Aspects of justice. Debate on ethical principles and social justice - ethische principes en sociale gerechtigheid. Referring to Hans Kelsen (1952); Chaïm Perelman (1945; 1960; 1961); Hanna F. Pitkin (1972); John Rawls (1971) -/- Aspecten van rechtvaardigheid - M.A. Thesis, Philosophy, University of Amsterdam, June 2, 1975 .

No sermão pelo bom sucesso das armas de Portugal contra as da Holanda, Vieira explana todos os seus dotes de prosador invulgar, teólogo eminente, jurista incontornável, humanista convicto e, acima de tudo, patriota assumido. O presente trabalho pretende, sobretudo, relevar o poder argumentative do orador, seguindo de perto as considerações de Chaïm Perelman sobre a Retórica como "discurso que visa convencer ou persuadir". Simultaneamente, desta-cam-se os голоl ou valores universais patenteados no texto de Vieira e que constituem a base (...) da teoria da argumentação de Oswald Ducrot. \\\ In the "Sermon for the good success of the Portuguese army against Holland's", Vieira displays all his gifts as an uncommon writer, an excellent theologian, a non negligeable jurist, a convinced humanist, and, above all, a wholehearted patriot. This essay is an attempt to put in evidence the preacher's argumentative power, on the basis of Chaïm Perelman's considerations on Rethoric as "a speech that aims to convince or persuade". At the same time, we emphasize, as displayed in Vieira's text, the "topoi", or universal values, that are the basis of Oswald Ducrot's argumentation theory. (shrink)

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...) mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

ALL THE MORE, by Avi Sion, Ph.D., comprises a merged list of 72 qal vachomer arguments in the Tanakh, i.e. of a fortiori arguments in the Hebrew Bible. This listing brings together lists proposed in past rabbinic literature and in more recent studies by the author. The literature research for it was carried out mainly by R. Yaakov Gabay, who looked into works in Hebrew by five rabbis who had proposed lists, namely: R. Shmuel Yaffe Ashkenazi (Yefeh Toar, 1597), R. (...) Zvi Hirsch Katzenellenbogen (Netivot Olam, 1822), R. Zeev Wolf Einhorn (Midrash Tannaim, 1839), R. Mattityahu Strashun (Mattat Yah, 1892), R. Chaim Hirschensohn (Berure HaMidot, 1928). The author of the present essay brought additional information from the Tanakh commentary of R. Shlomo Yitzchaki (Rashi, 11th Cent.) and an essay by R. Louis Jacobs (2005), as well as from his own past works (Judaic Logic, 1995, and A Fortiori Logic, 2013). The information thus gathered is here presented in a systematic manner, after careful evaluation by the author of each case with reference to narrative context, language used, and logical form. Efforts are made to identify which cases were known to each of the past authors, and to determine who found each case first and whether subsequent listings of the case (if any) were independent or derivative. (shrink)

In this paper we analyze the uses and misuses of argumentation schemes from verbal classification, and show how argument from definition supports argumentation based on argument from verbal classification. The inquiry has inevitably included the broader study of the concept of definition. The paper presents the schemes for argument from classification and for argument from definition, and shows how the latter type of argument so typically supports the former. The problem of analyzing arguments based on classification is framed in a (...) structure that reveals the crucial role it plays in the persuasion process. The survey of the literature includes the work of Hastings, Perelman, Kienpointner and Schiappa, but still finds much of value in Aristotle. Lessons drawn from Aristotle’s Topics are shown to be useful for developing new tools for assessing definitions and arguments from definition. (shrink)

A homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful physically. Furthermore, the conjecture can be (...) generalized and interpreted in relation to the pseudo-Riemannian space of general relativity therefore allowing for both mathematical and philosophical interpretations of the force of gravitation due to the mismatch of choice and ordering and resulting into the “curving of information” (e.g. entanglement). Mathematically, that homeomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. Philosophically, the same homeomorphism implies transcendentalism once the philosophical category of the totality is defined formally. The fundamental concepts of “choice”, “ordering” and “information” unify physics, mathematics, and philosophy and should be related to their shared foundations. (shrink)

An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means the invariance (...) to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. (shrink)

A Fortiori Logic: Innovations, History and Assessments is a wide-ranging and in-depth study of a fortiori reasoning, comprising a great many new theoretical insights into such argument, a history of its use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its purpose is nothing less than to lay the foundations for a new branch of logic and greatly develop it; and thus to once and for all dispel the many fallacious (...) ideas circulating regarding the nature of a fortiori reasoning. -/- The work is divided into three parts. The first part, Formalities, presents the author’s largely original theory of a fortiori argument, in all its forms and varieties. Its four (or eight) principal moods are analyzed in great detail and formally validated, and secondary moods are derived from them. A crescendo argument is distinguished from purely a fortiori argument, and similarly analyzed and validated. These argument forms are clearly distinguished from the pro rata and analogical forms of argument. Moreover, we examine the wide range of a fortiori argument; the possibilities of quantifying it; the formal interrelationships of its various moods; and their relationships to syllogistic and analogical reasoning. Although a fortiori argument is shown to be deductive, inductive forms of it are acknowledged and explained. Although a fortiori argument is essentially ontical in character, more specifically logical-epistemic and ethical-legal variants of it are acknowledged. -/- The second part of the work, Ancient and Medieval History, looks into use and discussion of a fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s approach to a fortiori argument is described and evaluated. There is a thorough analysis of the Mishnaic qal vachomer argument, and a reassessment of the dayo principle relating to it, as well as of the Gemara’s later take on these topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly acknowledged. Lists are drawn up of the use of a fortiori argument in the Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible and the Koran; and the specific moods used are identified. Moreover, there is a pilot study of the use of a fortiori argument in the Gemara, with reference to Rodkinson’s partial edition of the Babylonian Talmud, setting detailed methodological guidelines for a fuller study. There is also a novel, detailed study of logic in general in the Torah. -/- The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work of numerous (some thirty) recent contributors to a fortiori logic, as well as the articles on the subject in certain lexicons. Here, we discover that whereas a few authors in the last century or so made some significant contributions to the field, most of them shot woefully off-target in various ways. The work of each author, whether famous or unknown, is examined in detail in a dedicated chapter, or at least in a section; and his ideas on the subject are carefully weighed. The variety of theories that have been proposed is impressive, and stands witness to the complexity and elusiveness of the subject, and to the crying need for the present critical and integrative study. But whatever the intrinsic value of each work, it must be realized that even errors and lacunae are interesting because they teach us how not to proceed. -/- This book also contains, in a final appendix, some valuable contributions to general logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox. (shrink)

Argumentation theory underwent a significant development in the Fifties and Sixties: its revival is usually connected to Perelman's criticism of formal logic and the development of informal logic. Interestingly enough it was during this period that Artificial Intelligence was developed, which defended the following thesis (from now on referred to as the AI-thesis): human reasoning can be emulated by machines. The paper suggests a reconstruction of the opposition between formal and informal logic as a move against a premise of (...) an argument for the AI-thesis, and suggests making a distinction between a broad and a narrow notion of algorithm that might be used to reformulate the question as a foundational problem for argumentation theory. (shrink)