Logicians disagree on (1) criteria for the presence of an argument, (2) criteria for adding implicit premises and (3) criteria for linking premises. I attempt to resolve all three problems, and in the process to remove the main obstacles to teaching diagramming. The first problem is resolved by working with real discourse that students find on their own, rather than the artificial examples and problems found in logic texts; it is further reduced by examining the different uses of (...) argument and understanding the extent to which the basic rules of diagramming are the same for the various uses. The other disagreements persist because logicians neglect to clarify the principal type of eakness we remedy by adding implicit premises and linking premises: in real discourse we do so to block substantive counterexamples, an idea correlated with that of substantive deduction, discussed by Govier, Wright and others. (shrink)

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

How are dependent (or linked) premises to be distinguished from independent (or convergent) premises? Deductive validity, sometimes proposed as a necessary condition for depende'nce, cannot be, for the premises of both inductive and deductive but invalid arguments can be dependent. The question is really this: When do multiple premises for a certain conclusion fonn one argument for that conclusion and when do they form multiple arguments? Answer: Premises are dependent when the evidence they offer for their (...) conclusion is more than the ordinary sum of their probabilities. Ordinary sums are defined in the paper. (shrink)

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...) epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology. (shrink)

To analyze the argument structure, the linked vs convergent distinction is crucial. In applying this distinction, argumentation scholars test for variations of argument strength under premise revision. A relevance-based test assesses whether an argument’s premises are individually relevant to its conclusion, while a support-based test assesses whether premises support the conclusion independently. Both criteria presuppose that evaluating an argument’s strength is methodologically prior to identifying its structure. Yet, if ‘argument structure’ is a concept (...) of analysis, then a structural analysis would precede evaluating an argument’s strength. We problematize that state-of-the-art methods to identify structures fail, because they rely on evaluative judgments, and so “put the cart before the horse.”. (shrink)

To analyze the argument structure, the linked vs convergent distinction is crucial. In applying this distinction, argumentation scholars test for variations of argument strength under premise revision. A relevance-based test assesses whether an argument’s premises are individually relevant to its conclusion, while a support-based test assesses whether premises support the conclusion independently. Both criteria presuppose that evaluating an argument’s strength is methodologically prior to identifying its structure. Yet, if ‘argument structure’ is a concept (...) of analysis, then a structural analysis would precede evaluating an argument’s strength. We problematize that state-of-the-art methods to identify structures fail, because they rely on evaluative judgments, and so “put the cart before the horse.”. (shrink)

Sometimes logical support for a conclusion is provided exclusively by premises which are independently relevant to that conclusion. At other times, support is provided exclusively by independently irrelevant premises. On still other occasions, relevant and irrelevant premises may collectively offer a distinctive pattern of support. This paper provides a rigorous account of some of these differences in terms of a tripartite classification of convergent, linked and hybrid arguments. These various arguments are defined, diagrammed, and some of their logical (...) properties are explored. (shrink)

We can provisionally distinguish inference as logically drawing some new result out of given information from argument as advancing reasons in support of a challenged claim. Blair and Johnson place inference beyond the scope of informal logic, and Tou lmin considers inference to be the connection of premises with conclusion in a strong argument. Both approaches are inadequate to inference as distinguished here, and partly as a consequence argument analysts tend unwittingly to mark the distinction as (...) t hat between linked and convergent arguments. Here I urge that there are advantages to treating inference as inference. (shrink)

Many in the informal logic tradition distinguish convergent from linked argument structure. The pragma-dialectical tradition distinguishes multiple from co-ordinatively compound argumentation. Although these two distinctions may appear to coincide, constituting only a terminological difference, we argue that they are distinct, indeed expressing different disciplinary perspectives on argumentation. From a logical point of view, where the primary evaluative issue concerns sufficient strength of support, the unit of analysis is the individual argument, the particular premises put forward (...) to support a given conclusion. Structure is internal to this unit. From a dialectical point of view, where the focus concerns how well a critical discussion comes to a reasoned conclusion of some disputed question, the argumentation need not constitute a single unit of argument. The unit of dialectical analysis will be the entire argumentation made up of these several arguments. The multiple/co-ordinatively compound distinction is dialectical, while the linked/convergent distinction is logical. Keeping these two pairs of distinctions separate allows us to see certain attempts to characterize convergent versus linked arguments as rather characterizing multiple versus co-ordinatively compound arguments, in particular attempts of Thomas, Nolt, and Yanal, and to resolve straightforwardly conflicts, tensions, or anomalies in their accounts. Walton's preferred Suspension/Insufficient Proof test to identify linked argument structure correctly identifies co-ordinatively compound structure. His objection to using the concept of relevance to explicate the distinction between linked and convergent structure within co-ordinatively compound argumentation can be met through explicating relevance in terms of inference licenses. His counterexample to the Suspension/No Support test for identifying linked structure which this approach supports can itself be straightforwardly dealt with when the test is explicated through inference licenses. (shrink)

