In this paper I argue that the debate over the purported distinction between deductive and inductive arguments can be bypassed because making the distinction is unnecessary for successfully evaluating arguments. I provide a foundation for doing logic that makes no appeal to the distinction and still performs all the relevant tasks required of an analysis of arguments. I also reply to objections to the view that we can dispense with the distinction. Finally, I conclude that the distinction between inductive and (...) deductive arguments is not one of the most important and fundamental ideas in logic, but rather is unnecessary. (shrink)

Background: Clinical reasoning is at the core of medical practice and entangled in a conceptual confusion. The duality theory in probability allows to evaluate its objective and subjective aspects. -/- Objectives: To conduct a systematic review of the literature about clinical reasoning in decision making in medical education and to propose a "reasoning based on the Bayesian rule" (RBBR). -/- Methods: A systematic review on PubMed was conducted (until February 27, 2022), following a strict methodology, by a (...) researcher experienced in systematic review. The RBBR, presented in the discussion section, was constructed in his undergraduate dissertation in Philosophy at Minas Gerais Federal University. Heart failure was used as example. -/- Results: Of 3,340 articles retrieved, 154 were included: 24 discussing the uncertainty condition, 87 on vague concepts (case discussion, heuristics, list of cognitive biases, choosing wisely) subsumed under the term "art", and 43 discussing the general idea of inductive or deductive reasoning. RBBR provides coherence and reproducibility rules, inference under uncertainty, and learning rule, and can incorporate those vague terms classified as "art", arguments and evidence, from a subjective perspective about probability. -/- Conclusions: This systematic review shows that reasoning is grounded in uncertainty, predominantly probabilistic, and reviews possible errors of the hypothetico-deductive reasoning. RBBR is a two-step probabilistic reasoning that can be taught. The Bayes theorem is a linguistic tool, a general rule of reasoning, diagnosis, scientific communication and review of medical knowledge according to new evidence. (shrink)

The plausible reasoning class (called the JSM-reasoning in honour of John Stuart Mill) is described. It implements interaction of three forms of non-deductive procedures  induction, analogy and abduction. Empirical induction in the JSM-reasoning is the basis for generation of hypotheses on causal relations (determinants of social behaviour). Inference by analogy means that predictions about previously unknown properties of objects (individual’s behaviour) are inferred from causal relations. Abductive inference is performed to check on the explanatory adequacy of (...) generated hypotheses. To recognize rationality of respondents’ opinion deductive inference is used. Plausible reasoning, semantics of argumentation logic and deductive recognition of opinion rationality represent logical tool for cognitive sociology problems. (shrink)

In this paper I want to cast doubt on the claim that there is a legitimate process of reasoning to the best explanation which can serve as an alternative to either straightforward inductive reasoning or a combination of inductive and deductive reasoning. I shall argue a) that paradigmatic cases of acceptable arguments to the best explanation must be considered enthymemes and b) that when the suppressed premises are made explicit we have all of the premises we need (...) to present either a straightforward inductive argument or an argument employing both induction and deduction. (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 (categorical, hypothetical, and disjunctive); and induction (cause and effect, analogy, generalization, and hypothesis). 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)

A number of single- and dual-process theories provide competing explanations as to how reasoners evaluate conditional arguments. Some of these theories are typically linked to different instructions—namely deductive and inductive instructions. To assess whether responses under both instructions can be explained by a single process, or if they reflect two modes of conditional reasoning, we re-analysed four experiments that used both deductive and inductive instructions for conditional inference tasks. Our re-analysis provided evidence consistent with a single process. In two (...) new experiments we established a double dissociation of deductive and inductive instructions when validity and plausibility of conditional problems were pitted against each other. This indicates that at least two processes contribute to conditional reasoning. We conclude that single-process theories of conditional reasoning cannot explain the observed results. Theories that postulate at least two processes are needed to account for our findings. (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 (categorical, hypothetical, and disjunctive); and induction (cause and effect, analogy, generalization, and hypothesis). 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)

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)

Most authors seem to assume there are two types of argument, deductive ones and inductive ones. But there is wide disagreement about how those two are to be distinguished from one another, and about whether there are two kinds of logic, deductive and inductive, relevant to evaluating arguments of each type. In this paper, I argue that all attempts to distinguish a logic of inductive arguments from a logic of deductive ones fail. I argue that the distinction between induction and (...) deduction is not a logical distinction, but is rather a pragmatic one, pertaining to how “tight” the argument needs to be in order to provide adequate support of its conclusion within the context in which the argument occurs. The concepts found in deductive logic can be legitimately applied to any and all arguments, but in many cases deductive validity is not required for an argument to fulfill its purpose in providing strong reasons to accept its conclusion. Deductively invalid arguments can still be “tight” enough to be valuable, depending on the context in which they occur. (shrink)

