The wider topic to which the content of this paper belongs is that of the relationship between formal logic and real argumentation. Of particular potential interest in this connection are held to be substantive arguments constructed by philosophers reputed equally as authorities in logical theory. A number of characteristics are tentatively indicated by the author as likely to be encountered in such arguments. The discussion centers afterwards, by way of specification, on a remarkable piece of argument quoted in Cicero’s (...) dialog On Divination and ascribed to Stoic thinkers. The Stoics’ formal theory of inference is summarily referred to in this context, with special emphasis on their basic deductive schemata (‘indemonstrables’), some of them recognizable as links in the overall structure of the quoted argument. The main lines of Cicero’s criticism of the Stoic argument are next commented upon, with emphasis on his implied view as to the requirements of a good argument. Towards the end of the paper, a few considerations are added on the changes in the prevailing style of argumentation conspicuous in the three famous Roman Stoics. (shrink)

The article focuses on the New Rhetoric’s concept of quasi-logical arguments imitating logical or mathematical demonstrations, and examines it from point of view of pragma-dialectics as a device contributing towards resolving the difference of opinion. It is shown that the category of quasi-logical arguments cannot be considered as an argument scheme or a united type of strategic maneuvering. It is suggested to consider the category of quasi-logical arguments as a cluster of specific strategic maneuvers increasing the efficiency of arguments under (...) certain circumstances. This approach is demonstrated in a case study of pragma-dialectical analysis of the quasi-logical scheme of probability. (shrink)

The ability to analyze arguments is critical for higher-level reasoning, yet previous research suggests that standard university education provides at best modest improvements in students’ analytical reasoning abilities. What techniques are most effective for cultivating these skills? Here we investigate the effectiveness of a 12-week undergraduate seminar in which students practice a software-based technique for visualizing the logical structures implicit in argumen- tative texts. Seminar students met weekly to analyze excerpts from contemporary analytic philosophy papers, completed argument visualization problem (...) sets, and received individualized feedback on a weekly basis. We found that Seminar students improved substantially more on LSAT Logical Reasoning test forms than Control students (d = .71, p < .001), suggesting that learning how to visualize arguments in the seminar led to large generalized improvements in students’ analytical reasoning skills. Moreover, blind scoring of final essays from Seminar students and Control students, drawn from a parallel lecture course, revealed large differences in favor of seminar students (d = 0.87, p = .005). Seminar students understood the arguments better, and their essays were more accurate and effectively structured. Taken together, these findings deepen our understanding of how visualizations support logical reasoning, and provide a model for improving analytical reasoning pedagogy. (shrink)

The article focuses on the new rhetoric category of quasi-logical arguments, defined as arguments similar to logical or mathematical demonstrations, and therefore having an effect on the audience. Connecting the similarity of arguments to formal demonstrations with the claim of effect on audience is conceived in this article as the thesis of effectiveness of quasi-logical arguments. The components of the thesis are reconstructed and analyzed, and their precise definitions are proposed. The analysis shows that the category of quasi-logical arguments is (...) ambiguously defined and currently includes three different concepts based on a different understanding of similarity. Subsequently, it is showed that based on Perelman and Olbrechts-Tyteca’s works, the explanation of quasi-logical arguments’ effect on an audience can be offered in terms of socially shared standards of community or in terms of individual processing of arguments. It is shown that these explanations can be in conflict each other regarding the assumption of the addressee’s acquaintance with formal principles. (shrink)

Logic, Argumentation & Reasoning explores the links between Humanities and the Social Sciences, with theories including, decision and action theory as well as cognitive sciences, economy, sociology, law, logic, and philosophy of sciences. It’s two main ambitions are to develop a theoretical framework that will encourage and enable interaction between disciplines as well as to federate the Humanities and Social Sciences around their main contributions to public life: using informed debate, lucid decision-making and action based on reflection. The series (...) welcomes research from the analytic and continental traditions, putting emphasis on four main focus areas: • Argumentation models and studies • Communication, language and techniques of argumentation • Reception of arguments, persuasion and the impact of power • Diachronic transformations of argumentative practices The Series is developed in partnership with the Maison Européenne des Sciences de l’Homme et de la Société (MESHS) at Nord - Pas de Calais and the UMR-STL: 8163 (CNRS). Proposals should include : • A short synopsis of the work or the introduction chapter • The proposed Table of Contents • The CV of the lead author(s) • If available: one sample chapter We aim to make a first decision within 1 month of submission. In case of a positive first decision the work will be provisionally contracted: the final decision about publication will depend upon the result of the anonymous peer review of the complete manuscript. We aim to have the complete work peer-reviewed within 3 months of submission. The series discourages the submission of manuscripts that contain reprints of previous published material and/or manuscripts that are below 150 pages / 85,000 words. (shrink)