The argument diagramming method developed by Monroe C. Beardsley in his (1950) book Practical Logic, which has since become the gold standard for diagramming arguments in informal logic, makes it possible to map the relation between premises and conclusions of a chain of reasoning in relatively complex ways. The method has since been adapted and developed in a number of directions by many contemporary informal logicians and argumentation theorists. It has proved useful in practical applications and especially (...) pedagogically in teaching basic logic and critical reasoning skills at all levels of scientific education. I propose in this essay to build on Beardsley diagramming techniques to refine and supplement their structural tools for visualizing logical relationships in a number of categories not originally accommodated by Beardsley diagramming, including circular reasoning, reductio ad absurdum arguments, and efforts to dispute and contradict arguments, with applications and analysis. (shrink)

This paper presents preliminary findings of the project [name omitted for anonymity]. This interdisciplinary project builds on Argumentation theory and developmental sociocultural psychology for the study of children’s argumentation. We reconstruct children’s inferences in adult-child and child-child dialogical interaction in conversation in different settings. We focus in particular on implicit premises using the Argumentum Model of Topics for the reconstruction of the inferential configuration of arguments. Our findings reveal that sources of misunderstandings are more often than not due to (...) misalignments of implicit premises between adults and children; these misalignments concern material premises rather than the inferential-procedural level. (shrink)

What rational foundation underlies argument-critical judgements? What are the canons of argument criticism and how are they to be "justified"? This paper explores an analogy between art- and argument-criticism and argues that the analogy promises not only to illuminate the nature of argument criticism and capture the central goals of instruction in informal logic, but also to resolve fundamental problems at the foundations of normative theory of argument concerning the "justification" of standards of reasoning.

Some have suggested that images can be arguments. Images can certainly bolster the acceptability of individual premises. We worry, though, that the static nature of images prevents them from ever playing a genuinely argumentative role. To show this, we call attention to a dilemma. The conclusion of a visual argument will either be explicit or implicit. If a visual argument includes its conclusion, then that conclusion must be demarcated from the premise or otherwise the argument will (...) beg the question. If a visual argument does not include its conclusion, then the premises on display must license that specific conclusion and not its opposite, in accordance with some demonstrable rationale. We show how major examples from the literature fail to escape this dilemma. Drawing inspiration from the graphical logic of C. S. Peirce, we suggest instead that images can be manipulated in a way that overcomes the dilemma. Diagrammatic reasoning can take one stepwise from an initial visual layout to a conclusion—thereby providing a principled rationale that bars opposite conclusions—and the visual inscription of this correct conclusion can come afterward in time—thereby distinguishing the conclusion from the premises. Even though this practical application of Peirce’s logical ideas to informal contexts requires that one make adjustments, we believe it points to a dynamic conception of visual argumentation that will prove more fertile in the long run. (shrink)

The implicit dimension of enthymemes is investigated from a pragmatic perspective to show why a premise can be left unexpressed, and how it can be used strategically. The relationship between the implicit act of taking for granted and the pattern of presumptive reasoning is shown to be the cornerstone of kairos and the fallacy of straw man. By taking a proposition for granted, the speaker shifts the burden of proving its un-acceptability onto the hearer. The resemblance of the (...) tacit premise with what is commonly acceptable or has been actually stated can be used as a rhetorical strategy. (shrink)

When, if ever, is one justified in accepting the premises of an argument? What is the proper criterion of premise acceptability? Can the criterion be theoretically or philosophically justified? This is the first book to provide a comprehensive theory of premise acceptability and it answers the questions above from an epistemological approach that the author calls common sense foundationalism. It will be eagerly sought out not just by specialists in informal logic, critical thinking, and argumentation theory but also (...) by a broader range of philosophers and those teaching rhetoric. (shrink)

Informal logicians recognise the frequent use of unstated assumptions; some also recognise entertained arguments and recommend a suppositional approach to conditional statements. It is here argued that these two be put together to make argument diagrams more accurate and subtle. Philosophical benefits also accrue: insights into Jackson's apparent violations of modus tollens and contraposition and McGee's counterexamples to the validity of modus ponens.