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)

We present a reference model for finding evidence of discrimination in datasets of historical decision records in socially sensitive tasks, including access to credit, mortgage, insurance, labor market and other benefits. We formalize the process of direct and indirect discrimination discovery in a rule-based framework, by modelling protected-by-law groups, such as minorities or disadvantaged segments, and contexts where discrimination occurs. Classification rules, extracted from the historical records, allow for unveiling contexts of unlawful discrimination, where the degree of burden over protected-by-law (...) groups is evaluated by formalizing existing norms and regulations in terms of quantitative measures. The measures are defined as functions of the contingency table of a classification rule, and their statistical significance is assessed, relying on a large body of statistical inference methods for proportions. Key legal concepts and reasonings are then used to drive the analysis on the set of classification rules, with the aim of discovering patterns of discrimination, either direct or indirect. Analyses of affirmative action, favoritism and argumentation against discrimination allegations are also modelled in the proposed framework. Finally, we present an implementation, called LP2DD, of the overall reference model that integrates induction, through data mining classification rule extraction, and deduction, through a computational logic implementation of the analytical tools. The LP2DD system is put at work on the analysis of a dataset of credit decision records. (shrink)

Seldom does human reasoning fit the standards of deduction. Yet logicians have tended to use the strict standards of deductive validity for assessing all inferences. _Within Reason_ develops instead a way of assessing arguments and inferences that is directly appropriate to the non-deductive forms people regularly use. It uses analogy, and argument from analogy, to provide a thread that unites various forms: raising objections, inductions of various sorts, arguments to explanation, and arguments to action. The discussion is developed progressively, (...) at each stage building on the skills learned previously. And at each stage the book suggetss ways of assessing the strength of reasoning. Most of the examples are taken from the great texts of the Western tradition. In the exercises that form an integral part of each chapter an even broader range of writing is presented, offering instructors an extraordinary variety of texts at various levels ot assign to their students. The thesis implicit in the book is that induction, arguments to explanation and arguments to action are all sophisticated forms of arguments from analogy. Burbidge is concerned not simply to warn against the misuse of non-deductive reasoning but also to develop a more positive theory that allows us both to better udnerstand the workings of non-deductive reasoning, and to better employ it. (shrink)

This paper defends a new argument in the spirit of Golemon and Graber’s Deductive No-Miracles Argument (DNMA) for scientific realism, recently criticized by Kok Yong Lee. While Lee argues that the DNMA is invalid or leads to a collapse in probability assignments, I develop an Inductive No-Miracles Argument (INMA) that preserves logical strength without relying on abductive inference or explanatory premises. By introducing an “approximately equal” probabilistic operator (≈), I show how probabilistic reasoning can license a strong inductive inference (...) without collapsing probability calculus. The resulting INMA satisfies the desiderata motivating the DNMA and clarifies how probabilistic reasoning can underwrite realist inference without appeal to explanatory virtue. Moreover, the structure argued for seems ripe for use in other contexts where avoiding abduction in lieu of less theory-laden probability is attractive, such as fine-tuning arguments and evolutionary debunking arguments. (shrink)

A popular three-stage argument appraisal strategy calls for (1) identifying the parts of the argument, (2) classifYing the argument as deductive, inductive, or some other type, and (3) appraising the argument using the standards appropriate for the type. This strategy fails for a number of reasons. I propose a comprehensive alternative approach that distinguishes between inductive, deductive, and other standards; calls for the successive application of standards combined with assumption-ascription, according to policies that depend for their selection on the goals (...) of the appraiser; and provides for qualified reasoning. (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)

This chapter offers a short logic lesson as an introduction to what philosophers and other critical thinkers do when they offer and criticize arguments. Logic is the study of the principles of correct reasoning associated with the formation and analysis of arguments. The creators of South Park, for the most part, know these logical principles. They purposely violate them, though, to show the absurdities contained in certain beliefs, opinions, ideas, and arguments. In fact, much of South Park's humor concerns (...) logical violations and the absurdities, contradictions, and problems that result. The authors consider some basics of logic using examples from South Park episodes, and show some differences between correct and incorrect reasoning. There are two main kinds of arguments, deductive arguments and inductive arguments. The authors insist on the need to form good arguments, and the need to evaluate the arguments of others. (shrink)