We introduce a general approach for representing and reasoning with argumentation-based systems. In our framework arguments are represented by Gentzen-style sequents, attacks between arguments are represented by sequent elimination rules, and deductions are made according to Dung-style skeptical or credulous semantics. This framework accommodates different languages and logics in which arguments may be represented, allows for a flexible and simple way of expressing and identifying arguments, supports a variety of attack relations, and is faithful to standard methods of drawing (...) conclusions by argumentation frameworks. Altogether, we show that argumentation theory may benefit from incorporating proof theoretical techniques and that different non-classical formalisms may be used for backing up intended argumentation semantics. (shrink)

This book presents a comprehensive analysis of Kant’s justification of the categorical imperative. The book contests the standard interpretation of Kant’s views by arguing that he never abandoned his view about this as expressed in his Groundwork. It is distinctive in the way in which it places Kant’s argument in the context of his transcendental philosophy as a whole, which is essential to understand it as an argument from within human agential self-understanding. The book reviews that existing literature, then presents (...) a logical construction of Kant’s argument, which it defends by examining what Kant has to say about synthetic a priori practical propositions in the context of his transcendental philosophy as a whole, and by a detailed examination of how he presents his argument in the Second Critique and the Groundwork. Particular attention is given to the views of two scholars who share many of the views expressed in this book: Klaus Steigleder and Michael Wolff. Special attention is also given to the views of Owen Ware, who, while sharing many of our arguments has a very different overall view. The concluding chapter provides a statement about the validity of Kant’s argument. (shrink)

This book presents a comprehensive analysis of Kant’s justification of the categorical imperative. The book contests the standard interpretation of Kant’s views by arguing that he never abandoned his view about this as expressed in his Groundwork. It is distinctive in the way in which it places Kant’s argument in the context of his transcendental philosophy as a whole, which is essential to understand it as an argument from within human agential self-understanding. The book reviews that existing literature, then presents (...) a logical construction of Kant’s argument, which it defends by examining what Kant has to say about synthetic a priori practical propositions in the context of his transcendental philosophy as a whole, and by a detailed examination of how he presents his argument in the Second Critique and the Groundwork. Particular attention is given to the views of two scholars who share many of the views expressed in this book: Klaus Steigleder and Michael Wolff. Special attention is also given to the views of Owen Ware, who, while sharing many of our arguments has a very different overall view. The concluding chapter provides a statement about the validity of Kant’s argument. (shrink)

Logic: Techniques of Formal Reasoning, 2/e is an introductory volume that teaches students to recognize and construct correct deductions. It takes students through all logical steps--from premise to conclusion--and presents appropriate symbols and terms, while giving examples to clarify principles. Logic, 2/e uses models to establish the invalidity of arguments, and includes exercise sets throughout, ranging from easy to challenging. Solutions are provided to selected exercises, and historical remarks discuss major contributions to the theories covered.

In this paper, we present a survey of the development of the technique of argument diagramming covering not only the fields in which it originated - informal logic, argumentation theory, evidence law and legal reasoning – but also more recent work in applying and developing it in computer science and artificial intelligence. Beginning with a simple example of an everyday argument, we present an analysis of it visualised as an argument diagram constructed using a software tool. In the context (...) of a brief history of the development of diagramming, it is then shown how argument diagrams have been used to analyze and work with argumentation in law, philosophy and artificial intelligence. (shrink)

This paper analyses a hitherto unknown technique of using logic diagrams to create argument maps in eristic dialectics. The method was invented in the 1810s and -20s by Arthur Schopenhauer, who is considered the originator of modern eristic. This technique of Schopenhauer could be interesting for several branches of research in the field of argumentation: Firstly, for the field of argument mapping, since here a hitherto unknown diagrammatic technique is shown in order to visualise possible situations of arguments in (...) a dialogical controversy. Secondly, the art of controversy or eristic, since the diagrams do not analyse the truth of judgements and the validity of inferences, but the persuasiveness of arguments in a dialogue. (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)