Informal logicians recognise the frequent use of unstated assumptions; some (e.g. Fisher) also recognise entertained arguments and recommend a suppositional approach (such as Mackie's) to conditional statements. It is here argued that these two be put together to make argument diagrams more accurate and subtle. Philosophical benefits also accrue: insights into Jackson's apparent violations of modus tollens and contraposition and McGee's counterexamples to the validity of modus ponens.

Most recent writers of informal logic texts draw a distinction between "linked" and "convergent" arguments. According to its inventor, Stephen Thomas, the distinction is of the utmost importance; it "seems crucial to the analysis and evaluation of reasoning in natural language." I argue that the distinction has not been drawn in any way that makes it both clear and of any real originality or importance. Many formulations are obscure or conceptually incoherent. One formulation of the distinction does (...) seem tolerably clear and I develop another, but neither promises to make it matter much. We can well do without it. (shrink)

A Theory of Argument is an advanced textbook intended for students in philosophy, communications studies and linguistics who have completed at least one course in argumentation theory, information logic, critical thinking or formal logic. Containing nearly 400 exercises, Mark Vorobej develops a novel approach to argument interpretation and evaluation. One of the key themes of the book is that we cannot succeed in distinguishing good argument from bad arguments until we learn to listen carefully to others. Part (...) I develops a relativistic account of argument cogency that allows for rational disagreement. Part II offers a comprehensive and rigorous account of argument diagramming. Hybrid arguments are contrasted with linked and convergent arguments, and a novel technique is introduced for graphically recording disagreements with authorial claims. (shrink)

This paper focuses on an explanation in a newspaper article: why new European Union citizens will come to the UK from Eastern Europe (e.g., because of available jobs). Using a corpus-based method of analysis, I show how regular target readers have been positioned to generate premises in dialogue with the explanation propositions, and thus into an understanding of the explanation as an argument, one which contains a biased conclusion not apparent in the text. Employing this method, and in particular (...) ‘corpus comparative statistical keywords’, I show how two issues can be freshly looked at: implicit premise recovery; the argument/explanation distinction. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Logic Pamphlets of Charles Lutwidge Dodgson and Related PiecesIrving H. AnellisFrancine F. Abeles, editor. The Logic Pamphlets of Charles Lutwidge Dodgson and Related Pieces. The Pamphlets of Lewis Carroll, 4. New York-Charlottesville-London: Lewis Carroll Society of North America-University Press of Virginia, 2010. Pp. xx + 271. Cloth, $75.00.Until William Bartley’s rediscovery and reconstruction of Dodgson’s lost Part II of Symbolic Logic, Lewis Carroll’s reputation in logic, when (...) taken seriously, rested upon his few published articles on logical paradoxes and puzzles, while his published books, The Game of Logic and Symbolic Logic, were regarded as suitable perhaps as pedagogical tools, but dismissed otherwise as amusements, on a par with the Alice works. Richard Braithwaite asserted (“Lewis Carroll as Logician”) that “Carroll regarded formal and symbolic logic not as a corpus of systematic knowledge about valid thought nor yet as an art for teaching a person to think correctly.” He suggested that Dodgson used his pseudonym for his popular and whimsical writings, reserving his legal name only for his serious mathematical products. Philosophers practicing linguistic analysis in their assault on nonsense deriving from misuse of language meanwhile developed an interest in Carroll (e.g. George Pitcher, “Wittgenstein, Nonsense, and Lewis Carroll”). Abeles, on the contrary, stresses the seriousness of Dodgson’s pedagogical and popularizing mission (195–99).Bartley’s discovery opened the door for reevaluating Dodgson as a serious logician, and Abeles has been in the forefront of that reevaluation. Her general introduction and introductions to the main divisions of this collection of Carroll’s publications (and additional material from his Nachlass and a handful of publications of others, composed in response to Carroll’s published articles) place his serious logical work and its significance in historical perspective, providing a deeper, more sophisticated view than found in Bartley’s “Editor’s Introduction” to Lewis Carroll’s Symbolic Logic. Abeles also offers brief introductions to the individual entries, which describe their physical characteristics and circumstances of composition.Dodgson aligned with the majority of those British logicians of his day, starting with George Boole, who understood formal logic to be Aristotelian syllogistic, and symbolic logic to be syllogistic logic expressed algebraically. His notational innovation was employing indices to terms so that, independently of the arrangement of terms, propositions could easily be read; thus, “xy0” can be read as “no x are y” or “no y are x” and “x1y0” as “all x are not y” or “no x are y”. In dealing with the classical elimination problem in the class calculus—to determine the maximum information, without duplications, obtainable from a given set of premises—Dodgson in his later work and unpublished letters anticipated several concepts of automated theorem proving.Central to both geometry and to formal logic are the rules of logical inference that establish the validity of arguments and guarantee that conclusions inferred from true [End Page 506] premises are true. The modern analytic tableaux, or tree method, is a fundamental tool in this regard, both for deriving theorems and for determining the validity or invalidity of the proofs for propositional calculus and first-order predicate calculus.Introducing his reconstruction of Part II of Symbolic Logic, Bartley noted that, along with the logic diagrams that Carroll devised, he also devised a tableau method that strongly resembled Beth’s semantic tableaux. Abeles went more deeply and convincingly into that resemblance in her earlier research. Beth’s tableaux, together with Hintikka’s model sets, were the direct ancestors of Smullyan’s analytic tableaux, which in turn are the theoretical basis for the Robinson resolution method that continues to be central to much work in programming logic.Abeles has also shown that the work in Studies in Logic by Charles Peirce and his logic students at Johns Hopkins University served as a source of inspiration for Dodgson. More critically, she demonstrated that Dodgson devised and employed the tree method for carrying out proofs of syllogisms and chains of syllogisms, or soriteses, in Part II of Symbolic Logic (see her “Lewis Carroll’s Method of Trees: Its Origins in Studies in Logic,” Modern Logic 1 [1990]: 25–34). The tree... (shrink)