This interdisciplinary work is a collection of major essays on reasoning: deductive, inductive, abductive, belief revision, defeasible, cross cultural, conversational, and argumentative. They are each oriented toward contemporary empirical studies. The book focuses on foundational issues, including paradoxes, fallacies, and debates about the nature of rationality, the traditional modes of reasoning, as well as counterfactual and causal reasoning. It also includes chapters on the interface between reasoning and other forms of thought. In general, this last set (...) of essays represents growth points in reasoning research, drawing connections to pragmatics, cross-cultural studies, emotion and evolution. (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)

ExtractSome logic textbooks say, as if it were the received wisdom, that inductive arguments are partly defined by the thinker's intentions. The claim is that an inductive argument is one where the premises are intended to make the conclusion likely. This contrasts with a deductive argument, where the premises are intended to entail the conclusion. However, since entailing is one way of making more likely, a further way to distinguish induction is needed. The addition offered is that the premises are (...) not intended to entail the conclusion. Taken together, the result is: An argument is inductive if the premises are intended to make the conclusion likely, but not intended to entail the conclusion.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.NOTE ON INDUCTIONVolume 12, Issue 33Ted ParentDOI: https://doi.org/10.1017/S1477175612000322Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. NOTE ON INDUCTIONVolume 12, Issue 33Ted ParentDOI: https://doi.org/10.1017/S1477175612000322Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. NOTE ON INDUCTIONVolume 12, Issue 33Ted ParentDOI: https://doi.org/10.1017/S1477175612000322Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation. (shrink)

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The argument (...) view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn’t been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton’s fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position. (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)

In this paper, we set out to investigate the following question: if science relies heavily on induction, does philosophy of science rely heavily on induction as well? Using data mining and text analysis methods, we study a large corpus of philosophical texts mined from the JSTOR database (n = 14,199) in order to answer this question empirically. If philosophy of science relies heavily on induction, just as science supposedly does, then we would expect to find significantly more inductive arguments than (...) deductive arguments and abductive arguments in the published works of philosophers of science. Using indicator words to classify arguments by type (namely, deductive, inductive, and abductive arguments), we search through our corpus to find patterns of argumentation. Overall, the results of our study suggest that philosophers of science do rely on inductive inference. But induction may not be as foundational to philosophy of science as it is thought to be for science, given that philosophers of science make significantly more deductive arguments than inductive arguments. Interestingly, our results also suggest that philosophers of science do not rely on abductive arguments all that much, even though philosophers of science consider abduction to be a cornerstone of scientific methodology. (shrink)

This text introduces university students to the philosophical ethos of critical thinking, as well as to the essential skills required to practice it. The authors believe that Critical Thinking should engage students with issues of broader philosophical interest while they develop their skills in reasoning and argumentation. The text is informed throughout by philosophical theory concerning argument and communication—from Aristotle's recognition of the importance of evaluating argument in terms of its purpose to Habermas's developing of the concept of communicative (...) rationality. The authors' treatment of the topic is also sensitive to the importance of language and of situation in shaping arguments, and to the necessity in argument of some interplay between reason and emotion. Unlike many other texts in this area, then, Good Reasons for Better Arguments helps to explain both why argument is important and how the social role of argument plays an important part in determining what counts as a good argument. If this text is distinctive in the extent to which it deals with the theory and the values of critical thinking, it is also noteworthy for the thorough grounding it provides in the skills of deductive and inductive reasoning; the authors present the reader with useful tools for the interpretation, evaluation and construction of arguments. A particular feature is the inclusion of a wide range of exercises, rich with examples that illuminate the practice of argument for the student. Many of the exercises are self testing, with answers provided at the back of the text; others are appropriate for in-class discussion and assignments. Challenging yet accessible, Good Reasons for Better Arguments brings a fresh perspective to an essential subject. (shrink)

There are two meaning of the term “argument” – in the broad sense and in the narrow legal sense. In the first case, it is proof as the establishment of truth, the correspondence between the statement and reality. In the second case. it is evidence that serves to convince a judge and jurors that statements are true. At the same time, argument in the narrow sense can be considered from three sides: a) as a means of persuasion, b) as the (...) basis of persuasion, and c) as a process of proving. Since forensic evidence must meet not only legal, but also logical requirements, this article examines the use of rules of inference by lawyers. Leaving induction, analogy and abduction out of the current study, the authors focus on deduction in legal works. The subtleties of the use of deductive reasoning in the process of proving are considered. The analysis involved the reasoning of lawyers used to defend the accused in the trial, both famous and modern, as well as the construction of reasoning by fiction characters. It is shown that the correct construction of deductive reasoning ensures the effectiveness of argumentation. The examples show the complex use of deductive reasoning in legal argumentation. Lawyers consistently apply syllogisms, smoothly moving from one type to another, combining a categorical syllogism or a purely conditional syllogism with a conditionally categorical or divisive-categorical syllogism. The process of proof does not consist of a single deductive conclusion, but connects various syllogisms into a consistent chain, ensuring the effectiveness of judicial argumentation. (shrink)