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

The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free logic and supervaluations), and apply the (...) resulting approach to accommodate semantic paradoxes. (shrink)

In this paper, we introduce the methodology and techniques of meta-argumentation to model argumentation. The methodology of meta-argumentation instantiates Dung’s abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung’s basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung’s theory of abstract argumentation to itself, by instantiating Dung’s (...) abstract arguments with meta-arguments using a technique called flattening. We characterize the domain of instantiation using a representation technique based on soundness and completeness. Finally, we distinguish among various instantiations using the technique of specification languages. (shrink)

Perfect for students with no background in logic or philosophy, Simple Formal Logic provides a full system of logic adequate to handle everyday and philosophical reasoning. By keeping out artificial techniques that aren’t natural to our everyday thinking process, Simple Formal Logic trains students to think through formal logical arguments for themselves, ingraining in them the habits of sound reasoning. Simple Formal Logic features: a companion website with abundant exercise worksheets, study supplements (including flashcards for symbolizations and for deduction (...) rules), and instructor’s manual two levels of exercises for beginning and more advanced students a glossary of terms, abbreviations and symbols. This book arose out of a popular course that the author has taught to all types of undergraduate students at Loyola University Chicago. He teaches formal logic without the artificial methods–methods that often seek to solve farfetched logical problems without any connection to everyday and philosophical argumentation. The result is a book that teaches easy and more intuitive ways of grappling with formal logic–and is intended as a rigorous yet easy-to-follow first course in logical thinking for philosophy majors and non-philosophy majors alike. (shrink)

This is an introductory guidebook to the basic principles of how to construct good arguments and how to criticeze bad ones. It is non-technical in its approach and is based on 150 key examples, each discussed and evaluated in clear, illustrative detail. Professor Walton, a leading authority in the field of informal logic, explains how errors, fallacies, and other key failures of argument occur. He shows how correct uses of argument are based on sound strategies for reasoned persuasion and critical (...) responses. Among the many subjects covered are: forms of valid argument, relevance, appeals to emotion, personal attack, uses and abuses of expert opinion, problems in deploying statistics, loading terms, equivocation, arguments from analogy, and techniques of posing, replying to, and criticizing questions. The book will be ideally suited to courses in informal logic and in the introduction to philosophy. It will also prove valuable to studetns of pragmatics, rhetoric, and speech communication. (shrink)

This paper develops a logical theory that unifies all three standard types of argumentative attack in AI, namely rebutting, undercutting and undermining attacks. We build on default justification logic that already represents undercutting and rebutting attacks, and we add undermining attacks. Intuitively, undermining does not target default inference, as undercutting, or default conclusion, as rebutting, but rather attacks an argument’s premise as a starting point for default reasoning. In default justification logic, reasoning starts from a set of premises, which is (...) then extended by conclusions that hold by default. We argue that modeling undermining defeaters in the view of default theories requires changing the set of premises upon receiving new information. To model changes to premises, we give a dynamic aspect to default justification logic by using the techniques from the logic of belief revision. More specifically, undermining is modeled with belief revision operations that include contracting a set of premises, that is, removing some information from it. The novel combination of default reasoning and belief revision in justification logic enriches both approaches to reasoning under uncertainty. By the end of the paper, we show some important aspects of defeasible argumentation in which our logic compares favorably to structured argumentation frameworks. (shrink)

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

ABSTRACT The logic of humor has been acknowledged as an essential dimension of every joke. However, what is the logic of jokes, exactly? The modern theories of humor maintain that jokes are characterized by their own logic, dubbed “pseudo,” “playful,” or “local,” which has been the object of frequent criticisms. This article intends to address the limitations of the current perspectives on the logic of jokes by proposing a rhetorical approach to humorous texts. Building on the traditional development of Aristotle’s (...) almost neglected view of jokes as surprising enthymemes, the former are analyzed as rhetorical arguments. Like enthymemes, jokes are characterized by natural inferences that can be represented as topics, and quasi-formalized in argumentation theory as argumentation schemes. Like rhetorical arguments, jokes express a reason in support of different types of conclusions and proceed from distinct kinds of reasoning and semantic relations. (shrink)