In the paper, certain rational postulates for protocols describing real communicating are introduced.These rational postulates, on the one hand, allow assigning a certain typology of real systems of interactions, which is consistent with the reality of epistemic argumentation in systems of communicating, and on the other one – defining rules of using argumentation in real situations. Moreover, the presented postulates for protocols characterize information networks and administering knowledge in real interactivity systems. Due to the epistemic character of the considerations, the (...) problem undertaken in the paper concerns working out fundamental assumptions that refer to building of epistemic logics. They allow establishing the correctness of the discourse defined by rational postulates of protocols of real communication. In the context of the presented problem there are the following two research questions distinguished: 1) How do we determine the rule of building of real dynamic epistemic logics? and 2) How should we define semantics for these logics? Within the framework of considerations relating to the research questions asked, certain epistemic operators, relativized to types of communicating, are introduced. Basic logical relations between using these operators are established for these operators. The relations are presented by a diagram called the square of epis temic operators. On the basis of these logical relations some axioms for real dynamic epistemic logics are presented. The semantics of real dynamic epistem ic logics is extended by the methods of lower and upper approximation of formula evaluating. This allows defining ‘approximation Kripke models’. The results of conceptualization of knowledge on real premises of epistemic argum entation presented in this paper can be applied to rhetoric in real systems of interaction. (shrink)

Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed the (...) combined content of the premises. We show that this basic platitude can be used to characterise the extension of classical as well as non-classical consequence relations. The distinctive trait of an informational semantics is that truth-conditions are replaced by information-conditions. The latter leads to an inversion of the usual order of explanation: Considerations about logical discrimination (how finely propositions are individuated) are conceptually prior to considerations about deductive strength. Because this allows us to bypass considerations about truth, an informational semantics provides an attractive and metaphysically unencumbered account of logical consequence, non-classical logics, logical rivalry and pluralism about logical consequence. (shrink)

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

Some general, programmatic points about informal logic are addressed. The informal approach to argument analysis faces serious foundational problems which have been recognized by its practitioners – but informal logic has yet to come together as a clearly defined discipline. Another problem is the dilemma of the dialectician (Sextus Empiricus): informal logic is either trivial or powerless on its own (field expertise is needed). According to Johnson and Blair the central notion in theory of (...) class='Hi'>argument is cogency which replaces soundness. An argument is cogent if and only if (i) its premises are rationally acceptable, (ii) its premises are relevant to its conclusion and (iii) its premises provide sufficient reason to accept the conclusion. I propose to understand cogency as a broader notion that includes deductively valid inferences. The criteria of cogency are simply the basic ideals of scientific methodology which requires a respect for available evidence and “reasonable” inference, an awareness of alternatives and a willingness to modify or reject those beliefs that fail to conform to the evidence. Informal logic in the sense of elementary scientific methodology is concerned with proper reasoning and not with proper dialogue. Informal logic involves non-trivial argumentativeskills and abilities applied to the subject area and accessible to every normally intelligent and educated person. (shrink)

