This print edition of Read's account of logical thought includes the original publication's diagrams and tables. In this excellent book, Read commences by offering an overview of past attitudes and definitions of logic. Individual chapters consider the various means by which logical processes are conceived and developed in the mind. Philosophical arguments, spatial reasoning and mathematical forms of logic are discussed in great depth, with illustrations appended where deemed necessary. Read, an academic and philosopher, employs his decades long experience of (...) teaching students about the logical disciplines to write a detailed and comprehensive accounts of logic's aspects. Throughout this work, he attempts to retain a clarity of expression which makes the concepts discussed understandable for readers previously unversed in the types of logical expression. Read also sets out the principles behind setting up a hypothesis, and highlights the common logical fallacies which crop up in human reasoning. Extensive attention is given to the process of syllogism, by which sound conclusions are drawn from the premises offered. Throughout the book, Read is attentive in defining and explaining the esoteric terminology native to logic. As well as allowing the reader swift comprehension of the various subtopics, this explanatory style confers improved flow to the book. At the conclusion we are offered many questions corresponding to each chapter: these are intended to test the reader's understanding, and enforce the mental habits of utilising logical and critical thought. First published in 1898 and subject to several editions with revisions and refinements thereafter, Logic Deductive and Inductive retains a good reputation among academics and logicians. Its successful balance between striking a concise introductory tone with an embrace of the core elements of the subject has served to preserve its popularity into the modern day. (shrink)

In philosophy, an argument consists of a set of statements called premises that serve as grounds for affirming another statement called the conclusion. Philosophers typically distinguish arguments in natural languages (such as English) into two fundamentally different types: deductive and inductive. Each type of argument is said to have characteristics that categorically distinguish it from the other type. The two types of argument are also said to be subject to differing evaluative standards. Pointing to paradigmatic examples of each (...) type of argument helps to clarify their key differences. The distinction between the two types of argument may hardly seem worthy of philosophical reflection, as evidenced by the fact that their differences are usually presented as straightforward, such as in many introductory philosophy textbooks. Nonetheless, the question of how best to distinguish deductive from inductive arguments, and indeed whether there is a coherent categorical distinction between them at all, turns out to be considerably more problematic than commonly recognized. This article identifies and discusses a range of different proposals for marking categorical differences between deductive and inductive arguments while highlighting the problems and limitations attending each. Consideration is also given to the ways in which one might do without a distinction between two types of argument by focusing solely on the application of evaluative standards to arguments instead. (shrink)

This comprehensive text covers all the standard topics of the contemporary logic course--informal logic, classical deductive logic, induction and scientific reasoning, including the logical fallacies, legal reasoning, and the practice of argument analysis. Exceptionally fine examples and exercises illustrate and reinforce important points throughout. The text is accompanied by a Study Guide for students and an Instructor's Manual.

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)

Argumentation schemes are forms of argument that capture stereotypical patterns of human reasoning, especially defeasible ones like argument from expert opinion, that have proved troublesome to view deductively or inductively. Much practical work has already been done on argumentation schemes, proving their worth in A1 [19], but more precise investigations are needed to formalize their structures. The problem posed in this paper is what form justification of a given scheme, as having a certain precise structure of inference, should take. It (...) is argued that defeasible argumentation schemes require both a systematic and a pragmatic justification, of a kind that can only be provided by the case study method of collecting key examples of arguments of the types traditionally classified as fallacies, and subjecting them to comparative examination and analysis. By this method, postulated structures for schemes can be formulated as hypotheses to solve three kinds of problems: (1) how to classify such arguments into different types, (2) how to identify their premises and conclusions, and (3) how to formulate the critical questions used to evaluate each type of argument. (shrink)

Grennan bases his evaluation of arguments on two criteria: logical adequacy and pragmatic adequacy. He asserts that the common formal logic systems, while logically sound, are not very useful for evaluating everyday inferences, which are almost all deductively invalid as stated. Turning to informal logic, he points out that while more recent informal logic and critical thinking texts are superior in that their authors recognize the need to evaluate everyday arguments inductively, they typically cover only inductive fallacies, ignoring the (...) inductively sound patterns frequently used in successful persuasion. To redress these problems, Grennan introduces a variety of additional inductive patterns. Concluding that informal logic texts do not encourage precision in evaluating arguments, Grennan proposes a new argument evaluation procedure that expresses judgments of inferential strength in terms of probabilities. Based on theories of Stephen Toulmin, Roderick Chisholm, and John Pollock, his proposed system allows for a more precise judgment of the persuasive force of arguments. (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part of a (...) larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

Argumentation or reasoning is the act of rendering theses rationally justified or plausible, through appeal to specific premises and the use of logical inferences. The principal forms of logical inference are deductive, inductive, and abductive. The chapter outlines some common argumentative fallacies and discusses important modes of argumentation, such as the use of universalizing arguments, wedge arguments, arguments from authority, and arguments from analogy, arguing through thought experiments and allegories. In the light of the modern global turn, the (...) focus of research in the theory of reasoning and argumentation has shifted to the examination of how fundamental theses can be justified, as well as questions about how to engage in argumentation with people whose worldviews differ markedly from our own. Yet reasoning as a method of rational conviction still plays a decisive role in the comprehension, clarification, and critical questioning of one’s own positions, as well as that of others. (shrink)

Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.