In this paper, we introduce the methodology and techniques of metaargumentation to model argumentation. The methodology of meta-argumentation instantiates Dung's abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung's basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung's theory of abstract argumentation to itself, by instantiating Dung's abstract (...) arguments with meta-arguments using a technique called flattening. We characterize the domain of instantiation using a representation technique based on soundness and completeness. Finally, we distinguish among various instantiations using the technique of specification languages. (shrink)

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

William Parry conceived in the early thirties a theory of entail-
ment, the theory of analytic implication, intended to give a formal expression to the idea that the content of the conclusion of a valid argument must be included in the content of its premises. This paper introduces a system of analytic, paraconsistent and quasi-classical propositional logic that does not validate the paradoxes of Parry’s analytic implication. The interpretation of the expressions of this logic will be given in terms of a (...) four-valued semantics,and its proof theory will be provided by a system of signed semantic tableaux that incorporates the techniques developed to improve the efficiency of the tableaux method for many-valued logics.
1. Introduction. (shrink)

In elementary logic textbooks, Venn diagrams are used to analyze and evaluate the validity of syllogistic arguments. Although the method of Venn diagrams is shown to be a powerful analytical tool in these textbooks, it still has limitations. On the one hand, such method fails to represent singular statements of the form, “a is F.” On other hand, it also fails to represent identity statements of the form, “a is b.” Because of this, it also fails to give an account (...) of the validity of some obviously valid arguments that contain these types of statements as constituents. In this paper, owing to the developments in the literature on Venn diagrams, we offer a way of supplementing the rules of the Venn diagram found in textbooks, and show how this retooled Venn diagram technique could account for the problem cases. (shrink)

The covenant -- Signs and precedents -- The Sunna of God -- Rules, commands, and reasons why -- Legal arguments -- Comparison -- Contrast -- Categorical arguments -- Conditional and disjunctive arguments -- Technical terms and debating technique -- Conclusions.

During the past decade there has been a very effective campaign against any explanation of remembering whose basic concept is that of a causally mediating trace. This paper attempts to provide such an explanation by presenting an explicit deductive argument for the existence of the memory trace. The conclusion is shown to follow from reasonable, empirical assumptions of which the most interesting is a spatiotemporal contiguity thesis. Set-theoretic techniques are used to provide a framework of analysis and probabilistic definitions (...) of some causal notions, as that of a causal chain, are presented. (shrink)

In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. A previous edition of this book appeared under the title (...) _Natural Deduction_. This new edition adds clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration. (shrink)

This article considers individual rights and fundamental tenets of the criminal justice system in the context of DNA evidence, in particular recent advancements in genomics that have significantly advanced law enforcement investigative capabilities in this area. It discusses a technique known as Investigative Genetic Genealogy (IGG) which utilizes genomic data held by commercial direct-to-consumer ancestry and health companies to investigate the identity of suspects linked to serious crimes. Using this technique, even if only a small proportion of the population (e.g. (...) 5%) has submitted genomic data to these companies, almost anyone in the population can be identified. We discuss this phenomenon in the context of the existing literature and arguments in relation to universal forensic DNA databases, as well as relevant recent developments in both liberal democracies and authoritarian states. We introduce the concept of a quasi-universal forensic DNA database and consider associated implications for the criminal justice system and society from the perspectives of privacy, the right not to self-incriminate, joint rights, and collective responsibility. (shrink)

In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. A previous edition of this book appeared under the title (...) _Natural Deduction_. This new edition adds clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration. (shrink)

In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. A previous edition of this book appeared under the title (...) _Natural Deduction_. This new edition adds clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration. (shrink)

A structure (M, $ ,...) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal (...) ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1. (shrink)

