The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...) and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argument—as opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschrift has some gaps, but it is taken (...) as an essentially correct formal system for second-order logic: the first one in the history of logic. However, there is strong textual evidence that such an interpretation should be rejected. This evidence shows that the nature of the distinction between function and argument is stated by Frege in a significantly different way: it applies only to expressions and not to entities. The formal system based on this distinction is tremendously flexible and is suitable for making explicit the logical structure of contents as well as of deductive chains. We put forward a new reconstruction of the function-argument scheme and the quantification theory in Begriffsschrift. After that, we discuss the usual semantic interpretation of Begriffsschrift and show its inconsistencies with a rigorous reading of the text. (shrink)

In Begriffsschrift, Frege presented a formal system and used it to formulate logical definitions of arithmetical notions and to deduce some noteworthy theorems by means of logical axioms and inference rules. From a contemporary perspective, Begriffsschrift’s deductions are, in general, straightforward; it is assumed that all of them can be reproduced in a second-order formal system. Some deductions in this work present—according to this perspective—oddities that have led many scholars to consider it to be Frege’s inaccuracies which should be amended. (...) In this paper, we continue with the analysis of Begriffsschrift’s logic undertaken in an earlier work and argue that its deductive system must not be reconstructed as a second-order calculus. This leads us to argue that Begriffsschrift’s deductions do not need any correction but, on the contrary, can be explained in coherence with a global reading of this work and, in particular, with its fundamental distinction between function and argument. (shrink)

From ancient times to the beginning of the nineteenth century, mathematics was commonly viewed as the general science of quantity, with two main branches: geometry, which deals with continuous quantities, and arithmetic, which deals with quantities that are discrete. Mathematical logic does not fit neatly into this taxonomy. In 1847, George Boole [1] offered an alternative characterization of the subject in order to make room for this new discipline: mathematics should be understood to include the use of any symbolic calculus (...) “whose laws of combination are known and general, and whose results admit of a consistent interpretation.” Depending on the laws chosen, symbols can just as well be used to represent propositions instead of quantities; in that way, one can consider calculations with propositions on par with more familiar arithmetic calculations. Despite Boole’s efforts, logic has always held an uncertain place in the mathematical community. This can partially be attributed to its youth; while number theory and geometry have their origins in antiquity, mathematical logic did not emerge as a recognizable discipline until the latter half of the nineteenth century, and so lacks the provenance and prestige of its elder companions. Furthermore, the nature of the subject matter serves to set it apart; as objects of mathematical study, formulas and proofs do not have the same character as groups, topological spaces, and measures. Even distinctly mathematical branches of contemporary logic, like model theory and set theory, tend to employ linguistic classifications and measures of complexity that are alien to other mathematical disciplines. The Birth of Model Theory, by Calixto Badesa, describes a seminal step in the emergence of logic as a mature mathematical discipline. As its title suggests, the focus is on one particular result, now referred to as the L¨owenheim-Skolem theorem, as presented in a paper by L¨owenheim in 1915. But the book is, more broadly, about the story of the logic community’s gradual coming to the modern distinction between syntax and semantics, that is, between systems of symbolic expressions and the meanings that can be assigned to them.. (shrink)

Although it is commonly believed that the concept of brain death was developed to benefit organ transplants, it evolved independently. Transplantation owed its development to advances in surgery and immunosuppressive treatment; BD owed its origin to the development of intensive care. The first autotransplant was achieved in the early 1900s, when studies of increased intracranial pressure causing respiratory arrest with preserved heartbeat were reported. Between 1902 and 1950, the BD concept was supported by the discovery of EEG, Crile’s definition of (...) death, the use of EEG to demonstrate abolition of brain potentials after ischaemia, and Crafoord’s statement that death was due to cessation of blood flow. Transplantation saw the first xenotransplant in humans and the first unsuccessful kidney transplant from a cadaver. In the 1950s, circulatory arrest in coma was identified by angiography, and the death of the nervous system and coma dépassé were described. Murray performed the first successful kidney transplant. In the 1960s, the BD concept and organ transplants were instantly linked when the first kidney transplant using a brain-dead donor was performed; Schwab proposed to use EEG in BD; the Harvard Committee report and the Sydney Declaration appeared; the first successful kidney, lung and pancreas transplants using cadaveric donors were achieved; Barnard performed the first human heart transplant. This historical review demonstrates that the BD concept and organ transplantation arose separately and advanced in parallel, and only began to progress together in the late 1960s. Therefore, the BD concept did not evolve to benefit transplantation. (shrink)

