This paper consists primarily of a survey of results of Harvey Friedman about some proof-theoretic aspects of various forms of Kruskal's tree theorem, and in particular the connection with the ordinal Γ0. We also include a fairly extensive treatment of normal functions on the countable ordinals, and we give a glimpse of Verlen hierarchies, some subsystems of second-order logic, slow-growing and fast-growing hierarchies including Girard's result, and Goodstein sequences. The central theme of this paper is a powerful theorem due to (...) Kruskal, the ‘tree theorem’, as well as a ‘finite miniaturization’ of Kruskal's theorem due to Harvey Friedman. These versions of Kruskal's theorem are remarkable from a proof-theoretic point of view because they are not provable in relatively strong logical systems. They are examples of so-called ‘natural independence phenomena’, which are considered by most logicians as more natural than the metamathematical incompleteness results first discovered by Gödel. Kruskal's tree theorem also plays a fundamental role in computer science, because it is one of the main tools for showing that certain orderings on trees are well founded. These orderings play a crucial role in proving the termination of systems of rewrite rules and the correctness of Knuth-Bendix completion procedures. There is also a close connection between a certain infinite countable ordinal called Γo and Kruskal's theorem. Previous definitions of the function involved in this connection are known to be incorrect, in that, the function is not monotonic. We offer a repaired definition of this function, and explore briefly the consequences of its existence. (shrink)

In this contribution, I will develop a comprehensive tool for the reconstruction and evaluation of argumentation from expert opinion. This is done by analyzing and then combining two dialectical accounts of this type of argumentation. Walton’s account of the ‘appeal to expert opinion’ provides a number of useful, but fairly unsystematic suggestions for critical questions pertaining to argumentation from expert opinion. The pragma-dialectical account of ‘argumentation from authority’ offers a clear and systematic, but fairly general framework for the reconstruction and (...) evaluation of this type of argumentation. The tool is developed by incorporating Walton’s critical questions into a pragma-dialectical framework. (shrink)

The practice of justifying scientific explanations generates argumentative patterns in which several types of arguments may play a role. This paper is aimed at identifying these patterns on the basis of an exploration of the institutional conventions regarding the nature, the shape and the quality of scientific explanations as reflected in the writings of influential philosophers of science. First, a basic pattern for justifying scientific explanations is described. Then, two types of extensions of this pattern are presented. These extensions are (...) derived from philosophical accounts of requirements for the quality of explanations and the choice of the best explanation from a number of candidate explanations respectively. The description of the second extension will make clear how pragmatic argumentation plays a role in argumentative patterns within the scientific domain. (shrink)

The aim of this paper is to indicate the systematic place of arguments based on the concept of analogy within the theoretical framework of the Periodic Table of Arguments, a new method for describing and classifying arguments that integrates traditional dialectical accounts of arguments and fallacies and rhetorical accounts of the means of persuasion (logos, ethos, pathos) into a comprehensive framework. The paper begins with an inventory of existing approaches to arguments based on analogy, similarity and adjacent concepts. Then, the (...) theoretical framework of the table will be expounded and several concrete examples of arguments based on these concepts will be analyzed in terms of the framework. Finally, the results of these analyses will be summarized and it will be indicated how they can be refined in further research related to the Periodic Table of Arguments. (shrink)

The millennial interest in the fable told by Apuleius in The Golden Ass has produced periods of intense preoccupation. Of these uses of the legend none is more interesting, varied, and profound—none possesses greater implications for contemporary life and manners—than the obsessive concern of pre-Romantic and Romantic writers and artists. Hellenistic, Roman, and early Christian culture had produced at least twenty surviving statues of Psyche alone, some seven Christian sarcophagi that used the legend, and a set of mosaics on a (...) Christian ceiling in Rome from the early fourth century;1 and of course to late antiquity belongs the distinction of having produced the seminal telling of the tale by Apuleius in about A. D. 125. But what we possess from that remote time is thin and lacks the power to engage the modern spirit. The allegorizing and erotic responses made in the Renaissance, Mannerist, and Baroque culture produced monuments of painting that the later period cannot rival; but the impregnation of literature by the legend was slight, and the intellectual or moral content was often only a perfunctory and dutiful addendum. The revival of the story in the aesthetic movement of the late Victorians and early moderns has its examples of beauty, particularly in Rodin and in the lush harmonies and occasionally piercing melodies of César Franck's Psyché, a tone poem for chorus and orchestra; but the long retellings by Morris, Bridges, and John Jay Chapman oppress with luxuriant sweetness and remain of interest only as period pieces. · 1. See Elizabeth Hazelton Haight, Apuleius and His Influence , p. 164, and Maxime Collignon, "Essai sur les monuments grecs et romains . . . ," in Bibliothèque des écoles françaises d'Athène et de Rome , fasc. 2, pp. 285-446, esp. pp. 364, 436-38. Jean H. Hagstrum, John C. Shaffer Professor of English and Humanities at Northwestern University, is currently preparing a book on the theme of love in European literature and art from the mid-seventeenth century through the Romantic period. He is the author of books and articles on Blake and Samuel Johnson, and of The Sister Arts, a study of the relations of poetry and painting from antiquity through the eighteenth century. (shrink)