Abstract In order to be a general theory of human cognition, the theory of mental models needs to accommodate a variety of forms of reasoning in addition to deduction. The mental model theory of induction is a crucial step in establishing generality. After suggesting that the theory of mental models can also account for abduction and analogy, the paper points out that inductive performance is likely to be constrained both by the nature of the representation used and by strategic (...) factors. Since human cognition involves the communication of arguments, a final section explores the relationship between the theory of mental models and the notion of an argument. It proposes that models can contain tokens of inductive arguments which can be referred to in the course of other arguments. (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)

I set up two axiomatic theories of inductive support within the framework of Kolmogorovian probability theory. I call these theories ‘Popperian theories of inductive support’ because I think that their specific axioms express the core meaning of the word ‘inductive support’ as used by Popper (and, presumably, by many others, including some inductivists). As is to be expected from Popperian theories of inductive support, the main theorem of each of them is an anti-induction theorem, the stronger one of them saying, (...) in fact, that the relation of inductive support is identical with the empty relation. It seems to me that an axiomatic treatment of the idea(s) of inductive support within orthodox probability theory could be worthwhile for at least three reasons. Firstly, an axiomatic treatment demands from the builder of a theory of inductive support to state clearly in the form of specific axioms what he means by ‘inductive support’. Perhaps the discussion of the new anti-induction proofs of Karl Popper and David Miller would have been more fruitful if they had given an explicit definition of what inductive support is or should be. Secondly, an axiomatic treatment of the idea(s) of inductive support within Kolmogorovian probability theory might be accommodating to those philosophers who do not completely trust Popperian probability theory for having theorems which orthodox Kolmogorovian probability theory lacks; a transparent derivation of anti-induction theorems within a Kolmogorovian frame might bring additional persuasive power to the original anti-induction proofs of Popper and Miller, developed within the framework of Popperian probability theory. Thirdly, one of the main advantages of the axiomatic method is that it facilitates criticism of its products: the axiomatic theories. On the one hand, it is much easier than usual to check whether those statements which have been distinguished as theorems really are theorems of the theory under examination. On the other hand, after we have convinced ourselves that these statements are indeed theorems, we can take a critical look at the axioms—especially if we have a negative attitude towards one of the theorems. Since anti-induction theorems are not popular at all, the adequacy of some of the axioms they are derived from will certainly be doubted. If doubt should lead to a search for alternative axioms, sheer negative attitudes might develop into constructive criticism and even lead to new discoveries. I proceed as follows. In section 1, I start with a small but sufficiently strong axiomatic theory of deductive dependence, closely following Popper and Miller (1987). In section 2, I extend that starting theory to an elementary Kolmogorovian theory of unconditional probability, which I extend, in section 3, to an elementary Kolmogorovian theory of conditional probability, which in its turn gets extended, in section 4, to a standard theory of probabilistic dependence, which also gets extended, in section 5, to a standard theory of probabilistic support, the main theorem of which will be a theorem about the incompatibility of probabilistic support and deductive independence. In section 6, I extend the theory of probabilistic support to a weak Popperian theory of inductive support, which I extend, in section 7, to a strong Popperian theory of inductive support. In section 8, I reconsider Popper's anti-inductivist theses in the light of the anti-induction theorems. I conclude the paper with a short discussion of possible objections to our anti-induction theorems, paying special attention to the topic of deductive relevance, which has so far been neglected in the discussion of the anti-induction proofs of Popper and Miller. (shrink)

Applying good inductive rules inside the scope of suppositions leads to implausible results. I argue it is a mistake to think that inductive rules of inference behave anything like 'inference rules' in natural deduction systems. And this implies that it isn't always true that good arguments can be run 'off-line' to gain a priori knowledge of conditional conclusions.

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.

Chemical visualizations and models are special kinds of situated, inductive arguments. In this paper, I examine several historical case studies—an archive of images from museums, special collections, and popular magazines—as examples of emergent practices of physical modeling as theoretical play which became the basis for molecular biology and structural chemistry. Specifically, I trace a legacy of visualization tools that starts with Archibald Scott Cooper and Friedrich Kekulé in the late 1800s, crystallizes as material manipulatives in Kekulé’s student Jacobus Henricus Van’t (...) Hoff and his folded paper “toys,” is legitimized in the California lab of Linus Pauling, and is glorified in the popular imaginary with James Watson and Francis Crick’s model of DNA. My tracing then follows several threads into contemporary modeling practices. I ultimately argue that modeling play, originally outside of the boundary of deductive, positivist science, is now an accepted mode of inductive reasoning in these related chemical fields. (shrink)