_Critical Thinking_ is a comprehensive introduction to the essential skills of good reasoning, refined and updated through seven editions published over more than two decades. This concise edition offers a succinct presentation of the essential elements of reasoning that retains the rigor and sophistication of the original text. The authors provide a thorough treatment of such central topics as deductive and inductive reasoning, logical fallacies, how to recognize and avoid ambiguity, and how to distinguish what is relevant from (...) what is not. A companion website provides a range of interesting supplements, including interactive review materials, supplemental readings, and writing tips. (shrink)

There are passages in Fallacies suggesting a skeptical attitude to the very idea of inductive arguments, hence to the existence of inductive fallacies. Although the passages are brief and few in number, it would appear that Hamblin’s resistance stems from doubts about the existence of relations of inductive consequence. This paper attempts to find a case in which such skepticism might plausibly be grounded. The case it proposes is highly conjectural, but important if true. Its greater importance (...) lies in the threat it creates for the whole class of nonmonotonic logics. (shrink)

A leading expert in informal logic, Douglas Walton turns his attention in this new book to how reasoning operates in trials and other legal contexts, with special emphasis on the law of evidence. The new model he develops, drawing on methods of argumentation theory that are gaining wide acceptance in computing fields like artificial intelligence, can be used to identify, analyze, and evaluate specific types of legal argument. In contrast with approaches that rely on deductive and inductive logic (...) and rule out many common types of argument as fallacious, Walton’s aim is to provide a more expansive view of what can be considered "reasonable" in legal argument when it is construed as a dynamic, rule-governed, and goal-directed conversation. This dialogical model gives new meaning to the key notions of relevance and probative weight, with the latter analyzed in terms of pragmatic criteria for what constitutes plausible evidence rather than truth. (shrink)

What good is logic? -- Seventeen ways this book is different -- The two logics -- All of logic in two pages : an overview -- The three acts of the mind -- I. The first act of the mind : understanding -- Understanding : the thing that distinguishes man from both beast and computer -- Concepts, terms and words -- The problem of universals -- The comprehension and extension of terms -- II. Terms -- Classifying terms -- Categories -- (...) Predicables -- Division -- III. Material fallacies -- Fallacies of language -- Fallacies of diversion -- Fallacies of oversimplification -- Fallacies of argumentation -- Inductive fallacies -- Procedural fallacies -- Metaphysical fallacies -- Short story : love is a fallacy -- IV. Definition -- The nature of definition -- The rules of definition -- The kinds of definition -- The limits of definition -- V. Second act of the mind : judgment -- Judgments, propositions, and sentences -- What is truth? -- The four kinds of categorical propositions -- Logical form -- Euler's circles -- Tricky propositions -- The distribution of terms -- VI. Changing propositions -- Immediate inference -- Conversion -- Obversion -- Contraposition -- VII. Contradiction -- What is contradiction? -- The square of opposition -- Existential import -- Tricky propositions on the square -- Some practical uses of the square of opposition -- VIII. The third act of the mind : reasoning -- What does reason mean? -- The ultimate foundations of the syllogism -- How to detect arguments -- Arguments vs. explanations -- Truth and validity -- IX. Different kinds of arguments -- Three meanings of because -- The four causes -- A classification of arguments -- Simple argument maps -- Deductive and inductive arguments -- Combining deduction and induction : socratic method -- X. Syllogisms -- The structure and strategy of the syllogism -- The skeptics objection to the syllogism -- The empiricist's objection to the syllogism -- Demonstrative syllogisms -- How to construct convincing syllogisms -- XI. Checking syllogisms for validity -- By Euler's circles -- By Aristotle's six rules -- Barbara Celarent : mood and figure -- Venn diagrams -- XII. More difficult syllogisms -- Enthymemes : abbreviated syllogisms -- Sorites : chain syllogisms -- Epicheiremas : multiple syllogisms -- Complex argument maps -- XIII. Compound syllogisms -- Hypothetical syllogisms -- Reductio ad absurdum arguments -- The practical syllogism : arguing about means and ends -- Disjunctive syllogisms -- Conjunctive syllogisms -- Dilemmas -- XIV. Induction -- What is induction? -- Generalization -- Causal induction : Mill's methods -- Scientific hypotheses -- Statistical probability -- Arguments from analogy -- A fortiori and a minore arguments -- XV. Some practical applications of logic -- How to write a logical essay -- How to write a socratic dialogue -- How to have a socratic debate -- How to use socratic method on difficult people -- How to read a book socratically -- XVI. Some philosophical applications of logic -- Logic and theology -- Logic and metaphysics -- Logic and cosmology -- Logic and philosophical anthropology -- Logic and epistemology -- Logic and ethics. (shrink)

Introductory-level undergraduate classes in Logic or Critical Thinking are a staple in the portfolio of many Philosophy programs. A standard approach to these classes is to include teaching and learning activities focused on formal deductive and inductive logic, sometimes accompanied by teaching and learning activities focused on informal fallacies or argument construction. In this article, I discuss a proposal to include an additional element within these classes—namely, teaching and learning activities focused on intellectual virtues. After clarifying the proposal, (...) I identify three reasons in favor of implementing it and I discuss how to implement it, focusing on questions about pedagogical strategies and pedagogical resources. (shrink)