This article discusses two coextensive concepts of logical consequence that are implicit in the two fundamental logical practices of establishing validity and invalidity for premise-conclusion arguments. The premises and conclusion of an argument have information content (they ?say? something), and they have subject matter (they are ?about? something). The asymmetry between establishing validity and establishing invalidity has long been noted: validity is established through an information-processing procedure exhibiting a step-by-step deduction of the conclusion from the premise-set. Invalidity (...) is established by exhibiting a countermodel satisfying the premises but not the conclusion. The process of establishing validity focuses on information content; the process of establishing invalidity focuses on subject matter. Corcoran's information-theoretic concept of logical consequence corresponds to the former. Tarski's model-theoretic concept of logical consequence formulated in his famous 1936 no-countermodels definition corresponds to the latter. Both are found to be indispensable for understanding the rationale of the deductive method and each complements the other. This study discusses the ontic question of the nature of logical consequence and the epistemic question of the human capabilities presupposed by practical applications of these two concepts as they make validity and invalidity accessible to human knowledge. (shrink)

An accessible introduction to critical thinking and argument mapping with over 30 exercises per chapter, authentic examples, and examples drawn from diverse philosophical sources. Integration with the Argumentation argument mapping app allows readers to fully engage with argument maps with screen readers and key commands. Argumentation's inference boxes make possible novel explanations of inference objections, arguments for and against analogical arguments, inference rules, and the distinction between co-premises and independent arguments.

We provide a new link between deductive and probabilistic reasoning fallacies. Illusory inferences from disjunction are a broad class of deductive fallacies traditionally explained by recourse to a matching procedure that looks for content overlap between premises. In two behavioral experiments, we show that this phenomenon is instead sensitive to real-world causal dependencies and not to exact content overlap. A group of participants rated the strength of the causal dependence between pairs of sentences. This measure is a near perfect predictor (...) of fallacious reasoning by an independent group of participants in illusory inference tasks with the same materials. In light of these results, we argue that all extant accounts of these deductive fallacies require non-trivial adjustments. Crucially, these novel _indirect_ illusory inferences from disjunction bear a structural similarity to seemingly unrelated _probabilistic reasoning_ problems, in particular the conjunction fallacy from the heuristics and biases literature. This structural connection was entirely obscure in previous work on these deductive problems, due to the theoretical and empirical focus on content overlap. We argue that this structural parallelism provides arguments against the need for rich descriptions and individuating information in the conjunction fallacy, and we outline a unified theory of deductive illusory inferences from disjunction and the conjunction fallacy, in terms of Bayesian confirmation theory. (shrink)

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)

Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information beyond that of the premise-set. (...) This paper locates information-theoretic approaches historically, philosophically, and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyze validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...) computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (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)

This chapter contains sections titled: Introduction Statements The Square of Opposition Figure and Mood Deduction Counterexamples Independence Soundness Completeness: Syllogistic Arguments Completeness: Categorical Arguments Completeness: Arguments in General Note Bibliography.

The traditional No-Miracles Argument (TNMA) asserts that the novel predictive success of science would be a miracle, and thus too implausible to believe, if successful theories were not at least approximately true. The TNMA has come under fire in multiple ways, challenging each of its premises and its general argumentative structure. While the TNMA relies on explaining novel predictive success via the truth of the theories, we put forth a deductive version of the No-Miracles argument (DNMA) that avoids (...) inference to the best explanation entirely. Instead, a relatively simple empirical framework and a probabilistic analysis can accomplish the ambitious goals of the TNMA while entirely sidestepping its problems. This close-but-distinct argument has many independent strengths and comparatively few weaknesses. Indeed, objections tailored specifically to the DNMA reveal surprising insights into how exactly NMAs are neither circular nor question-begging, as has been widely speculated. (shrink)

