Offering an innovative approach to critical thinking, Good Reasoning Matters! identifies the essential structure of good arguments in a variety of contexts and also provides guidelines to help students construct their own effective arguments. In addition to examining the most common features of faulty reasoning--slanting, bias, propaganda, vagueness, ambiguity, and a common failure to consider opposing points of view--the book introduces a variety of argument schemes and rhetorical techniques. This edition adds material on visual arguments and more exercises.

During the last decade, one source of debate in argumentation theory has been the notion that there are different modes of arguing that need to be distinguished when analyzing and evaluating arguments. Visual argument is often cited as a paradigm example. This paper discusses the ways in which it and modes of arguing that invoke non-verbal sounds, smells, tactile sensations, music and other non-verbal entities may be defined and conceptualized. Though some attempts to construct a ‘multimodal’ theory of argument are (...) criticized, it advocates for an argumentation theory that makes room for visual arguing and for other non-verbal modes that have not been explored in depth. In the process, the paper provides a method for identifying the structure of multimodal arguments and argues that adding modes to our theoretical tool box is an important step toward a comprehensive account of argument. (shrink)

In the present article two possible meanings of the term mathematical structure are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of structure is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of view, a (...) superfluous undertaking. This is done by analyzing the role played by the concept, in the first place, within Bourbaki's own mathematical output. Likewise, the interaction between Bourbaki's work and the first stages of category theory is analyzed, on the basis of both published texts and personal documents. (shrink)

Most infonnallogic texts and articles assume a verbal account of reasoning which defines "argument" as a set of sentences. The present paper broadens this definition in order to account for "visual arguments" which are communicated with nonverbal visual images. Standard approaches to verbal arguments are extended in a way that allows them to explain and evaluate visual argumentation.

Informal logic is an attempt to develop a logic that can assess and analyze the arguments that occur in natural language discourse. Discussions in the field may address instances of scientific, legal, and other technical forms of reasoning, but the overriding aim has been a comprehensive account of argument that can explain and evaluate the arguments found in discussion, debate and disagreement as they manifest themselves in daily life — in social and political commentary; in news reports and editorials in (...) the mass media ; in advertising and corporate and governmental communications; and in personal exchange. (shrink)

The present paper elaborates a deductivist account of natural language argu-ment in the context of pragma-dialectics. It reviews earlier debates, criticizes some standard misconceptions in the literature, and argues that the identification and analysis of deductive argument schemes can be the basis of a compelling theory of argumentative discourse.

In the pioneering article and two papers, written jointly with McKinsey, Tarski developed the so-called algebraic and topological frameworks for the Intuitionistic Logic and the Lewis modal system. In this paper, we present an outline of modern systems with a topological tinge. We consider topological interpretation of basic systems GL and G of the provability logic in terms of the Cantor derivative and the Hausdorff residue.

Contextualizing the emergence of history of philosophy within eighteenth-century German Enlightenment, this book discusses the philosophical nature of the historiographical concept ‘system of philosophy’ and the concept’s influence upon the methods of history of philosophy and history of ideas.

In the ordinary way of representing relations, the order of the relata plays a structural role, but in the states themselves such an order often does not seem to be intrinsically present. An alternative way to represent relations makes use of positions for the arguments. This is no problem for the love relation, but for relations like the adjacency relation and cyclic relations, different assignments of objects to the positions can give exactly the same states. This is a puzzling situation. (...) The question is what is the internal structure of relations? Is the use of positions still justified, and if so, what is their ontological status? In this paper mathematical models for relations are developed that provide more insight into the structure of relations “out there” in the real world. (shrink)

Methods facilitating noetic ascent -- Contraction as an ontological concept -- Contraction and noesis -- Contraction and memory -- Physiologically induced contraction -- The scholastic tradition of contraction -- Cusanus and the scholastic tradition of contraction.

We announce and explain recent results on the computably enumerable (c.e.) sets, especially their definability properties (as sets in the spirit of Cantor), their automorphisms (in the spirit of Felix Klein's Erlanger Programm), their dynamic properties, expressed in terms of how quickly elements enter them relative to elements entering other sets, and the Martin Invariance Conjecture on their Turing degrees, i.e., their information content with respect to relative computability (Turing reducibility).