_Critical Thinking_ is a comprehensive and accessible introduction to the essential skills of good reasoning. The authors provide a thorough treatment of such central topics as deductive and inductive reasoning, logical fallacies, how to recognize and avoid ambiguity, and how to distinguish what is relevant from what is not. Later chapters discuss the application of critical thinking skills to particular topics and tasks, including scientific reasoning, moral reasoning, media analysis, and essay writing. This seventh edition is revised and (...) updated throughout, and includes a new chapter on legal reasoning as well as access to a companion website of additional questions and other useful resources. (shrink)

An outline of the material covered in courses on Formal and Informal Logic. The outline includes chapters on mathematical approaches to logic as well as on fallacies, deduction and induction, probability, and other major topics. Logic is traditionally taught by means of problem solving exercises, so the subject is well suited to a Schaum's Outline approach.

Improving Your Reasoning is an expanded version of Chapter 10 of the author's larger work, Principles of Logic. The first chapter of Improving Your Reasoning is a general survey of arguments--deductive and inductive, valid and invalid, syllogistic and nonsyllogistic--and serves as an introduction for the rest of the book which deals only with fallacies. The types of fallacies are divided by chapter into the following principal categories: begging the question, pseudoauthority, irrelevant appeals, confusion, faulty classification, political fallacies, and (...) inductive fallacies. Each of these categories is further divided into a comprehensive range of sub-categories, with each sub-category presented in a short and easily understandable section. For example, inductive fallacies are divided into hasty generalization, accident, false cause, gambler's, faulty analogy, central tendency, misleading percentages, and misleading totals. Problems and answers are provided. This book may be used as a supplementary text for introductory logic.--T. G. N. (shrink)

It has been said that there is no scholarly consensus as to why Aristotle’s logics of proof and refutation would have borne the title _Analytics._ But if we consulted Tarski’s (Introduction to logic and the methodology of deductive sciences, Oxford University Press, New York, 1941) graduate-level primer, we would have the perfect title for them: _Introduction to logic and to the methodology of deductive sciences._ There are two strings to Aristotle’s bow. The methodological string is the founding work (...) on the epistemology of science, and the logical string sets down conditions on the proofs that bring this knowledge about. The logic of proof presents a difficulty whose solution exceeds its theoretical reach. The logic of refutation takes the problem on board, and advances a solution whose execution is framed by fallacy-avoidance at the beginning and fallacy-adoption at the end. But with a difference: the avoidance-fallacies are of Aristotle’s own conception, whereas the adoption-fallacies, so judged in the modern tradition, aren’t fallacies at all for Aristotle. The avoidance-fallacies are begging the question and _ignoratio elenchi_, and the adoption-fallacies, fallacies in name only, are the _ad hominem_ and _ad ignorantiam_, an inductive turning in the first instance, and an abductive finish in the second. (shrink)

This paper is an evaluation of C. S. Peirce’s late essay “A Neglected Argument for the Reality of God”, based on the two logical values that he calls “productiveness” and “security.” After reviewing the unique logical form of “abduction” and noting that it is a formal fallacy—and so enjoys less “security” than deduction or induction—I turn to the extraordinary case of abduction that is found in “A Neglected Argument.” I argue that the productiveness of the Neglected Argument is found (...) in its ability to instigate practical results. The security of the Neglected Argument, on the other hand, is rooted in an activity Peirce calls “musement,” a kind of rational intuition. Moreover, I suggest that Peirce’s notion of “musement,” which has remained something of a mystery in Peirce studies, arose from hisearly reading of Friedrich von Schiller’s aesthetics. (shrink)

The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction to deduction. Haack compares (...) deduction to induction, and I will critically discuss her argument for the thesis that we cannot justify the principles of deduction next. In concluding I will defend the thesis that we can justify induction deductively relative to one end, and deduction inductively relative to a different end, and that we can do so in a non-circular way. Along the way I will show how we can understand deductive and inductive logic as normative theories, and I will briefly sketch an argument to the effect that there are only hypothetical, but no categorical imperatives. (shrink)