This text introduces university students to the philosophical ethos of critical thinking, as well as to the essential skills required to practice it. The authors believe that Critical Thinking should engage students with issues of broader philosophical interest while they develop their skills in reasoning and argumentation. The text is informed throughout by philosophical theory concerning argument and communication—from Aristotle’s recognition of the importance of evaluating argument in terms of its purpose to Habermas’s developing of the concept of communicative (...) rationality. The authors’ treatment of the topic is also sensitive to the importance of language and of situation in shaping arguments, and to the necessity in argument of some interplay between reason and emotion. Unlike many other texts in this area, then, _Good Reasons for Better Arguments_ helps to explain both why argument is important and how the social role of argument plays an important part in determining what counts as a good argument. If this text is distinctive in the extent to which it deals with the theory and the values of critical thinking, it is also noteworthy for the thorough grounding it provides in the skills of deductive and inductive reasoning; the authors present the reader with useful tools for the interpretation, evaluation and construction of arguments. A particular feature is the inclusion of a wide range of exercises, rich with examples that illuminate the practice of argument for the student. Many of the exercises are self testing, with answers provided at the back of the text; others are appropriate for in-class discussion and assignments. Challenging yet accessible, _Good Reasons for Better Arguments_ brings a fresh perspective to an essential subject. (shrink)

Although people can recognize and make deductively valid arguments on occasion, one perspective is that there might be no psychologically valid distinction between the deductive correctness of a conclusion and its inductive strength. This perspective is called reasoning imperialism: the attempts of one theoretical camp to assimilate the data explained by another. This chapter shows that an element crucial to extending a mental models theory of deduction to handle inductive-strength judgments is unavailable, namely, the specification of constraints on what (...) counts as relevant counterexamples to the inductive inference under consideration. It is argued that reasoning imperialism may not work for deduction and induction, for people may hold different sorts of arguments to different sorts of standards and evaluate them in qualitatively different sorts of ways. (shrink)

Passmore examines a number of kinds of argument frequently used by philosophers, in an attempt to find out whether there is any kind of reasoning which is especially appropriate for philosophy. He discusses the ways in which philosophers have used deduction, induction, reminders about obvious facts, infinite regress arguments, paradigm case arguments, claims that certain views are self-refuting, and accusations of meaninglessness. Numerous illustrations of these moves in argument, drawn from philosophers from Plato to Popper, help to make this (...) an interesting essay in the philosophy of philosophy.--J. B. S. (shrink)

Number theory abounds with conjectures asserting that every natural number has some arithmetic property. An example is Goldbach’s Conjecture, which states that every even number greater than 2 is the sum of two primes. Enumerative inductive evidence for such conjectures usually consists of small cases. In the absence of supporting reasons, mathematicians mistrust such evidence for arithmetical generalisations, more so than most other forms of non-deductive evidence. Some philosophers have also expressed scepticism about the value of enumerative inductive evidence in (...) arithmetic. But why? Perhaps the best argument is that known instances of an arithmetical conjecture are almost always small: they appear at the start of the natural number sequence. Evidence of this kind consequently suffers from size bias. My essay shows that this sort of scepticism comes in many different flavours, raises some challenges for them all, and explores their respective responses. (shrink)

It is well known that Kant used inductive arguments in his pre-critical philosophy, for example, in his 1764 Prize essay according to which metaphysics should follow Newton’s “analytic method” of natural science. However, his critical metaphysics of nature also uses several inductive tools, contrary to the widespread belief that his apriorism is only compatible with deductive reasoning. In this chapter, we pre- sent three cases of inductive reasoning found in his critical metaphys- ics of nature. First, Kant carries (...) out an “experiment of pure reason” in Preface B of the Critique of Pure Reason to rule out transcendental realism via the cosmological antinomy. Second, he argues in the Ap- pendix to the Transcendental Dialectic that the transcendental ideas of traditional metaphysics can only serve as regulative principles for expanding our knowledge of nature, and he uses an inference to the best explanation (IBE) in the Metaphysical Foundations of Natural Science. Third, at the end of the Critique, he claims that these prin- ciples support doctrinal belief. The chapter shows how each of these cases of inductive reasoning can be understood as a kind of IBE and discusses the significance of Kant’s arguments. (shrink)