Which properties are characteristic of the enthymeme in Aristotle's Rhetoric? There is no consensus on this point. The present discussion centres on three properties. 1. Is there always an implicit premise? (Answer: Above all, a pragmatic level and a logical level must be distinguished.) 2. Do the premises consist by definition of probabilities and signs? (Answer: No.). 3. Are all enthymemes reducible to a syllogistic form? (Answer: The literature pertaining to this question is dominated by a false dilemma: an (...) enthymeme does not have either a topical or a syllogistic structure). In general, Aristotle's approach to the enthymeme in the Rhetoric appears to shift from argumentation theory to logic. (shrink)

In his Logic, Pierre Gassendi proposes that our inductive inferences lack the information we would need to be certain of the claims that they suggest. Not even deductivist inference can insure certainty about empirical claims because the experientially attained premises with which we adduce support for such claims are no greater than probable. While something is surely amiss in calling deductivist inference "probabilistic," it seems Gassendi has hit upon a now-familiar, sensible point—namely, the use of deductive reasoning in empirical contexts, (...) while providing certain formal guarantees, does not insulate empirical arguments from judgment by the measure of belief which we invest in their premises. The more general point, which distinguishes Gassendi among his contemporaries, is that the strength shared by all empirical claims consists in the warrant from experience for those claims we introduce in their support. (shrink)

There is a crisis in philosophical rationality today—in which modern logic is implicated—that can be traced to the abandonment of a common background of principles. The situation has no parallel within the pre-modern tradition, which not only admits of such principles, but also refers them back to a set of assumptions grounded in a clearly religious frame of mind. Modern conceptions of rationality claim complete independence from religious sources, as from tradition more generally, and typically end up disposing of first (...) principles altogether. The result is a fragmentation of reason, which can be seen to be dramatically exemplified in the realm of modern logic, populated by countless different systems and incompatible conceptions of what it is to be a logic. Many of the conceptual choices that became implicit in the philosophical discussions eventually leading to the rejection of the religious picture, and ultimately to the aforementioned crisis, were themselves originally linked to religious premises, so that all along, a kind of religious subconscious has subsisted throughout those disputations; however, the lack of any proper recognition of this background obstructs the possibility of making a reasonable assessment of the nature and causes of the crisis. Alasdair MacIntyre, whose thought inspires the argument developed here, reached similar conclusions regarding practical rationality and the effects of abandoning the teleological framework of Aristotelian philosophy. MacIntyre’s arguments can be adapted, as he suggests, to deal with reason more generally, and his insistence upon the tradition-laden character of rational enquiry can help point toward the grounding of human reason in religion. (shrink)

Cogency is the central normative concept of informal logic. But it is a loose evaluative concept and I argue that a generic notion covering all of the qualities of a well-reasoned argument is the most plausible conception. It is best captured by the standard RSA criterion: in a good argument acceptable (A) and relevant (R) premises provide sufficient (S) grounds for the conclusion. Logical qualities in a broad sense are affected by the epistemic qualities of the premises (...) and “consequence” in a broad sense exhibits an interplay of form and content. There are four proposals for the premise—conclusion relation: (i) no strictly logical connection (“non-logical” consequence); (ii) one type of connection only (deductivism); (iii) a few types of connection (deduction, induction, perhaps conduction and analogical reasoning); (iv) many types of connection (argumentation schemes). Deductivism is a serious option but in its strong version, as the discussion about petitio shows, it fails to establish that arguments which are not cogent are thereby invalid. And weak deductivism, very attractive from the pedagogical point of view, has some deficiencies (implausible hidden premises; preservation of truth, not probability). I argue that the idea of a counterexample, when we regard certain components of the argument as fixed and others as variable, is the best approach to the analysis of the illative core of every-day arguments (the approach of David Hitchcock on material consequence). (shrink)

This paper describes how bodily positions and gestures were used to teach argument diagramming to a student who cannot see. After listening to short argumentative passages with a screen reader, the student had to state the conclusion while touching his belly button. When stating a premise, he had to touch one of his shoulders. Premises lending independent support to a conclusion were thus diagrammed by a V-shaped gesture, each shoulder proposition going straight to the conclusion. Premises lending dependent (...) support were diagrammed by a T-shaped gesture, the shoulder premises meeting at the collar bone before moving down to the belly button. Arguments involving two pairs of entailments were diagrammed by an I-shaped gesture, going from the collar bone to a mid-way conclusion above the abdomen before travelling to the final conclusion at the belly button. The student’s strong performance suggests that placing propositions at different locations on the body and uniting them with gestures can help one discern correct argumentative structures. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

