple logical properties of these games will be stated together with the relation of such games of imperfect information to higher-order logic. Finally, a set of applications will be outlined.

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness (...) of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optinal sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in logic, mathematics, philosophy, and computer science. (shrink)

Proceedings of the Tenth Brazilian Conference on Mathematical Logic. Coleção CLE, volume 14, 1995. Centro De Lógica, Epistemologia e História da Ciência, Unicamp, Campinas, SP, Brazil.

Intended for the first course in logic, The Power of Logic (POL) is written with the conviction that logic is the most important course that college students take. POL preserves the balance between informal and formal logic. Layman;s direct and accessible writing style, along with his plentiful examples, imaginative exercises, and POL;s accompanying Logic Tutor make this the best text for logic classes today.day.

This paper discusses the distinctions indicated in its title. It is argued that the distinction between syntax and semantics is much more important for the present situation in logic than other distinctions. In particular, doing formal syntax and formal semantics requires the use of an informal melanguage based on ordinary mathematics.

For more than twenty years, introductory logic students have relied on this text to provide clear lessons as well as practical applications of the discipline. Robert Baum emphasizes formal logic and utilizes such elements of popular culture as cartoons and advertisements to illustrate technical concepts. Logic, 4/e addresses all the basic concepts, including informal analysis of statements, arguments, Aristotelian logic, propositional logic, quantificational logic, enumerative induction, the scientific method, probability, informal fallacies, definitions, (...) and applied logic. As with previous editions, Logic, 4/e is extremely flexible--most of the chapters can be included or excluded from a particular course depending on the goals of the course and the time available. This fourth edition features hundreds of additional exercises throughout. (shrink)

Basic concepts -- Identifying arguments -- Logic and language -- Informal fallacies -- Categorical logic: statements -- Categorical logic: syllogisms -- Statement logic: truth tables -- Statement logic: proofs -- Predicate logic -- Induction -- Probability.

Argument and explanation are distinct forms of reasoning with an underappreciated complementary relationship. In this essay I define these terms precisely, identify the mischief that results from conflating them, elucidate their complementary relationship and employ this relationship to provide a fruitful approach to analyzing the logical structure of the common editorial.

We discuss the differences between first-order set theory and second-order logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if second-order logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if it is given a weak semantics, it loses its power in expressing concepts categorically. First-order set theory and second-order (...) class='Hi'>logic are not radically different: the latter is a major fragment of the former. (shrink)

In this sequel to “The logic and meaning of plurals. Part I”, I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of (...) truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages. (shrink)

This is a critical examination of Antoine Arnauld's Logic or the Art of Thinking (1662), commonly known as the Port-Royal Logic. Rather than reading this work from the viewpoint of post-Fregean formal logic or the viewpoint of seventeenth-century intellectual history, I approach it with the aim of exploring its relationship to that contemporary field which may be labeled informal logic and/or argumentation theory. It turns out that the Port-Royal Logic is a precursor of this (...) current field, or conversely, that this field may be said to be in the same tradition. (shrink)

We introduce a substructural propositional calculus of Sequential Dynamic Logic that subsumes a propositional part of dynamic predicate logic, and is shown to be expressively equivalent to propositional dynamic logic. Completeness of the calculus with respect to the intended relational semantics is established.

We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, in logics whose semantics is based on teams instead of assignments, e.g., IF-logic and Dependence logic. Both the monotone and the non-monotone case is considered. It is argued that to handle quantifier scope dependencies of generalized quantifiers in a satisfying way the dependence atom in Dependence logic is not well suited and that the multivalued dependence atom is a better choice. This atom is in (...) fact definably equivalent to the independence atom recently introduced by Väänänen and Grädel. (shrink)

This article advances the view that propositional logic can and should be taught within general education logic courses in ways that emphasizes its practical usefulness, much beyond what commonly occurs in logic textbooks. Discussion and examples of this relevance include database searching, understanding structured documents, and integrating concepts of proof construction with argument analysis. The underlying rationale for this approach is shown to have import for questions concerning the design of logic courses, textbooks, and the general (...) education curriculum, particularly the sequencing of formal and informal logic courses. (shrink)

We examine the transitions between sets of possible worlds described by the compositional semantics of Modal Dependence Logic, and we use them as the basis for a dynamic version of this logic. We give a game theoretic semantics, a (compositional) transition semantics and a power game semantics for this new variant of modal Dependence Logic, and we prove their equivalence; and furthermore, we examine a few of the properties of this formalism and show that Modal Dependence (...) class='Hi'>Logic can be recovered from it by reasoning in terms of reachability. Then we show how we can generalize this approach to a very general formalism for reasoning about transformations between pointed Kripke models. (shrink)

A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived.