In this paper, we formulate a procedure for assessing reasoning as it is expressed in natural arguments. The procedure is a specification of one of the three aspects of argumentation assessment distinguished in the Comprehensive Assessment Procedure for Natural Argumentation that makes use of the argument categorisation framework of the Periodic Table of Arguments. The theoretical framework and practical application of both the CAPNA and the PTA are described, as well as the evaluation procedure that combines the two. The procedure (...) is illustrated through an evaluation of the reasoning of two example arguments from a recently published text. (shrink)

In this paper, we use a pseudo-algorithmic procedure for assessing an AI-generated text. We apply the Comprehensive Assessment Procedure for Natural Argumentation (CAPNA) in evaluating the arguments produced by an Artificial Intelligence text generator, GPT-3, in an opinion piece written for the Guardian newspaper. The CAPNA examines instances of argumentation in three aspects: their Process, Reasoning and Expression. Initial Analysis is conducted using the Argument Type Identification Procedure (ATIP) to establish, firstly, that an argument is present and, secondly, its specific (...) type in terms of the argument classification framework of the Periodic Table of Arguments (PTA). Procedural Questions are then used to test the acceptability of the argument in each of the three aspects. The analysis shows that while the arguments put forward by the AI text generator are varied in terms of their type and follow familiar patterns of human reasoning, they contain obvious weaknesses. From this we can conclude that the automated generation of persuasive, well-reasoned argumentation is a far more difficult task than the generation of meaningful language, and that if AI systems producing arguments are to be persuasive, they require a method of checking the plausibility of their own output. (shrink)

Recent scholarship in the field of argumentation theory has shown an increasing interest in rethinking the relation between dialectic and rhetoric. In the debate concerning this issue, some scholars take the position of ‘isolationists’. They think that fundamental differences exist between the two disciplines and that it is impossible to translate insights developed within the one discipline in terms of the other. Other scholars can be characterized as ‘combinationalists’. They take the position that insights from dialectic and rhetoric can be (...) combined for the purpose of analyzing or evaluating argumentative discourse. Finally, there are ‘integrationalists’, who are of the opinion that the differences between dialectic and rhetoric can be overcome by reconceptualizing the two disciplines and integrating them into an encompassing theory of argumentation. According to these scholars, dialectic and rhetoric study one and the same phenomenon—argumentation understood as the ju .. (shrink)

This paper examines the conceptual and terminological overlap between theories and models of practical deliberation developed within the fields of Practical Reasoning (PR) and Practical Argumentation (PA). It carefully delineates the volitional, epistemic, normative, and social commitments invoked and explicates various rationales for attributing the label ‘practical’ to instances of reasoning and argumentation. Based on these analyses, the paper develops a new approach to practical deliberation called the Stakeholder Commitment Approach (SCA). By distinguishing between ‘problem holder’ and ‘problem solver’, and (...) specifying the distributions of attributable commitments among the stakeholders, the SCA introduces an extension and refinement of the grounds for assigning the label ‘practical’ that brings PR and PA closer together. (shrink)

We define a new class of Kripke structures for the second-order λ-calculus, and investigate the soundness and completeness of some proof systems for proving inequalities as well as equations. The Kripke structures under consideration are equipped with preorders that correspond to an abstract form of reduction, and they are not necessarily extensional. A novelty of our approach is that we define these structures directly as functors A: → Preor equipped with certain natural transformations corresponding to application and abstraction . We (...) make use of an explicit construction of the exponential of functors in the Cartesian-closed category Preor, and we also define a kind of exponential ΠΦs ε T to take care of type abstraction. However, we strive for simplicity, and we only use very elementary categorical concepts. Consequently, we believe that the models described in this paper are more palatable than abstract categorical models which require much more sophisticated machinery . We obtain soundness and completeness theorems that generalize some results of Mitchell and Moggi to the second-order λ-calculus, and to sets of inequalities. (shrink)

It was observed by Curry that when λ-terms can be assigned types, for example, simple types, these terms have nice properties . Coppo, Dezani, and Veneri, introduced type systems using conjunctive types, and showed that several important classes of terms can be characterized according to the shape of the types that can be assigned to these terms. For example, the strongly normalizable terms, the normalizable terms, and the terms having head-normal forms, can be characterized in some systems and Ω. The (...) proofs use variants of the method of reducibility. In this paper, we present a uniform approach for proving several meta-theorems relating properties of λ-terms and their typability in the systems and Ω. Our proofs use a new and more modular version of the reducibility method. As an application of our metatheorems, we show how the characterizations obtained by Coppo, Dezani, Veneri, and Pottinger, can be easily rederived. We also characterize the terms that have weak head-normal forms, which appears to be new. We conclude by stating a number of challenging open problems regarding possible generalizations of the realizability method. (shrink)