Although it is commonly believed that the concept of brain death was developed to benefit organ transplants, it evolved independently. Transplantation owed its development to advances in surgery and immunosuppressive treatment; BD owed its origin to the development of intensive care. The first autotransplant was achieved in the early 1900s, when studies of increased intracranial pressure causing respiratory arrest with preserved heartbeat were reported. Between 1902 and 1950, the BD concept was supported by the discovery of EEG, Crile’s definition of (...) death, the use of EEG to demonstrate abolition of brain potentials after ischaemia, and Crafoord’s statement that death was due to cessation of blood flow. Transplantation saw the first xenotransplant in humans and the first unsuccessful kidney transplant from a cadaver. In the 1950s, circulatory arrest in coma was identified by angiography, and the death of the nervous system and coma dépassé were described. Murray performed the first successful kidney transplant. In the 1960s, the BD concept and organ transplants were instantly linked when the first kidney transplant using a brain-dead donor was performed; Schwab proposed to use EEG in BD; the Harvard Committee report and the Sydney Declaration appeared; the first successful kidney, lung and pancreas transplants using cadaveric donors were achieved; Barnard performed the first human heart transplant. This historical review demonstrates that the BD concept and organ transplantation arose separately and advanced in parallel, and only began to progress together in the late 1960s. Therefore, the BD concept did not evolve to benefit transplantation. (shrink)

O objetivo que o autor persegue nesta obra é a apreensão e a explicação das diferentes modalidades da natureza, bem como as suas interdependências respectivas. Para isso, ele desenvolve um sistema filosófico original, fundamentado sobre a tríade neoplatônica: imanência, processão e retorno. A natureza, enquanto conceito universal englobando Deus e a criatura, é concebida a partir de um duplo movimento: de saída, o mundo é auto-manifestação de Deus; de retorno, o processo criacional tende a reunificação de todas as coisas em (...) Deus. A noção de nada exerce uma função essencial nessa perspectiva, pois os primeiros exercícios dialéticos do Periphyseon, essenciais ao sistema filosófico erigeniano, estabelece como divisão fundadora da natureza ou Physis (o conceito de maxima extensio), a divisão que intervém entre o ser e o não-ser. (shrink)

O sermão número 48, “O dia santificado” (Sermo XLVIII: Dies Santificatus), proferido em Mainz na data de 6 de Janeiro de 1445, na Festa da Epifania do Senhor, traz alguns temas de interesse na compreensão do desenvolvimento da filosofia cusana no período imediatamente posterior à obra A douta ignorância (De docta ignorantia, 1440) e As conjecturas (1442). Este sermão é citado no opúsculo A busca de Deus (De querendo deum, I, 16, 3), de 1445, como sendo a primeira tentativa cusana (...) de tratar do tema dos “modos de conhecimento” (modi cognoscendi) a partir da perspectiva do tema da “luz e das cores”, caro à tradição de comentadores escolásticos do De anima aristotélico, tentativa essa que viria a ser aprimorada no referido opúsculo. Nele, Cusa busca uma “conjectura” capaz de simbolizar a relação paradoxal de imanência e transcendência entre Deus e a criação, mediante a relação que se estabelece entre a luz sensível e as cores do arco-íris. A luz, embora explicada em suas determinações, isto é, nas cores, ainda permanece transcendente às mesmas, as complicando enquanto luz pura. Do mesmo modo, Cusa evoca o exemplo do “sentido comum” da tradição escolástica, que em sua interpretação neoplatonizante, seria responsável por “complicar” todos os sentidos. Por fim, mediante tais exemplos da luz e dos sentidos, Cusa encaminha sua reflexão à visão do “modo de ser divino”, que, segundo ele, também poderia ser intuído no exemplo do nome divino IHWH. Esse nome inominável que complica todos os nomes, assim como os exemplos tratados, simboliza aquela realidade divina que complica e explica todas as coisas. A reunião desses exemplos é abalizada por uma coleção de citações escriturais, que buscam trazer respaldo às suas interpretações. (shrink)