A Fortiori Logic: Innovations, History and Assessments is a wide-ranging and in-depth study of a fortiori reasoning, comprising a great many new theoretical insights into such argument, a history of its use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its purpose is nothing less than to lay the foundations for a new branch of logic and greatly develop it; and thus to once and for all dispel the many fallacious (...) ideas circulating regarding the nature of a fortiori reasoning. -/- The work is divided into three parts. The first part, Formalities, presents the author’s largely original theory of a fortiori argument, in all its forms and varieties. Its four (or eight) principal moods are analyzed in great detail and formally validated, and secondary moods are derived from them. A crescendo argument is distinguished from purely a fortiori argument, and similarly analyzed and validated. These argument forms are clearly distinguished from the pro rata and analogical forms of argument. Moreover, we examine the wide range of a fortiori argument; the possibilities of quantifying it; the formal interrelationships of its various moods; and their relationships to syllogistic and analogical reasoning. Although a fortiori argument is shown to be deductive, inductive forms of it are acknowledged and explained. Although a fortiori argument is essentially ontical in character, more specifically logical-epistemic and ethical-legal variants of it are acknowledged. -/- The second part of the work, Ancient and Medieval History, looks into use and discussion of a fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s approach to a fortiori argument is described and evaluated. There is a thorough analysis of the Mishnaic qal vachomer argument, and a reassessment of the dayo principle relating to it, as well as of the Gemara’s later take on these topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly acknowledged. Lists are drawn up of the use of a fortiori argument in the Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible and the Koran; and the specific moods used are identified. Moreover, there is a pilot study of the use of a fortiori argument in the Gemara, with reference to Rodkinson’s partial edition of the Babylonian Talmud, setting detailed methodological guidelines for a fuller study. There is also a novel, detailed study of logic in general in the Torah. -/- The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work of numerous (some thirty) recent contributors to a fortiori logic, as well as the articles on the subject in certain lexicons. Here, we discover that whereas a few authors in the last century or so made some significant contributions to the field, most of them shot woefully off-target in various ways. The work of each author, whether famous or unknown, is examined in detail in a dedicated chapter, or at least in a section; and his ideas on the subject are carefully weighed. The variety of theories that have been proposed is impressive, and stands witness to the complexity and elusiveness of the subject, and to the crying need for the present critical and integrative study. But whatever the intrinsic value of each work, it must be realized that even errors and lacunae are interesting because they teach us how not to proceed. -/- This book also contains, in a final appendix, some valuable contributions to general logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox. (shrink)

_The Critical Thinking Book_ covers not only standard topics such as definitions, fallacies, and argument identification, but also other pertinent themes such as consumer choice in a market economy and political choice in a representative democracy. Interesting historical asides are included throughout, as are images, diagrams, and reflective questions. A wealth of exercises is provided, both within the text and on a supplemental website for instructors. The author also offers additional exercises, videos, and other teaching and study materials that can (...) be digitally integrated into Learning Management Systems. (shrink)

This essay is basically divided into two parts. The first deals with the similarities between reductio ad absurdum arguments and slippery slope arguments. The chief example comes from Thomas Hobbes’s Leviathan, which advances an argument for the necessity of government for humane living. The second addresses some pedagogical concerns centered around another pair of arguments: the argument by complete enumeration and the argument by inductive generalization. The illustration for this pair comes from the arts. I finish with a suggestion (...) that pairs like the above can be as effectively used in shorter, non-regular critical reasoning or introductory logic courses as those in mid-term or summer courses. Such pairing can demonstrate a good use of mixing and matching deductive and non-deductive arguments in teaching logic. (shrink)

Judaic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the impartial perspective of a logician. Judaic Logic attempts to honestly estimate the extent to which the logic employed within Judaism fits into the general norms, and whether it has any contributions to make to them. The author ranges far and wide in Jewish lore, finding clear evidence of both inductive and deductive reasoning in the Torah and other books of the (...) Bible, and analyzing the methodology of the Talmud and other Rabbinic literature by means of formal tools which make possible its objective evaluation with reference to scientific logic. The result is a highly innovative work – incisive and open, free of clichés or manipulation. Judaic Logic succeeds in translating vague and confusing interpretative principles and examples into formulas with the clarity and precision of Aristotelean syllogism. Among the positive outcomes, for logic in general, are a thorough listing, analysis and validation of the various forms of a-fortiori argument, as well as a clarification of dialectic logic. However, on the negative side, this demystification of Talmudic/Rabbinic modes of thought (hermeneutic and heuristic) reveals most of them to be, contrary to the boasts of orthodox commentators, far from deductive and certain. They are often, legitimately enough, inductive. But they are also often unnatural and arbitrary constructs, supported by unverifiable claims and fallacious techniques. Many other thought-processes, used but not noticed or discussed by the Rabbis, are identified in this treatise, and subjected to logical review. Various more or less explicit Rabbinic doctrines, which have logical significance, are also examined in it. In particular, this work includes a formal study of the ethical logic (deontology) found in Jewish law, to elicit both its universal aspects and its peculiarities. With regard to Biblical studies, one notable finding is an explicit formulation (which, however, the Rabbis failed to take note of and stress) of the principles of adduction in the Torah, written long before the acknowledgement of these principles in Western philosophy and their assimilation in a developed theory of knowledge. Another surprise is that, in contrast to Midrashic claims, the Tanakh (Jewish Bible) contains a lot more than ten instances of qal vachomer (a-fortiori) reasoning. In sum, Judaic Logic elucidates and evaluates the epistemological assumptions which have generated the Halakhah (Jewish religious jurisprudence) and allied doctrines. Traditional justifications, or rationalizations, concerning Judaic law and belief, are carefully dissected and weighed at the level of logical process and structure, without concern for content. This foundational approach, devoid of any critical or supportive bias, clears the way for a timely reassessment of orthodox Judaism (and incidentally, other religious systems, by means of analogies or contrasts). Judaic Logic ought, therefore, to be read by all Halakhists, as well as Bible and Talmud scholars and students; and also by everyone interested in the theory, practise and history of logic. (shrink)

Despite the fact that the reductio ad absurdum argument is a valid deductive form, while the slippery slope argument is most often presented as a fallacious form of inductive argument, the two argument types bear some striking similarities. Investigation of these similarities reveals some more universal difficulties in the teaching of informal logic, and, in particular the difference between strong informal arguments and fallacious ones.