Why does the law spurn win-win transactions? -- Things we can't consent to, though no one knows why -- A parable -- Lessons -- The social choice connection -- Why is the law so full of loopholes? -- The irresistible wrong answer -- What is wrong with the irresistible answer? -- The voting analogy -- Turning the analogy into an identity -- Intentional fouls -- Why is the law so either/or? -- The proverbial rigidity of the law -- Line drawing (...) as a matter of life and death -- Why don't we punish all we condemn? -- The undercriminalization problem -- Multicriterial ranking and the undercriminalization problem -- Final thoughts. (shrink)

Though the common sense defense of affirmative action (or employment equity) appeals to principles of restitution, philosophers have tried to defend it in other ways. In contrast, I defend it by appealing to the notion of restitution, arguing (1) that alternative attempts to justify affirmative action fail; and (2) that ordinary affirmative action programs need to be supplemented and amended in keeping with the principles this suggests.

This paper responds to two aspects of Ralph Johnson's Manifest Rationality (2000). The first is his critique of deductivism. The second is his failure to make room for some species of argument (e.g., visual and kisceral arguments) proposed by recent commentators. In the first case, Johnson holds that argumentation theorists have adopted a notion of argument which is too narrow. In the second, that they have adopted one which is too broad. I discuss the case Johnson makes for both claims, (...) and possible objections to his analysis. (shrink)

Thomas Taylor’s interpretation of Plato’s works in 1804 was condemned as guilty by association immediately after its publication. Taylor’s 1804 and 1809 reviewer thus made a hasty generalisation in which the qualities of Neoplatonism, assumed to be negative, were transferred to Taylor’s own interpretation, which made use of Neoplatonist thinkers. For this reason, Taylor has typically been marginalised as an interpreter of Plato. This article does not deny the association between Taylor and Neoplatonism. Instead, it examines the historical and historiographical (...) reasons for the reviewer’s assumption that Neoplatonic readings of Plato are erroneous by definition. In particular, it argues that the reviewer relied on, and tacitly accepted, ethical and theological premises going back to the historiography of philosophy developed by Jacob Brucker in his Historia critica philosophiae . These premises were an integral part of Brucker’s Lutheran religiosity and thus theologically and ethically biased. If these premises are identified, articulated and discussed critically—which they have not been so far in connection with Taylor’s reception—it becomes less obvious that the reviewer was justified in his assumption that the Neoplatonic reading was erroneous by definition. This, in turn, leaves Taylor’s Plato interpretation in a more respectable position. (shrink)

We study the logical structure of relations, and in particular the notion of occurrences of objects in a state. We start with formulating a number of principles for occurrences and defining corresponding mathematical models. These models are analyzed to get more insight in the formal properties of occurrences. In particular, we prove uniqueness results that tell us more about the possible logical structures relations might have.

The prodigious development of argumentation theory over the last three decades has raised many issues that challenge some of the long held assumptions that characterize the traditional study of argument. One of these issues is the role of emotion in argument and argument analysis. While rhetoric has, with its emphasis on persuasion, always recognized that emotions play some role determining which arguments we accept and reject, a long tradition sees appeals to emotion as fallacies that violate the standards of rationality (...) and objectivity reason and argument require. (shrink)

Argument-places play an important role in our dealing with relations. However, that does not mean that argument-places should be taken as primitive entities. It is possible to give an account of relations in which argument-places play no role. But if argument-places are not basic, then what can we say about their identity? Can they, for example, be reconstructed in set theory with appropriate urelements? In this article, we show that for some relations, argument-places cannot be modeled in a neutral way (...) in V[A], the cumulative hierarchy with basic ingredients of the relation as urelements. We argue that a natural way to conceive of argument-places is to identify them with abstract, structureless points of a derivative structure exemplified by positional frames. In case the relation has symmetry, these points may be indiscernible. (shrink)