Cet article a comme objetif analyser les liens possibles entre deux thèmes de grande relevance de la philosophie de Nicolas de Cues : la théophanie comme manifestation de Dieu et la filiatione dei ou visio Dei, comme modes de clairvoyance de l'infini divin. Cette « voie divine » de la connaissance est la fin d'un voyage où la créature « court » vers le fondement radical qui se révèle em tant que présence infinie dans le fini grâce une « vision (...) » intellectuelle. Le principe de la non-contradiction doit donc être remplacé par celui de la coïncidence des contraires ; cependant, ce dernier doit finalement être dépassé par l'ignorance savante. A son tour, selon Nicolas de Cues, dans cette vision théophanique, le « ne pas savoir » de la créature coincide avec le « savoir » que Dieu a de lui-même, c'est-à-dire de sa connaissance de soi comme infini et non pas en tant qu’une chose parmi d’autres. Dans la tradition néoplatonicienne latine, l’univers théorique où gravitent les concepts de monè, proódos et epistrophé (manence, procession et retour), Nicolas de Cues apporte cependant des nouveautés par rapport à ses prédécesseurs, comme Jean Scot Erigène, puisqu'il se lance dans une tentative ambitieuse d’utiliser la négativité comme outil d'un « discours ignorant » radical, c'est-à-dire un discours qui cherche une expression positive de la « racine » de cette relation paradoxale Créateur-créature. A travers l'itinéraire d'élaboration des noms divins et des énigmes de plus en plus « capables » d'orienter l'intellect vers cette vision du principe incompréhensible dans sa relation active de création/vision avec l'Univers, le Cardinal parcourt le chemin philosophique proposé dans son De coniecturis : une recherche sans fin de l'expression positive de Dieu à travers la négativité visant dépasser l’anonymat classique qui caractérise la tradition néoplatonicienne. Mots-clés : Nicolas de Cues, Visio de Dieu, Docte ignorance, infini, néoplatonisme. (shrink)

Nicolas de Cues (1401-11 août 1464) assume pour l’essentiel la thèse érigénienne et alanienne de l’incognoscibilité de Dieu et de la quiddité des choses. Il développe et approfondit la conscience de la supériorité de la négation sur l’affirmation in divinis qui avait permis au Néoplatonisme Médiéval d’élaborer une théorie sémantique du langage en nette rupture avec le triptyque aristotélicien qui établit la nécessité d’une correspondance entre chose, pensée et signe : pour Nicolas de Cues, l’essence du langage est dans la (...) production d’un sens, et celui-ci peut être entièrement indépendant de la possibilité d’appréhension de son objet. La présente recherche entend démontrer que cette thèse de l’incognoscibilité divine est intimement liée à une autre thèse d’ordre épistémologique qui décrète radicalement que toute affirmation est une conjecture au sujet du réel et que notre esprit est dans l’impossibilité d’atteindre la vérité de façon adéquate. Il n’existe pas de connaissance humaine certaine, car la quiddité des choses qui détermine leurs essences véritables est inaccessible. (shrink)

Cette étude a pour objectif de démontrer que chez Alain de Lille, la problématique de l’affirmation et de la négation in divinis n’est pas celle de la montée vers Dieu par l’abandon de toute créature. Chez Alain de Lille, la négation constitue l’élément qui permet de penser, au niveau du langage, la différence ontologique qui existe entre Dieu et le monde. Cela n’a été possible que grâce à la convergence de deux traditions : celle de Jean Scot Érigène et celle (...) de Boèce. Parce qu’Alain de Lille approfondit la structure métaphorique du nom divin, il est alors à même de reposer d’une façon originale la problématique de la négation et de l’affirmation dans le discours théologique. Il n’est plus question chez lui de la possibilité ou non de discourir sur la divinité, il est davantage question de règles de sémantique, et donc d’herméneutique, convenant aux discours affirmatif et négatif sur la divinité. (shrink)

Apresentar ao pesquisador da história da filosofia os fundamentos e o quão rico e fértil são as contribuições do Neoplatonismo no decorrer da Idade Média, o objeto da organização deste volume. Para tal foram mobilizados grandes especialistas da área que generosamente colaboraram na elaboração do presente número da Revista de Ética e Filosofia Política da Universidade Federal de Juiz de Fora. Palavras-chave: Neoplatonismo, Filosofia Medieval, Plotino, Gnosticismo, Proclo, Agostinho, João Escoto Erígena, Al-Kindi, Alberto Magno, Mestre Eckhart, Nicolau de Cusa, Ficino.