Since at least the 1938 publication of Hans Reichenbach’s Experience and Predication , there has been widespread agreement that, when discussing the beliefs that people have, it is important to distinguish contexts of discovery and contexts of justification. Traditionally, when one conflates the two contexts, the result is a “genetic fallacy”. This paper examines genealogical critiques and addresses the question of whether such critiques are fallacious and, if so, whether this vitiates their usefulness. The paper concludes that while there (...) may be one or more senses in which genealogical critiques are fallacious, this does not vitiate their value. (shrink)

Making Up Your Mind is oriented toward the writing of arguments. It gives students techniques that they can use to better understand, organize, and present their own thoughts. The book provides an exceptionally clear statement of what critical thinking adds to the study of logic, along with complete and systematic coverage of all crucial logical operators and major logical relations. It also offers exceptionally clear and informative discussions of the definition of argument, the distinction between induction and deduction, and the (...) role of emotion in argument. The second half of the book presents an argument outline which students can use to organize virtually any ethical argument. This outline is also used to illustrate the most important informal fallacies and how they can be avoided. In its closing chapters, the book discusses the nature of good evidence and good sources of evidence and their role in argument. Included are discussions of scientific method, the logical form of arguments about causal theories, and arguments from analogy. (shrink)

Designed for students with no prior training in logic, INTRODUCTION TO LOGIC AND CRITICAL THINKING offers an accessible treatment of logic that enhances understanding of reasoning in everyday life. The text begins with an introduction to arguments. After some linguistic preliminaries, the text presents a detailed analysis of inductive reasoning and associated fallacies. This order of presentation helps to motivate the use of formal methods in the subsequent sections on deductive logic and fallacies. Lively and straightforward prose assists (...) students in gaining facility with the sometimes challenging concepts of logic. By combining a sensitive treatment of ordinary language arguments with a simple but rigorous exposition of basic principles of logic, the text develops students' understanding of the relationships between logic and language, and strengthens their skills in critical thinking. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. (shrink)

In this paper I examine five distinctions between deductive and inductive arguments, concluding that the best of the five defines a deductive argument as one in which conclusive favorable relevance to its conclusion is attributed to its premises, and an inductive argument as any argument that is not deductive. This distinction, unlike its rivals, is both exclusive and exhaustive; permits both good and bad arguments of each kind; and is both useful and needed in evaluating (...) at least some arguments. (shrink)