Moderate realists hold that scientific theories are truthlike, rather than exactly true. Although scientific realism has been challenged by arguments such as the pessimistic induction, moderate realism hasn’t been challenged directly on the grounds that it makes scientific progress rely on inferences from theories that are only truthlike. This paper shows that moderate realism is incompatible with the claim that deductive arguments from scientific theories are reliable. Using truthlike claims as the premises of some patterns of deductive reasoning renders (...) the argument dramatically unreliable. The conclusion is not guaranteed to be true. Nor is the conclusion guaranteed to be at least as truthlike as the premises. Nor even is the conclusion shown to be likely to be true. This is because the consequences of truthlike theories are neither guaranteed to be true, nor even more likely to be truthlike than not. Truthlike theories cannot function like true theories in deductive arguments; instead they function as radically false theories would. In short, truthlike theories behave exactly like radically false theories for the purposes of their deductive consequences. And since scientists would not trust deductions from radically false theories, they should not trust deductions from truthlike theories either. Furthermore, this applies to a wide range of logics and patterns of deductive argument. The moderate realist must either reject bivalence, deny that theories are truth-apt, or accept that scientific theories are not used in deductive arguments. (shrink)

I. The argument from design or ‘teleological argument’ purports to be an inductive proof for the existence of God, proceeding from the evidence of the order exhibited by natural phenomena to the probable conclusion of a rational agent responsible for producing that order. The argument was severely criticized by David Hume in his Dialogues Concerning Natural Religion, and it was widely conceded that Hume's objections had cast serious doubt on the adequacy of the teleological argument, if not destroyed its credibility (...) entirely. However, there has been a recent reappraisal of this claim by R. G. Swinburne, who maintains that none of Hume's criticisms have any validity against a ‘carefully articulated version of the argument’. Using an analogical argument based on temporal regularities rather than on spatial regularities, Swinburne claims to have shown that the teleological argument is a legitimate inference to the best explanation whose force depends only on the strength of the analogy and on the degree to which the resulting theory makes explanation of empirical matters simpler and more coherent. Moreover, he claims to have shown that the argument provides support for the Christian monotheistic hypothesis and not merely for the weak claim that the universe was designed. This is an important claim since it has long been thought that Hume's most devastating blow was dealt when he showed that the teleological argument provides just as much support for the negation of certain propositions considered essential to Christian monotheism as it does for their affirmation. (shrink)

Hilary Kornblith (1993) has recently offered a reliabilist defense of the use of the Law of Small Numbers in inductive inference. In this paper I argue that Kornblith's defense of this inferential rule fails for a number of reasons. First, I argue that the sort of inferences that Kornblith seeks to justify are not really inductive inferences based on small samples. Instead, they are knowledge-based deductive inferences. Second, I address Kornblith's attempt to find support in the work of Dorrit Billman (...) and I try to show that close attention to the workings of her computational model reveals that it does not support Kornblith's argument. While the knowledge required to ground the inferences in question is perhaps inductively derived, Billman's work does not support the notion that small samples provide a reliable basis for our generalizing inferences. (shrink)

This book is a version of a D.Phil. thesis done at Oxford under the direction of Richard Swinburne and Basil Mitchell. Its basic premise is one shared by both these philosophers, namely, the putative inadequacy of traditional deductive and inductive arguments in philosophical theology. The central argument of the book is that the alternative proposed by Mitchell is superior to the one proposed by Swinburne. Roughly half the book is devoted to supporting this claim. Particular attention is given to showing (...) that Bayes' theorem as used by Swinburne is inadequate for assessing the probability of a theistic hypothesis. Other chapters are devoted to informal reasoning in philosophical theology, criteria of explanatory adequacy within a nondeductive framework, causality, and God as a logically necessary being. In these chapters the author attempts to develop further Mitchell's work. A final chapter undertakes to defend the book's basic thesis against some positions that in various ways contradict the author's approach. It includes replies to two attacks on the very idea of philosophical theology by J. L. Mackie and Stewart Sutherland, a response to John Hick's most recent attack on the personhood of God, and a criticism of the version of Thomistic philosophical theology held by E. L. Mascall. (shrink)