Discursive (or discussive) logic, D₂, introduced by Jaśkowski, is widely recognized as a first formal approach to paraconsistency. Jaśkowski applied a quite extraordinary technique at that time to describe his logic. He neither gave a set of the axiom schemata nor presented a direct semantics for D₂ but used a translation function to express his philosophical and logical intuitions. Discursive logic was defined by an interpretation in the language of S₅ of Lewis. The aim of this paper is to present (...) a modified system of the discursive logic that allows some of the weaker versions of Duns Scotus's thesis to be valid. The initial idea is to consider a different characteristic of the connective of negation. We introduce both a direct semantics and an axiomatization of the new system, prove the key metatheorems, and describe labeled tableaux for the system. (shrink)

An instantia is a technique to refute other's arguments, found in many tracts from the latter half of the twelfth century. An instantia has (or appears to have) the same form as the argument to be refuted and its falsity is more evident than that of the argument.Precursors of instantiae are among the teachings of masters active in the first half of the century. These masters produce counter-arguments against various inferential forms in order to examine their validity. But the aim (...) of producing counter-arguments change in the latter half of the century into refuting other's arguments to win in debate by any means available. Logicians of that period do not care whether the counter-arguments (instantiae) are sophistical or not, viz. the falsity of instantiae is or is not due to the flaw common to the argument to be refuted.Many instantiae they produce involve logical entanglements into which they themselves have little clear insight. Some instantiae and the attempts to explain them grows into the new theories in the “terminist texts” around 1200 A.D., when instantia literature itself disappears. Some instantiae and the issues they raise have no place in terminist texts, and sink into oblivion. (shrink)

Logic: Techniques of Formal Reasoning, 2/e is an introductory volume that teaches students to recognize and construct correct deductions. It takes students through all logical steps--from premise to conclusion--and presents appropriate symbols and terms, while giving examples to clarify principles. Logic, 2/e uses models to establish the invalidity of arguments, and includes exercise sets throughout, ranging from easy to challenging. Solutions are provided to selected exercises, and historical remarks discuss major contributions to the theories covered.

Designed to make logic interesting and accessible -- without sacrificing content or rigor -- this classic introduction to contemporary propositional logic explains the symbolization of English sentences and develops formal-proof, truth-table, and truth-tree techniques for evaluating arguments. Organizes content around natural-deduction formal-proof procedures, truth tables, and truth trees. Also presents logical statement connectives gradually, one per chapter, and finally, increases readers' awareness of the arguments they read and hear every day by providing examples of actual arguments to which they (...) can readily relate. (shrink)

The study of argumentation is prospering. After its brilliant start in Antiquity, highlighted in the classical works of Aristotle, after an alternation of ups and downs during the following millennia, in the post-Renaissance period its gradual decline set in. Revitalization took place only after Toulmin and Perelman published in the same year their landmark works The Uses of Argument and La nouvelle rhétorique. The model of argumentation presented by Toulmin and Perelman’s inventory of argumentation techniques inspired (...) a great many scholars in various ways to take up the study of argumentation in a serious manner. Nowadays there are well-established logical approaches to argumentation, but also social and socio-psychological, linguistic, juridical and other approaches. In most of these approaches traces can be found of the influence of the classical and neo-classical argumentation theories just mentioned. (shrink)

Quasi-classical logic is a propositional logic for reasoning under inconsistency pointed out recently in the literature [3] [21]. Compared with several other paraconsistent logics, it has the nice feature that no special attention needs to be paid to a special form of premises. However, only few is known about its computational behaviour up to now. In this paper, we fill this gap by pointing out a linear time translation that maps every instance of the quasi-classical entailment problem for CNF formulas (...) into an instance of the classical entailment problem. This enables us to show that quasi-classical entailment for CNF formulas is “only” coNP -complete, take advantage of all existing automated reasoning techniques for classical entailment in order to improve quasi-classical inference from the practical side. Especially, tractable classes of formulas for quasi-classical entailment are pointed out. (shrink)

The study of argumentation is prospering. After its brilliant start in Antiquity, highlighted in the classical works of Aristotle, after an alternation of ups and downs during the following millennia, in the post-Renaissance period its gradual decline set in. Revitalization took place only after Toulmin and Perelman published in the same year their landmark works The Uses of Argument and La nouvelle rhétorique. The model of argumentation presented by Toulmin and Perelman’s inventory of argumentation techniques inspired (...) a great many scholars in various ways to take up the study of argumentation in a serious manner. Nowadays there are well-established logical approaches to argumentation, but also social and socio-psychological, linguistic, juridical and other approaches. In most of these approaches traces can be found of the influence of the classical and neo-classical argumentation theories just mentioned. (shrink)

Richard Arthur’s _Natural Deduction_ provides a wide-ranging introduction to logic. In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python.