The ArgumentThe belief in the existence of eternal mathematical truth has been part of this science throughout history. Bourbaki, however, introduced an interesting, and rather innovative twist to it, beginning in the mid-1930s. This group of mathematicians advanced the view that mathematics is a science dealing with structures, and that it attains its results through a systematic application of the modern axiomatic method. Like many other mathematicians, past and contemporary, Bourbaki understood the historical development of mathematics as a series of (...) necessary stages inexorably leading to its current state — meaning by this, the specific perspective that Bourbaki had adopted and were promoting. But unlike anyone else, Bourbaki actively put forward the view that their conception of mathematics was not only illuminating and useful for dealing with the current concerns of mathematics, but that this was in fact the ultimate stage in the evolution of mathematics, bound to remain unchanged by any future development of this science. In this way, they were extending in an unprecedented way the domain of validity of the belief in the eternal character of mathematical truths, from the body to the images of mathematical knowledge.Bourbaki were fond of presenting their insistence on the centrality of the modern axiomatic method as a way to ensure the eternal character of mathematical truth as an offshoot of Hilbert's mathematical heritage. A detailed examination of Hilbert's actual conception of the axiomatic method, however, brings to the fore interesting differences between it and Bourbaki's conception, thus underscoring the historically conditioned character of certain, fundamental mathematical beliefs. (shrink)

We present some results on algebraic and modal analysis of polynomial distortions of the standard provability predicate in Peano Arithmetic PA, and investigate three provability-like modal systems related to the Gödel–Löb modal system GL. We also present a short review of relational and topological semantics for these systems, and describe the dual category of algebraic models of our main modal system.

A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let ε denote the structure of the computably enumerable sets under inclusion, $\varepsilon = (\{W_e\}_{e\in \omega}, \subseteq)$ . We previously exhibited a first order ε-definable property Q(X) such that Q(X) guarantees that X is not Turing complete (i.e., does not code complete information about c.e. sets). Here we show first that Q(X) implies that X has (...) a certain "slowness" property whereby the elements must enter X slowly (under a certain precise complexity measure of speed of computation) even though X may have high information content. Second we prove that every X with this slowness property is computable in some member of any nontrivial orbit, namely for any noncomputable A ∈ ε there exists B in the orbit of A such that X ≤ T B under relative Turing computability (≤ T ). We produce B using the Δ 0 3 -automorphism method we introduced earlier. (shrink)

This article critically explores the history and nature of a hermeneutic assumption which frequently guided interpretations of Plotinus from the 18th century onwards, namely that Plotinus advanced a system of philosophy. It is argued that this assumption was introduced relatively late, in the 18th and 19th centuries, and that it was primarily made possible by Brucker’s methodology for the history of philosophy, dating from the 1740s, to which the concept of a ‘system of philosophy’ was essential. It is observed that (...) the concept is absent from Ficino’s commentary from the 15th century, and that it remained absent in interpretations produced between the 15th and 18th centuries. It is also argued that the assumption of a ‘system of philosophy’ in Plotinus is historically incorrect—we do not find this concept in Plotinus’ writings, and his own statements about method point in other directions. Eduard Zeller is typically regarded as the first to give a satisfying account of Plotinus’ philosophy as a whole. In this article, on the other hand, Zeller is seen as having finalised a tradition initiated in the 18th century. Very few Plotinus scholars have examined the interpretative development prior to Zeller. Schiavone and Bonetti , for instance, have given little attention to Brucker’s introduction of the concept of a ‘system of philosophy’. The present analysis, then, has value for an understanding of Plotinus’ Enneads. It also explains why “pre-Bruckerian” interpretations of Plotinus appear alien to the modern reader; the analysis may even serve to make some sense of the hermeneutics employed by Renaissance Platonists and commentators, who are often eclipsed from the tradition of Platonism. (shrink)

The Description for this book, Narrative Form in History and Fiction: Hume, Fielding, and Gibbon, will be forthcoming.

How we talk about relations has a great influence on how we think about relations. By saying that Spain defeated the Netherlands we obviously say something entirely different from saying that the Netherlands defeated Spain. This makes many of us think that in the underlying relation itself one of the relata comes first and the other comes second. However, there are good reasons to view the order as a representational artifact. In this paper I present a new logic that allows (...) us to think and talk about relations in a coordinate-free manner. The logic is minimalistic in the sense that it has no predicates except equality, but its expressive power is the same as that of first-order predicate logic. (shrink)

The human body is a multifaceted reality. As such, it has become a reference pole for a new positivity. Among the various areas of corporeal expression and recuperation, sport has become the most absorbing and efficient. Sport as a system shapes the human body in all its aspects, and confers on it a new status: the "corps sportif" which is a new paradigm of our civilization.