The social exchange theory of reasoning, which is championed by Leda Cosmides and John Tooby, falls under the general rubric “evolutionary psychology” and asserts that human reasoning is governed by content-dependent, domain-specific, evolutionarily-derived algorithms. According to Cosmides and Tooby, the presumptive existence of what they call “cheater-detection” algorithms disconfirms the claim that we reason via general-purpose mechanisms or via inductively acquired principles. We contend that the Cosmides/tooby arguments in favor of domain-specific algorithms or evolutionarily-derived mechanisms fail and that (...) the notion of a social exchange rule, which is central to their theory, is not correctly characterized. As a consequence, whether or not their conclusion is true cannot be established on the basis of the arguments they have presented. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume and the Lockean Background: Induction and the Uniformity Principle David Owen Introduction What has come to be called Hume's problem of induction is special in many ways. It is arguably his most important and influential argument, especially when seen in its overall context of the more general argument about causaUty. It has come to be one of the great "standard problems" ofphilosophyandyetis,by most accounts, almost unique in having (...) no ancient precursor. Interestingly, the argument is frequently presented in terms that the author never used. Itis difficult for us not to think of the problem in terms of the contrast between deductive vs. inductive reasoning (or logic, or whatever). But this is a contrast nowhere to be found in Hume: he talks of demonstrative vs. probable (or moral) reasoning. Hume uses the word "induction" only twice in the Treatise1 and in neither case is it clear that the word is used toreportapieceofprobablereasoning.2One ofthefewoccurrences of"deduce" or "deducing" occurs in the second Enquiry, where he talks about "following the experimental method, and deducing general maximsfrom acomparisonofparticularinstances,"3hardlyaparadigm of what we would call deductive reasoning.4 Many modern studies of Hume that make a real attempt to understand what Hume meant by demonstration and probability, in the context of his argument about induction, tend towards the ahistorical,6 treating Hume's writings as contemporary texts. But failure to take into account some of the background concerning the nature of demonstrative and probable reason makes it unlikely, I think, that we can understand Hume's argument. Part ofthe problem is the failure to identify Hume's targets in that famous negative argument about induction (vague reference is sometimes made to the "rationalists") and part of the problem is identifying the role the uniformity principle plays in Hume's famous argumentand thelightitsheds on the conception ofprobablereasoning Hume was attacking. In this paper I want to argue that a careful look at Locke solves some ofthese problems: he has a well developed view ofdemonstrative and probable reasoning, his confidence in conformity as a ground of probability is a Ukely target of Hume's attack and his Volume XVIII Number 2 179 DAVID OWEN accountshedsmuchlightonwhatrole the principleofuniformitymight play in Hume's account.6 Of course, at a certain level of philosophical abstraction it is irrelevant whether we have understood what Hume "really meant." Theproblemofinductionhas emergedas a central onein epistemology, philosophical logic, and philosophy of science. It would be an interesting question in philosophical historiography to trace the development ofthe "problem" from Hume's time to our own but that is not my task here. I trust one needs no justification for taking an historical look at a famous problem rather than tackling the problem head-on in one's own terms. But if one is needed, here is mine: sometimes, by looking at a problem from a different, historical perspective, one sees a different problem or afamiliar problem in a new light. One's philosophical horizons are broadened. Furthermore, one may make an interesting historical discovery, or at least draw some interesting historical connections. I take it as uncontroversial that Locke, following Descartes, rejected a formal, logical account of demonstrative reasoning. Instead ofusing a formal, syllogistic account ofhow two propositions can entail a third, Locke concentrated on the relation two ideas bear one to another.7 Thus a demonstration, for Locke, getsits force, notfrom what we would call a deductive relation between one set of propositions (.the premises) and anotherproposition (the conclusion), butrather from the relation one idea bears to another, either directly, or via a chain of intermediate ideas. It is true that Locke frequently talks of inferring one proposition from another, but this is always cashed out in terms of relations ofideas via a chain ofintermediate ideas.8 It is also true that Locke occasionally uses the terms "deduce" and "deduction." But these are never used in our sense that has to do with formal deductive validity. Rather, they are simply used loosely in the informal sense of "argue" or "infer," and "argument" or "inference."9 In the rest of this paper, all uses ofthe word"deduction" andits cognates shouldbe taken as having the modern sense, unless flagged as having "Locke... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:@ @ Notes and Dlscussaons A NOTE ON CHARLES PEIRCE'S THEORY OF INDUCTION By "Peirce's theory of induction," I refer to a system or collection of ideas which Peirce formulated about the nature and validity of inductive inference or inductive reasoning. This system or collection of ideas covers Peirce's writings from 1867 to 1905.1 During this period of his long philosophical career from 1857 to 1914, Peirce wrote (...) his most important papers on the logic of science and probability. ~ These papers, though only a minor portion of Peirce's philosophical works, constitute a self-explanatory unit of study, simply because they deal with one single subject: the validity of synthetic inference. In the year 1867, Peirce wrote his paper "On the Natural Classification of Arguments," which provides a natural introduction to his treatment of inference and its validity in syllogistic terms and to his trichotomy of inference into deduction, induction, and hypothesis. Through the year 1877 to 1878, Peirce wrote a series of papers on "Illustrations of the Logic of Science." Beside the well-known "The Fixation of Belief" and "How to Make our Ideas Clear," there are four other important but comparatively little discussed papers which are essentially concerned with the logic of science and probability. They are in the following order: "Doctrine of Chances" (with corrections, 1893 and notes, 1910), "The Probability of Induction" (with corrections, 1893), "Deduction, Induction, and Hypothesis" (with corrections, 1893), and "The Order of Nature." In these papers, Peirce laid out his rationale for the validity of ampliative or synthetic inference and indicated a justification of induction in terms of probability. He also made explicit his conception of probabilty in terms of empirical frequency. But very often his ideas concerning the validity of synthetic inference appear disconnected and do not fit into a consistent, not to say wellorganized, whole. It was not until 1883 that Peirce wrote a comparatively systematic treatise on his general theory concerning the validity of ampliative or synthetic inference. This is his "A Theory of Probable inference," in which we find Peirce's statement of what a probable inference is and his argument that inductive inference is valid on account of its being a probable inference. After the year 1883, Peirce's philosophical writings appear to bear little upon his earlier problems in logic of science and probubility. But here and there we find a variety of topics under which Peirce touched the problem of justifying kinds of inference. One significant feature among these is Peirce's recurrent distinction between kinds of induction, a distinction which he had never made in his earlier writings. The distinction is between a "crude induction" (or "pooh-pooh" argument ), a "quantitative induction," and a "qualitative induction." This distinc1See the "Chronological Listing of Peirce's Papers Directly Bearing upon Induction and Probability" in the appendix. 2The earfiest of his papers which we have is dated 1857,and his philosophical activity continued until his death in 1914. [361] 362 HISTORY OF PHILOSOPHY tion is found in the following three short papers: "Three Kinds of Induction" (from "The Logic of Drawing History from Ancient Documents," 1901), "Kinds of Induction" (1903), and "The Varieties and Validity of Induction," (c. 1905). What Peiree calls a "crude induction" is an inference which concludes a universal generalization from what has been found in common in a group of instances. It is induction by simple enumeration. A quantitative induction is an inference from our knowledge of a statistical proportion of individual things having a certain character in a given sample to a conclusion regarding that in the population, from which the sample is chosen. ~ A qualitative induction, on the other hand, is a method of ascertaining factual truths by postulating hypotheses and confirming them on the basis of relevant evidences. That all these three forms of inference are considered induction by Peirce is due to the fact that they do not usually have the form of deduction, and they usually give rise to generalizations which are not deductively warranted by their premises. They differ, nevertheless, because they have different bases for generalizations and their generalizations have different contents. 4 In the light of Peirce's distinction between these three forms... (shrink)