This work is in two parts. The main aim of part 1 is a systematic examination of deductive, probabilistic, inductive and purely inductive dependence relations within the framework of Kolmogorov probability semantics. The main aim of part 2 is a systematic comparison of (in all) 20 different relations of probabilistic (in)dependence within the framework of Popper probability semantics (for Kolmogorov probability semantics does not allow such a comparison). Added to this comparison is an examination of (in all) (...) 15 purely inductive dependence relations. ————Part 1 leads in an axiomatic step-by-step development from the elementary classical truth value semantics of a sentential-logical language, called ‘L’, (chapter 1) to the elementary Kolmogorov probability semantics of L (chapter 2), which is then extended to four axiomatic semantical theories of dependence relations between the formulae of L. First the elementary Kolmogorov probability semantics of L is extended to a theory, called ‘Kdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 3). Then Kdd is extended to a theory, called ‘Kpd1’, of the degree to which formulae of L probabilistically depend on each other in regard to a given probability distribution on the set of all formulae of L (chapter 4). Kpd1, in its turn, gets extended to a theory, called ‘Kpd2’, of the relations of probabilistic dependence and independence, relativized to unary Kolmogorov probability functions defined on L (chapter 5). Then Kpd2 is extended to a theory, called ‘Kid’, of the relations of inductive dependence and inductive independence, again relativized to unary Kolmogorov probability functions defined on L (chapter 6). Finally, Kid is extended to a theory, called ‘Kpid’, of the relations of purely inductive positive and negative dependence, relativized to unary Kolmogorov probability functions defined on L (chapter 7). ——Chapter 1, which deals with the familiar notions of truth value functions, tautologies, consequence relations and relations of logical opposition, is naturally the shortest chapter of part 1.——In chapter 2, the elementary classical semantics of L is extended to the elementary Kolmogorov probability semantics of L, i.e. to an axiomatic theory of unary and of binary Kolmogorov probability functions defined on the set of formulae of L. Because of the elementary character of this theory, chapter 2 is also rather short.——Chapter 3 introduces the first theory on dependence relations, to wit: Kdd, the theory of deductive (in)dependence between formulae of L. I follow here the well-known idea of Popper and Miller, who have used it in a famous discussion on the nature of probabilistic support for their arguments that probabilistic support is deductive, not inductive. I develop Kdd in the form of about 100 theorems, making ample use of the fact that deductive independence is nothing but subcontrary opposition, and close with a remark on the fundamental difference between deductive and logical dependence—two relations the ideas of which are all too easily mixed up.——Chapters 4 and 5 deal extensively with the traditional ideas of probabilistic (in)dependence, applied to formulae rather than to events. As always, I proceed axiomatically in a step-by-step process under systematic viewpoints and obtain about 300 theorems in this way. In the formulation of the theorems, I took special care to state clearly and expressly so-called tacit assumptions, especially those concerning the probability values of the formulae said to be dependent on each other. These assumptions are usually missing in the literature, due either to economy of writing or to sloppiness of thinking. Presumably, both chapters contain little that is new, their value lying more in the systematic grouping and organic development of the theorems than in the newness of these.——In chapter 6, I extend the axiomatic theory about probabilistic (in)dependence which has been elaborated in chapter 5, to an axiomatic theory of inductive (in)dependence by requiring of the relation of inductive (in)dependence that it be probabilistic (in)dependence, but not also logical implication or logical opposition. I point out the differences between probabilistic and inductive (in)dependence by means of some 60 theorems and close my examination of inductive (in)dependence by considering its relationship to the notion of support in the philosophy of science.——Finally, in chapter 7, the last of part 1, I take the step from inductive dependence to what I call ‘purely inductive dependence’ by combining the idea of inductive dependence with that of deductive independence in a way which is suggested by writings of Popper and Miller. I arrive at two noteworthy theorems. Firstly, there is indeed no purely inductive support. But secondly, and perhaps amazingly, countersupport is purely inductive.————Whereas the probabilistic framework of part 1 of the present work is Kolmogorov probability semantics, the framework of part 2 is Popper probability semantics, which is not only worth examining as a fascinating alternative to orthodox Kolmogorov probability semantics, but also allows us to examine dependence relations more deeply, than Kolmogorov probability semantics does. Part 2 leads—again in an axiomatic step-by-step development—from the basic Popper probability semantics of L, called ‘Pb’, (chapter 8) via a probabilistic theory of logical attributes, called ‘Ps’, (chapter 9) to four axiomatic semantical theories of dependence relations between the formulae of L. First, Ps is extended to a theory, called ‘Pdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 10). Then Pdd is extended to a theory, called ‘Ppd’, of (in all) 20 relations of probabilistic (in)dependence, relativized to binary Popper probability functions defined on L (chapter 11). Ppd, in its turn, is extended to a theory, called ‘Pid’, of (in all) 10 relations of inductive dependence, again relativized to binary Popper probability functions defined on L (first part of chapter 12). Finally, Pid is extended to a theory, called ‘Ppid’, of (in all) 15 relations of purely inductive positive and negative dependence, relativized to binary Popper probability functions defined on L (second part of chapter 12).——Chapter 8, the first chapter of part 2 of the present work, is entirely preparatory. It introduces the axioms and about 180 theorems (150 of them together with their proofs) of basic Popper probability semantics in order to set this kind of semantics under way.——Then, in chapter 9, basic Popper probability semantics is extended to a probabilistic theory of logical properties of and relations between the formulae of L. Although I think that the way I did this extension is of some interest in itself, the main task of chapter 9 is again a preparatory one: to yield the indispensable lemmata (about 90 in number) for the theorems concerning probabilistic dependence relations in chapter 11 and concerning inductive dependence relations in chapter 12.——Chapter 10 brings the extension of Ps to the theory Pdd of deductive (in)dependence. Only half a dozen theorems are noted here for later use in the Pdd-extensions Ppd and Ppid. In view of the over 100 theorems already gained on this topic in the Kolmogorovian framework (cf. chapter 3), a similar extensive elaboration of Pdd would have been superfluous.——Chapter 11 is the most important one of part 2. It consists of a systematic comparison of 20 probabilistic (in)dependence concepts by means of about 230 theorems, obtained within the axiomatic theory Ppd, which is built up as an extension of Pdd. The main points of comparison were: differences in logical strength; reflexivity and symmetry; behaviour under the condition that the probability values of the formulae in question are extreme. It turned out that each of the examined concepts violates a strong and straightforward version of the intuitive requirement that probabilistic dependence should go with logical dependence. Whereas the corresponding chapter 5 in part 1 of the present work may not have led to new theorems, chapter 11 yields dozens of them in the process of comparison of concepts of dependence and independence which had—as far as I know—never before been treated in a single theoretical framework. With Popper probability semantics, this framework has become available, and here I have simply made full use of it.——In chapter 12, I extend the theory Ppd of probabilistic (in)dependence to the theories Pid and Ppid of inductive and purely inductive dependence, in a way very similar to that in which I have extended the theory Kpd2 to the theories Kid and Kpid in chapters 6 and 7. The first main result of Kpid (roughly: there is no purely inductive support) could be repeated for four of the five purely inductive positive dependence relations considered in chapter 12, whereas the second main result of Kpid (roughly: there is purely inductive countersupport ) could be repeated for each of the five examined purely inductive negative dependence relations. Chapter 12 closes with a brief recapitulation and critical discussion of the main results. (shrink)

