The Epsilon Calculus and Herbrand Complexity

Hilbert's ε-calculus is based on an extension of the language of predicate logic by a term-forming operator e _x . Two fundamental results about the ε-calculus, the first and second epsilon theorem, play a rôle similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.     

From Figure to Argument: <Emphasis Type="Italic">Contrarium</Emphasis> in Roman Rhetoric

In Roman rhetoric, contrarium was variably considered either a figure of speech or an argument. The paper examines the logical pattern of this type of argument, which according to Cicero is based on a third Stoic indemonstrable syllogism: The persuasiveness of this type of argument, however, vitally depends on the validity of the alleged ‹incompatibility’ forming its major premiss. Yet this appears to be the argument’s weak point, as the ‹incompatibilities’ employed generally hold for the most part only, and are reducible to topical argument schemes. This is why in practical usage such arguments are most often phrased as rhetorical questions, the persuasive force of which, enhanced by certain strategical maneuverings and fallacies, makes the audience swallow the argument.     

Evaluating Dialectical Structures

This paper develops concepts and procedures for the evaluation of complex debates. They provide means for answering such questions as whether a thesis has to be considered as proven or disproven in a debate or who carries a burden of proof. While being based on classical logic, this framework represents an (argument-based) approach to non-monotonic, or defeasible reasoning. Debates are analysed as dialectical structures, i.e. argumentation systems with an attack- as well as a support-relationship. The recursive status assignment over the arguments is conditionalised on proponents in a debate. The problem of multiple status assignments arising on circular structures is solved by showing that uniqueness can be guaranteed qua reconstruction of a debate. The notion of burden of proof as well as other discursive aims rational proponents pursue in a debate is defined within the framework.     

RESPONSES TO NUCCETELLI, LEMOS, AND BUENO

Abstract: Susana Nuccetelli discusses critically my account of Moore's Proof of the External World. Noah Lemos takes up my views on skepticism and my distinction between animal knowledge and reflective knowledge. Otávio Bueno focuses on my treatment of dream skepticism. In this article I offer replies to my three critics.     

A Deep Inference System for the Modal Logic S5

We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference. Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct design: the rules are few and the modal rules are in exact correspondence to the modal axioms. Presented by Heinrich Wansing     

The Normative Structure of Adjudicative Dialogue

Resolution-oriented dialogue has a normative structure that is largely subject to theoretical explication. This paper develops a simple model that sheds light on how moves in a reason-giving game alter the distribution of discursive commitments and entitlements. By clarifying the practice of deontic scorekeeping, we can enhance our collective capacity to resolve conflicts dialogically.     

Reason,Education and Liberalism: Family Resemblance within an Overlapping Consensus

This paper focuses on recent debates over the nature ofliberalism and its central feature of reason, both inside and outside ofeducational philosophy. Central ideas from Jonathan and Hirst contributeas do those from Rawls, Gadamer, Wittgenstein, Taylor, and Ackermantoward a less traditional contextualized and contingent view.     

Assessing the process of desensitization therapy: Five practical measures

Assessment of phobic behavior has included self-report, physiological, and in vivobehavioral measures. While self-report measures are convenient, they suffer from subject bias and a low predictive validity. Physiological and in vivobehavioral measures are often too cumbersome to implement in standard clinical practice. The current study investigated the validity of five convenient measures of phobic behavior during the process of desensitization therapy. Responses of 14 clinically phobic patients were compared on phobic and neutral scenes presented within the context of systematic desensitization therapy. Phobic scenes resulted in less clarity of scene visualization, a longer latency to clear scene visualization, higher subjective units of discomfort (SUDs) at clear visualization, a longer latency to relaxation, and higher SUDs at relaxation. The measures seemed to reflect accurately the process and stages of desensitization therapy and showed low to high intercorrelations. The pragmatic value of these measures is discussed, as well as suggestions for future validational research.     

Critical thinking in North America: A new theory of knowledge,learning, and literacy

The pace of change in the world is accelerating, yet educational institutions have not kept pace. Indeed, schools have historically been the most static of social institutions, uncritically passing down from generation to generation outmoded didactic, lecture-and-drill-based, models of instruction. Predictable results follow. Students, on the whole, do not learn how to work by, or think for, themselves. They do not learn how to gather, analyze, synthesize and assess information. They do not learn how to analyze the diverse logic of the questions and problems they face and hence how to adjust their thinking to those problems. They do not learn how to enter sympathetically into the thinking of others, nor how to deal rationally with conflicting points of view. They do not learn to become critical readers, writers, speakers and listeners. They do not learn how to use their native languages clearly, precisely, or persuasively. They do not, therefore, become literate, in the proper sense of the word. Neither do they gain much in the way of genuine knowledge since, for the most part, they could not explain the basis for what they believe. They would be hard pressed to explain, for example, which of their beliefs were based on rational assent and which on simple conformity to what they have been told. They have little sense as to how they might critically analyze their own experience, or identify national or group bias in their own thinking. They are much more apt to learn on the basis of irrational than rational modes of thought. They lack the traits of mind of a genuinely educated person: intellectual humility, courage, integrity, perseverance, and faith in reason.Happily, there is a movement in education today striving to address these problems in a global way, with strategies and materials for the modification of instruction at all levels of education. At its foundation is an emerging new theory of knowledge, learning, and literacy, one which recognizes the centrality of independent critical thinking to all substantial learning, one which recognizes that higher-order, multilogical thinking is as important to childhood as to adult learning, and as important to foundational learning in monological as in multilogical disciplines. This educational reform movement is not proposing an educational miracle cure, for its leading proponents recognize that many social and historical forces must come together before the ideals of the critical thinking movement will become a full academic reality. Schools do not exist in a social vacuum. To the extent that the broader society is uncritical so, on the whole, will be society's schools. Nevertheless, the social conditions necessary for fundamental changes in schooling are increasingly apparent. The pressure for fundamental change is growing. Whether and to what extent these needed basic changes will be delayed or side-tracked, thus requiring new periodic resurgences of this movement, with new, more elaborate articulations of its ideals, goals, and methods — only time will tell.     

Argumentative aspects of indirect proof

While direct proof is widely considered the paradigm of the acquisition of knowledge by deductive means, indirect proof has traditionally been criticized as showing merely that its conclusion is true and not why it is true. This paper accounts for the traditional objection by emphasizing the argumentative role in indirect proof of logical principles such as excluded middle and non-contradiction.