Whereas an inference (deductive as well as inductive) is usually viewed as being valid in virtue of its argument form, the present paper argues that scientific reasoning is material inference, i.e., justified in virtue of its content. A material inference is licensed by the empirical content embodied in the concepts contained in the premises and conclusion. Understanding scientific reasoning as material inference has the advantage of combining different aspects of scientific reasoning, such as confirmation, discovery, and explanation. (...) This approach explains why these different aspects (including discovery) can be rational without conforming to formal schemes, and why scientific reasoning is local, i.e., justified only in certain domains and contingent on particular empirical facts. The notion of material inference also fruitfully interacts with accounts of conceptual change and psychological theories of concepts. (shrink)

Essential to Peirce's distinction among three kinds of reasoning, deduction, induction and abduction, is the claim that each is correlated to a unique species of validity irreducible to that of the others. In particular, abductive validity cannot be analyzed in either deductive or inductive terms, a consequence of considerable importance for the logical and epistemological scrutiny of scientific methods. But when the full structure of abductive argumentation — as viewed by the mature Peirce — is clarified, every inferential step (...) in the process can be seen to dissolve into familiar forms of deductive and inductive reasoning. Specifically, the final stage is a special type of practical inference which, if correct, is deductively valid, while the creative phase, surprisingly, is not inferential at all. In neither is abduction a type of inference to the best explanation. The result is a major reassessment of the relevance of Peirce's views to contemporary methodological studies. (shrink)

This commentary agrees with Mercier and Sperber's (M&S's) thesis on the argumentative function of reasoning but suggests that an account of argument strength is required. A Bayesian account of argument strength (Hahn & Oaksford 2007) shows how the deployment of deductive fallacies, weak inductive arguments, and judgment fallacies such as base-rate neglect, can all be rationally defended in the right argumentative context.

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.

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)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (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)

How do you tell what’s right from what’s wrong? Can you always? What’s the difference between deduction, induction, and abduction? What are the best techniques for making an argument logically sound? In this fascinating little book, the smallest on its subject ever produced, philosopher Earl Fontainelle explores the ancient art of discursive Logic and demonstrates some of the techniques that have long been used to triumph over the debates and deceptions that assail us every day. Filled with helpful examples of (...) good and bad reasoning, Logic is an invaluable introduction to a defining human characteristic. (shrink)