Le corps humain est une réalité plurielle. En tant que tel, il est devenu un pôle de référence pour une nouvelle positivité. De tous les lieux d'expression et de récupération du corps, le sport est devenu le plus accaparant et le plus efficace. Le système sportif façonne le corps humain dans tous ses aspects et lui confère un statut nouveau, celui de corps sportif, ce nouveau paradigme des temps actuels.The human body is a multifaceted reality. As such, it has become (...) a reference pole for a new positivity. Among the various areas of corporeal expression and recuperation, sport has become the most absorbing and efficient. Sport as a system shapes the human body in all its aspects, and confers on it a new status: the "corps sportif" which is a new paradigm of our civilization. (shrink)

A persistent criticism of Edmund Husserl’s transcendental phenomenology is that it begs the question of its own possibiIity as science. In this essay I propose a reading of Husserl which addresses this question and attempts to show that the phenomenological ideal of freedom from all presuppositions, that is, the ideal of radical methodological autonomy, is not dogmatically assumed as valid but rests on a conception of philosophy which, although not explicitly formulated by Husserl, nevertheless informs his thinking on questions of (...) method and, ultimately, the nature of science. According to this conception, phiIosophy, phenomenological or otherwise, is not sui generis the ground of is own possibiIity but is derived from the logic of experience itself and so is immanent to conscious, intentional life in all of its manifold occupations and interests. That is, experience ultimately fulfills itself not in the accumulation of objective facts but in its continued faithfulness to the idea of a more perfect knowledge. Thus, in the end, I hope to show that the question of the status and possibiIity of phenomenological philosophy is not of interest to phenomenologists alone but addresses the enterprise of philosophy itself. (shrink)

Abstract: In responding to the cases that motivate epistemic contextualism, invariantists sometimes use a warranted assertability maneuver (WAM), according to which we mistakenly judge an assertion to be true because we confuse conversational propriety with truth. I argue that no invariantist WAM against Stewart Cohen's Airport Case can succeed. The problem is that such a WAM is inconsistent with the known ways of accounting for the evidence that motivates the knowledge account of assertion.

A new logic is presented without predicates—except equality. Yet its expressive power is the same as that of predicate logic, and relations can faithfully be represented in it. In this logic we also develop an alternative for set theory. There is a need for such a new approach, since we do not live in a world of sets and predicates, but rather in a world of things with relations between them.

In this essay I examine and discuss the concept “system of philosophy” as a methodological tool in the history of philosophy; I do so in two moves. First I analyze the historical origin of the concept in the seventeenth and eighteenth centuries. Thereafter I undertake a discussion of its methodological weaknesses—a discussion that is not only relevant to the writing of history of philosophy in the seventeenth and eighteenth centuries, but also to the writing of history of philosophy in our (...) times, where the concept remains an important methodological tool. My first move is to analyze Jacob Brucker’s employment of the concept in his influential history of philosophy, Historia critica philosophiae, dating from 1742–1744. To Brucker, a “system of philosophy” is characterized by the following four features: it is autonomous in regard to other, non-philosophical disciplines; all doctrines stated within the various branches of philosophy can be deduced from one principle; as an autonomous system it comprises all branches of philosophy; the doctrines stated within these various branches of philosophy are internally coherent. Brucker employed the concept on the entire history of philosophy, and he gave it a defining role in regard to two other methodological concepts, namely “eclecticism” and “syncretism,” which he regarded as more or less successful forms of systematic philosophy. My second move is to point out the weakness of the concept of “system of philosophy” as a methodological tool in the history of philosophy. I argue that the interdisciplinary nature of much premodern philosophy makes Brucker’s methodological concept “system of philosophy” inadequate, and that we may be better off leaving it behind in our future exploration of premodern philosophy. (shrink)