Arnold Gehlen's attempt to give anthropological grounds for morality stems from Kant's idea that being freed from the compulsion of instinct left human beings in need of compensation for the loss of the practical guidance which instinct had hitherto provided. Whereas Kant thought this compensation was to found only in reasoned morality, Gehlen would argue that morality provides recompense by becoming a quasi-instinct that functions without reflection and that needs to be bred into human beings. The author maintains that in (...) comparing animals and human beings. Gehlen posits will as a deficient instinct as deficient will; because each side is characterized as the negative of the other, Gehlen's starting point fails to meet the conditions for a valid comparison. (shrink)

We study the provability in subsystems of second-order arithmetic of two theorems of Harrington and Shelah [6] about Borel quasi-orderings of the reals. These theorems turn out to be provable in ATR0, thus giving further evidence to the observation that ATR0 is the minimal subsystem of second-order arithmetic in which significant portion of descriptive set theory can be developed. As in [6] considering the lightface versions of the theorems will be instrumental in their proof and the main techniques employed (...) will be the reflection principles and Gandy forcing. (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)

How to make sense of Kant's theory of radical evil is a controversial problem, for the solution of which three approaches have been attempted: (1) the anthropological, (2) the transcendental, and (3) the quasi‐transcendental. This article aims at developing a new quasi‐transcendental approach to radical evil, and its main innovation consists in reinterpreting the propensity to evil as a potential for moral evil, whose nuanced modality (i.e., potentiality) lies between full actuality and logical (empty) possibility. This evil potential inherent to (...) our species' nature can be actualized by individual Willkür in one's evil Gesinnung. Thanks to this reinterpretation, not only the compatibility of radical evil with individual freedom will be convincingly demonstrated, because the potential for evil only strongly pushes rather than necessitating individuals to do evil, but also Kant's bold statement “the human being is by nature evil” becomes easily confirmable, because even a single individual's illegal action provides sufficient empirical evidence to a regressive argument for the transcendental precondition for evil in his species' nature. (shrink)

Instead of paralysing readers with a technical account of its nature and genealogy, I aim to accumulate a sense of Derrida's quasi-transcendental thinking over a series of expositions. I begin with a critical account of the most prevalent misreading of Derrida's work, generated by attempts, such as Rorty's, to place it on one side of a clear duality that sets old-fashioned “philosophical” foundationalism against contemporary anti-foundationalist “textuality.” In contrast, through an analogy between what occurs in the giving of a gift (...) and the happening of différance, I shall try to articulate the more complex, quasi-transcendental “logic” of Derrida's thinking, which refuses a clear-cut “either/or” choice between the poles of this duality, precisely because these alternatives stand in a relation, not of analytical contradiction, but of aporia, or dilemma. If this exposition proves to be too abstruse and metaphysical for some, a second, more practical, example concerning the aporias of ethical decision- making should go some way to wards compensation. Through these expositions, I aim to show that a complex, quasi-transcendental way of thinking serves as a more sophisticated and accurate key to the interpretation of Derrida's texts than attempts to reduce it to the anti-foundationalist side of supposedly contradictory opposites. To support this claim, I return with a critical eye to Rorty's rejection of Jonathan Culler's argument that Derrida must and does maintain a philosophy/literature distinction, and of Christopher Norris's explanation for Derrida's claim that one cannot escape philosophy. I also try to answer Rorty's rejection of the very idea of quasi-transcendentality by reducing this mode of thinking to a mere restatement of the co-implication of binaries. I conclude with a brief outline of what deconstructive practice amounts to when understood in the light of quasi-transcendental thinking. S. Afr. J. Philos. Vol.23(3) 2004: 244-266. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy called 'argument by repetition' (ABR). ABR controls the script by repeating the script, and it often distracts audiences in the process. Truthiness is a key to how ABR is a pervasive propaganda technique. ABR takes many forms: jingles for advertising shampoo, phrases politicians use to evoke fear or gain favor, and narratives to malign certain groups of people. Adolf Hitler's Big Lie technique in Mein Kampf extols the usefulness (...) of this technique in swaying masses of people. Hitler and his Propaganda Minister, Joseph Goebbels, utilized this Big Lie technique to repeat the narrative of an “International Jewry”, which launched World War I to kill all Germans; this repeated lie helped turn cultural anti‐ Semitism into the Holocaust, as many would argue. ABR seeks to convince an audience not by facts or logic but by the psychological and emotional power of repetition. (shrink)