There are two necessary conditions for effective learning. First, learning must occur within a context. Second, a learner must be genuinely interested in the subject matter (that is, motivated to learn it). In the case of critical thinking, studying problems in a textbook fails to meet both of these conditions. This paper presents a strategy for supplying context and motivation to critical thinking students: a semester-long investigation of the Kennedy assassination. After reviewing the perils of traditional, non-contextual teaching methods, the (...) author argues that this strategy captures students’ attention as an engaging “whodunit” of great historical importance. Moreover, the prodigious amount of evidence associated with the assassination provides students with ample opportunity to learn and practice critical thinking skills. Sifting through forensic reports, eye- and earwitness testimony, expert opinions, autopsy findings, and the Zapruder film teaches students the basics of informal and formal logic (e.g. evaluating appeals to authority, finding inconsistencies and contradictions, identifying false cause fallacies, and recognizing good and bad inductive and deductive arguments). After reviewing the course materials and requirements, the author concludes by offering several alternate themes for a critical thinking class which are capable of accomplishing the same pedagogical goals. (shrink)

In this paper I focus on two contrasting concepts of deduction and induction that have appeared in introductory (formal) logic texts over the past 75 years or so. According to the one, deductive and inductive arguments are defined solely by reference to what arguers claim about the relation between the premises and the conclusions. According to the other, they are defined solely by reference to that relation itself. Arguing that these definitions have defects that are due to their (...) simplicity, I develop definitions that remove these defects by assigning a combination of roles to both arguers’ claims concerning the premises/conclusion relation and the relation itself. Along the way I also present and briefly defend definitions of both deductive and inductive validity that are significantly different from the norm. (shrink)

This article demonstrates the fallacy of legal deduction as a method which is supposed to guarantee the certainty and predictability of the law. The Author asserts that legal deduction is in fact not of a logical nature. Their premises are of an uneven character or else one of them must be created in a non-mechanical way. This in turn makes legal deduction that is comprehended as a mode of inference that is infallible, provided its premises are true / valid (...) nothing more than misunderstanding and fallacy. In addition, in this paper, the outcomes of legal deduction are shown to be highly dependent on the direct and indirect context under the threat of their being utterly absurd. Since the lack of fixity and clarity, these contexts, however, may lead one to madness, i. e. at least unless she or he abandons the idea that only logical types of inferences govern legal deduction and are solely responsible for its outcomes. (shrink)

This focused text is directed consistently towards teaching students to write their own arguments so as to better understand their own thoughts and present them to others in a clear written form. The text also provides a distinctive discussion of the role of emotion in argument under the concept of "emotional intelligence," and includes a wide range of exercises. In introducing students to the nature of argument (and especially ethical argument), Making Up Your Mind features a comprehensive introduction to the (...) logical forms of assertions and the most common forms of expression in English. The book then shows how to use all the main terms of argument, and provides a brief introduction to the most common forms of syllogism. The deductive and inductive aspects of argument are treated, and students are taught a basic technique of testing arguments for validity. Making Up Your Mind provides an argument outline, which can be used to organize virtually any ethical argument. This argument outline also provides a realistic context in which to study the most important informal fallacies and learn how to avoid them. In its closing chapters, the book discusses the nature of good evidence and good sources of evidence and their role in argument. Included are discussions of scientific method, the logical form of arguments about causal theories, and arguments from analogy. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy, argument from fallacy. Also known as argumentum ad logicam, argument to logic, fallacy fallacy, and fallacist's fallacy, the argument from fallacy occurs when one reasons that because the argument for some conclusion is fallacious, the conclusion of that argument is false. Truth and falsity are features of claims. Fallacies are errors in reasoning, not errors about truth or falsity. That is, if someone has (...) committed a fallacy, then he has made an error in reasoning; but it does not follow that he has made a factual error. As a deductive argument, fallacy of affirming the consequent is invalid ‐ one cannot draw/infer the conclusion from the premises ‐ and yet the conclusion is true. As such, it should be clear that poor reasoning (committing a fallacy) does not entail a false conclusion. (shrink)

In a priori analogies, the analogue is constructed in imagination, sharing certain properties with the primary subject. The analogue has some further property clearly consequent on those shared properties. Ceteris paribus the primary subject has that property also. The warrant involves non-empirical, e.g., moral intuition but is also defeasible. The argument is thus neither deductive nor inductive, but an additional type. In an inductive analogy, the analogues back the warrant from below. Distinguishing these two types of arguments (...) by analogy gives epistemic evaluative factors primacy over resemblance factors in classifying arguments—a prescient insight on Govier’s part. (shrink)

'You shouldn't drink too much. The Earth is round. Milk is good for your bones.' Are any of these claims true? How can you tell? Can you ever be certain you are right? For anyone tackling philosophical logic and critical thinking for the first time, Critical Thinking: An Introduction to Reasoning Well provides a practical guide to the skills required to think critically. From the basics of good reasoning to the difference between claims, evidence and arguments, Robert Arp and Jamie (...) Carlin Watson cover the topics found in an introductory course. Now revised and fully updated, this Second Edition features a glossary, chapter summaries, more student-friendly exercises, study questions, diagrams, and suggestions for further reading. Topics include: the structure, formation, analysis and recognition of arguments deductive validity and soundness inductive strength and cogency inference to the best explanation truth tables tools for argument assessment informal and formal fallacies With real life examples, advice on graduate school entrance exams and an expanded companion website packed with additional exercises, an answer key and help with real life examples, this easy-to-follow introduction is a complete beginner's tool set to good reasoning, analyzing and arguing. Ideal for students in basic reasoning courses and students preparing for graduate school. (shrink)

Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. (...) Perennial philosophic problems, epistemic and ontic, related to argumentations are put in perspective. So much of what has been regarded as logic is seen to be involved in the study of argumentations that logic may be usefully defined as the systematic study of argumentations, which is virtually identical to the quest of objective understanding of objectivity. (shrink)

Current practice in logic increasingly accords recognition to abductive, presumptive or plausible arguments, in addition to deductive and inductive arguments. But there is uncertainty about what these terms exactly mean, what the differences between them are (if any), and how they relate. By examining some analyses ofthese terms and some of the history of the subject (including the views of Peirce and Cameades), this paper sets out considerations leading to a set of definitions, discusses the relationship of these (...) three forms of argument to argumentation schemes and sets out a new argumentation scheme for abductive argument. (shrink)

Lively, comprehensive, and contemporary, The Voice of Reason: Fundamentals of Critical Thinking covers three principal areas: thought and language, systematic reasoning, and modes of proof. It employs highly accessible explanations and a multitude of examples drawn from social issues and various academic fields, showing students and other readers how to construct and criticize arguments using the techniques of sound reasoning. The Voice of Reason examines the traditional elements of the field and also explores new ground. The first section of the (...) book elucidates the relationship between thought and language, explaining how words function. It discusses meaning, connotation, vagueness, ambiguity, and definition, identifying the linguistic elements that can produce mistakes in thinking. The next section describes the rules of systematic reasoning, examining such topics as truth, relevance, and adequacy; deductive logic ; and induction. Sixteen fallacies in thinking are also described through extensive illustrations and applications. The final section of the book offers a unique study of what constitutes proof in several different areas--including politics, advertising, law, and social issues--as well as in the academic disciplines of literature, science, history, and ethics. The author describes the various rules of evidence, using essays by major figures in each field as examples. An ideal text for courses in critical thinking, informal logic, and reasoning and writing, The Voice of Reason offers numerous pedagogical features including a host of examples; assignments, exercises, and puzzles at both the halfway point and at the end of each chapter; cartoons and quotations throughout; and practical applications of theoretical concepts. An extensive Instructor's Manual contains answers to the exercises that appear throughout the text. (shrink)

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)

This paper critically examines a formal argument against deducing ‘ought’-judgments from ‘is’-judgments, an argument suggested by a literal reading of a famous passage in Hume'sTreatise of Human Nature. According to this argument, judgments of the two kinds have different logical structures (i.e., their subjects are differently related to their predicates) and this difference disallows cross-categorical deductive inferences. I draw on Fregean accounts of the ‘is’- copula and on syntactical interpretations of ‘ought’-judgments that have become standard in deontic logic to (...) argue that twentieth century work in philosophical grammar and logic casts doubt on all three of the argument's premises. (shrink)

In this paper, I respond to the paper “The Validation of Induction” by Robert Pargetter and John Bigelow (Australasian Journal of Philosophy, 75:1, 1997), in which the authors propound the thesis that the arguments commonly thought of as good inductive arguments “properly construed, are deductively valid”. I maintain that they have not established this claim, and neither have they established a number of associated but logically independent claims that they make about inductive arguments and inductive inferences.

In the middle of a conference on the logic of science, an eminent biologist once said: “Does it not bother you guys that we scientists do not use any logic at all.” This statement was meant to be a friendly provocation, but there also was a serious message. Scientists often say that the logical analyses are exercises in formal logic and fail to illuminate what the scientists are doing, actual scientific practice. This recurring complaint, although not completely as I will (...) suggest, has not gone unnoticed in the philosophy of science. Indeed, the current trend in analytic philosophy of science as well as in teaching the method of science has been away from logic as a means of illuminating scientific inquiry. (shrink)

A simple summary of the difference between induction and deduction.

This paper defends the view that the classification of an argument as being deductive ought to rest exclusively upon psychological considerations; specifically, upon whether the argument's author holds certain beliefs. This account is justified on theoretical and pedagogical grounds, and situated within a general taxonomy of competing proposals. Epistemological difficulties involved in the application of psychological definitions are recognized but claimed to be ineliminable from the praetice of argumentation. The paper concludes by discussing embryonic arguments where the author's relevant (...) beliefs are not sufficiently fine-grained so as to accord the argument deductive or inductive status. (shrink)

Conductive arguments, as a separate category of reasoning, has experienced a revival. In 2010, the University of Windsor’s Centre for Research in Reasoning, Argumentation, and Rhetoric dedicated a two-day symposium to the topic and later published the proceedings. In this article, I argue against the existence of conductive arguments as a usefully distinct type of argument. Some of what are deemed conductive arguments are simply inductive arguments and some are best construed as subsets of the constituents of what is (...) commonly called a position paper. (shrink)

The definitions of ‘deduction’ found in virtually every introductory logic textbook would encourage us to believe that the inductive/deductive distinction is a distinction among kinds of arguments and that the extension of ‘deduction’ is a determinate class of arguments. In this paper, we argue that that this approach is mistaken. Specifically, we defend the claim that typical definitions of ‘deduction’ operative in attempts to get at the induction/deduction distinction are either too narrow or insufficiently precise. We conclude by (...) presenting a deflationary understanding of the inductive/deductive distinction; in our view, its content is nothing over and above the answers to two fundamental sorts of questions central to critical thinking. (shrink)