It is argued here that Prior's non-standard modal system Q, and the Parry?Dunn system of analytic implication, though entirely independent and independently motivated systems, together provide a rationale for explicating the concept of validity in a non-standard way; their implications are explored for the theory of natural deduction as well as for modal logic and the concept of entailment. I give an account of formal logic from this non-standard viewpoint, together with an informal presentation of the system (...) that unites the insights of Prior (drawing on Russell) and, Parry (drawing on Kant), and the motivations for both in the concept of the contingent existence ? as opposed to the contingent truth or falsehood ? of a proposition. (shrink)

Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to (...) reasoning fail, so that ignorance of their nature is profound. (shrink)

The properties of the ${\forall^{1}}$ quantifier defined by Kontinen and Väänänen in [13] are studied, and its definition is generalized to that of a family of quantifiers ${\forall^{n}}$ . Furthermore, some epistemic operators δ n for Dependence Logic are also introduced, and the relationship between these ${\forall^{n}}$ quantifiers and the δ n operators are investigated.The Game Theoretic Semantics for Dependence Logic and the corresponding Ehrenfeucht- Fraissé game are then adapted to these new connectives.Finally, it is proved that the (...) ${\forall^{1}}$ quantifier is not uniformly definable in Dependence Logic, thus answering a question posed by Kontinen and Väänänen in the above mentioned paper. (shrink)

We explore the relationship between argument and narrative with reference to parables. Parables are typically thought to convey a message. In examining a parable, we can ask what that message is, whether the story told provides reasons for the message, and whether those reasons are good reasons. In exploring these questions, we employ as an inves-tigative technique the strategy of reconstructing parables as argu-ments. We then proceed to con-sider the cogency of those argu-ments. One can offer arguments through narratives and, (...) in particu-lar, through parables, but that do-ing so likely brings more risks than benefits, from an epistemic point of view. (shrink)

We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and (...) a corresponding reading of such De Morgan style syllogistics in the previously referred to fragment of linear logic. (shrink)

First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the aforementioned proof (...) systems when capacity limits are put on the cognitive resources. Finally, we investigate the correlation between a number of mathematical complexity measures defined on graphs and sentences and some psychological complexity measures that were recorded in the experiment. (shrink)

With clear explanations and many examples drawn right out of day-to-day life, Paul Herrick untangles the complexities of logical theory in The Many Worlds of Logic. This new edition adds new chapters on informal logic and critical thinking. It also breaks out longer chapters from the previous edition into shorter, more focused chapters. Herrick has added many new explanations and examples; in in each chapter, he covers the fundamentals completely before moving on to more challenging areas. Features (...) * Difficult terms are highlighted and explained carefully * End-of-chapter glossaries help students remember important terms * Hundreds of examples demonstrate the application of concepts * Hundreds of excercises help students learn logic by actually doing it * Truth-trees in an appendix help students go beyond the basics. (shrink)

Essential Logic offers: BL Readability. A dialogue-like yet challenging style makes this introductory logic textbook engaging and interesting. BL Essentials. Deductive and inductive reasoning, formal and informal logic are placed within a philosophical perspective. BL Rigor. A careful sequence of learning steps communicates the essential skills of reasoning and directs students to write, support, and argue by connecting criticism to key concepts. BL Relevance. Explanations and examples take students' lives into consideration and are designed for students (...) with diverse backgrounds and a wide range of experiences. BL A Theme. Traditional concepts are integrated with a discussion of modern technological issues and the world view of modern science. A unique chapter on Logic and Hope addresses questions students often ask and suggests a global perspective. BL Controversy. Students are encouraged to defend and critique positions--including those presented by the author. A unique final chapter on Fuzzy Logic is framed as a debate between Western and Eastern philosophy. BL Exercises. Students gain confidence in recognizing arguments, structuring them into premises and conclusions, identifying and critiquing informal fallacies, while learning to create, follow, and appreciate symbolic reasoning trails. BL Coverage. Chapters cover Argument Recognition and Language Analysis, Inductive Reasoning, Structuring Informal Fallacies, Symbolic Translation, Truth Tables, Formal Proofs of Validity, Quantification, and the basics of Fuzzy Set Theory and Propositional Logic. (shrink)

Quantum theory is a probabilistic theory that embodies notoriously striking correlations, stronger than any that classical theories allow but not as strong as those of hypothetical ‘super-quantum’ theories. This raises the question ‘Why the quantum?’—whether there is a handful of principles that account for the character of quantum probability. We ask what quantum-logical notions correspond to this investigation. This project isn’t meant to compete with the many beautiful results that information-theoretic approaches have yielded but rather aims to complement that work.

Qualitative Reasoning (QR) is an area of research within Artificial Intelligence that automates reasoning and problem solving about the physical world. QR research aims to deal with representation and reasoning about continuous aspects of entities without the kind of precise quantitative information needed by conventional numerical analysis techniques. Order-of-magnitude Reasoning (OMR) is an approach in QR concerned with the analysis of physical systems in terms of relative magnitudes. In this paper we consider the logic OMR_N for order-of-magnitude reasoning with (...) the bidirectional negligibility relation. It is a multi-modal logic given by a Hilbert-style axiomatization that reflects properties and interactions of two basic accessibility relations (strict linear order and bidirectional negligibility). Although the logic was studied in many papers, nothing was known about its decidability. In the paper we prove decidability of OMR N by showing that the logic has the strong finite model property. (shrink)