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

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into (...) these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic. (shrink)

These arguments are fairly well known today. It is interesting to note that v. Kries already knew them, and that they have been ignored by Reichenbach and v. Mises in their original account of probability.2This observation leads to the interesting question why the frequency theory of probability has been adopted by many people in our century in spite of severe counterarguments. One may think of a change in scientific attitude, of a scientific revolution put forward by Feyerabendarian propaganda- and who (...) would deny that Reichenbach was an excellent propagandist!My suggested explanation is the following:J. v. Kries is still a mentalist in the tradition of Descartes and Locke. This can be shown very well from his logic, which he wrote even much later (1916). A mentalist does not pose semantical questions in a proper sense: he rather asks which ideas in the human mind make up a concept. And studying probability in this way, he will find in any case that what is in the human mind is first of all an expectation. Therefore, his analysis of the concept of probability will be centered around the concept of expectation.People tended to approach the problem in quite a different way after the scientific revolution which led from mentalism to lingualism. They tended in many cases to use operationalism and to ask how probabilities are determined in science, if they wanted to clear up the meaning of probability. This new aspect of probability, which was caused by looking at it from a new position or standpoint, suggested it to be the limit of relative frequencies in the first instance. This suggestion was so strong that all objections were ignored, and all counterarguments encountered deaf ears.Of course I have used here an oversimplification. Neither was J. v. Kries untouched by Poincaré's conventionalism, which is essentially a movement leading to the breakdown of mentalism; nor was Reichenbach, when he wrote his thesis in 1915, already a lingualist in any respect.Nevertheless, I think that the lingualist revolution, which took place particularly in mathematics and physics, has also changed the attitude towards probability. It would be interesting to corroborate this thesis by extensive study of the history of science in the late 19th century.Besides this historical aspect of v. Kries' theory, there is a systematic one which should be noticed. Though his theory still has a mentalist outlook, many of v. Kries' statements can be translated into the present lingualist idiom and then become most interesting contributions to the present discussion. We shall then state that for v. Kries probabilities appear first of all in probabilistic hypotheses which may or may not be confirmed by empirical data. Therefore, they have a role similar to theoretical concepts.3But that is not the only predominant feature of v. Kries' theory. He is approaching objective probability in a way which is quite unfamiliar to present day philosophers or mathematicians. Objective probabilities are connected with other concepts in three different ways. First of all, probabilistic hypotheses are confirmed by empirically found relative frequencies in a finite series of events. Secondly, they serve as an aid for decisions. And finally, there is a third relationship. Probabilities have to be explained by theories which are in many cases not formulated in probabilistic terms themselves. We can try to understand probability in one of the first two ways via their connection to other concepts. That is what is usually done by interpretations in terms of frequencies or decisions. A third approach, however, is to understand the nature of probability by the way probabilities are explained, and that is what v. Kries does. Such an approach does not seem unusual at all. In many cases the nature of a kind of objects is characterized by giving an explanation. If somebody asks what an eclipse of the moon is, we shall answer - as Aristotle already proposed - by giving an explanation of it. Thus it is quite natural to answer a question as to the nature of probability by describing the general type of explanation of probability distributions in natural or social science. The answer given by v. Kries is - as we know today — of limited validity. Quantum mechanical probabilities are not explainable by Spielräume. V. Kries solution, however, is remarkable in one important respect. It accounts for the time direction of objective probabilities, which are always predictive or forward probabilities, while retrodictive or backward probabilities are always subjective. The relation of objective probabilities to time direction is surely of utmost importance for natural philosophy. I do not know of any other philosophical foundation of probability which takes into account this deep-rooted relation. Therefore, v. Kries' interpretation may help us to understand one of the most intricate puzzles of philosophy. It may be nearly one hundred years old, but is by no means out of date. (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)