In 2001, France became one of the few countries to require corporate social responsibility reporting through its Nouvelles Régulations Économiques #2001-420. However, initial compliance with the statute was low, a factor implying the law lacked normativity. In this exploratory study, we attempt to determine whether there is movement toward normativity by examining the change in CSR disclosure from 2004 in comparison to 2010 for a sample of 81 publicly traded French firms. We measure both the space and the quality of (...) CSR disclosures, including in the latter a measure based on informational quality attributes as discussed by the International Accounting Standards Board, the Financial Accounting Standards Board, and the Global Reporting Initiative. We find significant increases in the space allocated to CSR disclosure, as well as some evidence of increased quality; although the informational quality of the disclosures remains quite low and fewer firms are including negative performance information in their reports. Finally, we document that differences in disclosure space and quality in 2004 appeared to be associated with legitimacy-based variables and that those relations remain largely unchanged in 2010. As such, it appears that the NRE’s goals of increased transparency remain unmet. (shrink)

Building a coherent discourse on professionalism is a challenge for corporate social responsibility practitioners, as there is not yet an established knowledge basis for CSR, and CSR is a contested notion that covers a wide variety of issues and moral foundations. Relying on insights from the literature on micro-CSR, new professionalism, and Boltanski and Thévenot’s economies of worth framework, we examine the discourses of 56 CSR practitioners in South Korea on their claimed professionalism. Our analysis delineates four distinct discourses of (...) CSR professionalism—strategic corporate giving, social innovation, risk management, and sustainability transition—that are derived from a plurality of more or less compatible moral foundations whose partial overlaps and tensions we document in a systematic manner. Our results portray these practitioners as compromise makers who selectively combine morally distant justifications to build their own specific professionalism discourse, with the aim to advance CSR within and across organizations. By uncovering the moral relationality connecting these discourses, our findings show that moral pluralism is a double-edged sword that can not only bolster the justification of CSR professionalism but also threaten collective professionalism at the field level. Overall, our study suggests paying more attention to the moral relationality and tensions that underlie professional fields. (shrink)

Cultural difference has been largely ignored within bioethics, particularly within the end-of-life discourses and practices that have developed over the past two decades in the U.S. healthcare system. Yet how should culturebe taken into account?

The financial sector likes to call itself a "service industry". As such, its role is to guarantee the fluidity of transactions which are essential to economic activity by ensuring the best possible use of available capital. If finance is a service activity, it is important to specify what services it renders, to whom, in return for what, and for what purpose. In the absence of such clarification, finance may slide out of control and be left at the mercy of mass (...) enthusiasm or hysteria. This document, which is the result of work by people who hold senior positions in Geneva's financial sector or are external observers of the financial world identifies the issues and suggests some avenues for possible solutions. (shrink)

Les trente dernières années du XX e siècle ont été marquées par une très forte inflation des règles du droit du travail visant à protéger l’emploi. Ces règles encadrent notamment le licenciement et tentent d’endiguer le recours aux contrats précaires. Mais on s’aperçoit aujourd’hui qu’il n’existe pas de rapport mécanique entre les objectifs poursuivis (protéger l’emploi), leur traduction législative et les résultats produits qui sont décevants. Prenant acte de son impuissance le législateur entend désormais changer de paradigme en concentrant ses (...) efforts sur la protection des transitions professionnelles. Toutefois les lois les plus récentes qui s’inscrivent dans cette perspective connaissent de nombreux déboires, et pour l’instant il ne semble pas évident que la prospection sur ces nouvelles terres donne plus de résultats que ceux obtenus sur les anciennes. (shrink)

Victor Dudman's revolutionary English Grammar brings grammar and logic together by conceiving grammar as 'the necessary preliminary to logic'. The focus, for logicians, is the discussion of 'conditionals'; for grammarians it is the concise and accurate explanation of the infamous English modals.

We argue that analyses of civil religious ideologies in civil rights contention must include the interplay of both movement and countermovement ideologies and must recognize the ways in which such discourse amplifies conflict as well as serves as a basis for unity. Based on in-depth interviews, archival research, and content analysis of civil religious language, this article examines how priestly and prophetic civil religious discourses, and the infusion of Black power ideologies, provided significant and dynamic resources for both movement and (...) countermovement ideologies during periods of civil rights contention in Cairo, Illinois, especially from 1969 to 1972. We compare the ways in which Cairo’s civil rights leaders mobilized prophetic versions of civil religion, and concomitantly, how white countermovement organizations used a priestly civil religion. On the prophetic side the themes of “equality,” “freedom,” “justice,” and the “right to revolt” against worldly socio-political arrangements were employed. On the priestly side, the theme of “law” and “order” was played up, with a secondary theme that connected religious acquiescence to worldly power with God’s will. The former rhetoric saw calls for economic and employment integration within God’s will and the nation’s destiny. The latter rhetoric contrasted civil rights claims as essentially “un-American.”. (shrink)