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

There is a crisis in philosophical rationality today—in which modern logicisimplicated—thatcanbetracedtotheabandonmentofacommonbackground of principles. The situation has no parallel within the pre-modern tradition, which not only admits of such principles, but also refers them back to a set of assumptions grounded in a clearly religious frame of mind. Modern conceptions of rationality claim complete independence from religious sources, as from tradition more generally, and typically end up disposing of first principles altogether. The result is a fragmentation of reason, which can be (...) seen to be dramatically exemplified in the realm of modern logic, populated by countless different systems and incompatible conceptions of what it is to be a logic. Many of the conceptual choices that became implicit in the philosophical discussions eventually leading to the rejection of the religious picture, and ultimately to the aforementioned crisis, were themselves originally linked to religious premises, so that all along, a kind of religious subconscious has subsisted throughout those disputations; however, the lack of any proper recognition of this background obstructs the possibility of making a reasonable assessment of the nature and causes of the crisis. Alasdair MacIntyre, whose thought inspires the argument developed here, reached similar conclusions regarding practical rationality and the effects of abandoning the teleological framework of Aristotelian philosophy. MacIntyre’s arguments can be adapted, as he suggests, to deal with reason more generally, and his insistence upon the tradition-laden character of rational enquiry can help point toward the grounding of human reason in religion. (shrink)

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 importance of teaching critical thinking skills at the college level cannot be overemphasized. Teaching a subcategory of these skills—argument analysis—we believe is especially important for first-year students with their college careers, as well as their lives, ahead of them. The struggle, however, is how to effectively teach argument analysis skills that will serve students in a broad range of disciplines.

This book brings together in one place David Hitchcock’s most significant published articles on reasoning and argument. In seven new chapters he updates his thinking in the light of subsequent scholarship. Collectively, the papers articulate a distinctive position in the philosophy of argumentation. Among other things, the author:• develops an account of “material consequence” that permits evaluation of inferences without problematic postulation of unstated premises.• updates his recursive definition of argument that accommodates chaining and embedding of arguments and (...) allows any type of illocutionary act to be a conclusion. • advances a general theory of relevance.• provides comprehensive frameworks for evaluating inferences in reasoning by analogy, means-end reasoning, and appeals to considerations or criteria.• argues that none of the forms of arguing ad hominem is a fallacy.• describes proven methods of teaching critical thinking effectively. (shrink)

It is commonly claimed that the conclusion of a valid deductive argument is contained in its premises and says nothing new. In 'Deduction and Novelty,' in The Reasoner 5 (4), pp. 56-57, I refuted that claim. In The Reasoner, 8 (3), pp. 24-25, David McBride criticised my refutation. I show that McBride’s arguments are unsound.

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

The ampliativity of deduction has been defended in several ways—such as the semi-decidability of the theories, the surprise of unexpected consequences, the need of new individuals in deduction, or ampliative inference as deduction with suppressed premises (Dummett, Frege. Philosophy of mathematics. Duckworth, London, 1991; Hintikka, Logic, language-games and information. Oxford University Press, Oxford, 1973; Musgrave, Imre Lakatos and theories of scientific change. Kluwer, Boston, 1989; Rota, Indiscrete thoughts. Birkhäuser, Boston, 1997). These lines of defensive arguments fail if (...) we characterize ampliativity in a strong way, that is, in terms of ‘novelty’ stricto sensu, as an inferential process producing genuinely new pieces of information in the conclusion of a reasoning (Cellucci, Rethinking logic. Springer, Dordrecht, 2013; Ippoliti, Heuristic reasoning. Springer, Basel, 2015). Nevertheless, it is possible to defend a weaker stance of the ampliativity of deduction and its usefulness. This requires interpreting novelty more loosely, that is, as the inferential production of new relations among known entities. This stance maintains that, in this sense, deduction can provide us with new knowledge. Thus, a typical deductive activity, as re-proving theorems, can be thought as heuristic and ampliative because it establishes new relations between known elements (e.g. between given axioms or properties and the statement of the theorem). I argue that also this line of defence is defective for it does not account for the necessity and usefulness of reproving theorems. In particular, a foundationalist, axiomatic-deductive viewpoint does not fully account for the usefulness and the weak ampliative power of deduction. (shrink)