Jean Greisch3 (1942-), ainda pouco conhecido no Brasil, é um filósofo e professor luxemburguês. Realizou seus estudos em filosofia e teologia em seu próprio país, completando-os com um doutorado em filosofia, no Instituto Católico de Paris, onde defendeu sua tese sobre Martin Heidegger. Suas principais pesquisas estão relacionadas com as problemáticas contemporâneas da ontologia, da hermenêutica e da religião. Em A idade hermenêutica da razão, instigado em como a hermenêutica se inseriu no coração da filosofia ao ponto de hoje tratarmos (...) como corrente filosófica o que, antes, era uma disciplina auxiliar, Greisch analisa três sentidos possíveis da expressão razão hermenêutica: (i) o sentido descritivo, onde é realizada uma investigação histórica; (ii) o sentido crítico, onde se analisa os debates que envolve tal expressão; (iii) o sentido heurístico, onde ele questiona o quanto esta expressão implica ou não em uma ideia própria de razão. (shrink)

A ciência, inicialmente prevista para servir ao homem, se desvia de sua finalidade original e começa a ameaçá-lo. A questão se põe, então, com acuidade em saber qual homem corresponderia à ciência de hoje. Face à visão fortemente cientificista do homem, caberia, entre outros, recorrer a Charles de Bovelles (1479-1566), a quem se deve recorrer para retornar a um conhecimento de si, que é o conhecimento da atividade de sua alma que, por seu turno, deve conhecer o corpo. A philautia (...) (amor de sua condição humana) torna-se, pois, o ponto de partida de uma antropologia filosófica sapiencial em uma perspectiva de conhecimento de si, pelo “sistere in homine” (permanecer no homem) para uma verdadeira ipsologia (discurso de si sobre si). O humanismo encontrado deve, então, se abrir, segundo Bovelles, à transcendência, a este traço de Deus sempre no homem que a ciência busca apagar. Palavras-chave: Homem - científico - Ipsologia - Conhecimento - Philautia - Humanismo. (shrink)

A Ciência da Informação tem apresentado campos de estudo e modelos de compreensão variados. Assim, este trabalho tem como objetivo analisar o conceito de informação na perspectiva da Ciência da Informação. As contribuições teóricas dos autores Saracevic e Wood, Adkinson, Borko, Buckland e Rayward foram adotadas para trilhar a narrativa deste relato. A metodologia adotada é do tipo descritiva e bibliográfica, de abordagem dedutiva baseada em artigos científicos, relatórios técnicos, correspondências por e-mail, obituários, currículos entre outros documentos. Com relação ao (...) conceito “informação”, criou-se um desenho de instrução sintetizado das visões e perspectivas dos autores citados sobre o termo em estudo. (shrink)

O seguinte artigo tem como objetivo apresentar a interpretação realizada pelo filósofo e místico alemão Mestre Eckhart, das figuras de Marta e Maria no sermão de número 86 A Excelência de Marta sobre Maria. Apoiado neste sermão, faremos algumas análises filosóficas dos conceitos de vida contemplativa e vida ativa, pois compreendemos que ao realizar a interpretação da superioridade de Marta sobre Maria, Mestre Eckhart estabelece um novo paradigma interpretativo da vida contemplativa e ativa na filosofia medieval. Palavras-chaves: Mestre Eckhart. Mística. (...) Vida contemplativa. Vida ativa. Marta e Maria. (shrink)

Le présent article se donne comme tâche démontrer que la reprise dionysienne de l’hénologie néoplatonicienne ne se fait pas sans quelques déplacements dus à l’influence de la théologie chrétienne sur le néoplatonisme. Le plus important d’entre eux étant la revalorisation du discours positif sur la divinité, rendue possible grâce à la négation par transcendance qui permet d’affirmer de Dieu qu’il est, tout en tenant compte du fait que l’Etre divin, à cause de sa transcendance, est au-delà de nos connaissances. Le (...) premier enjeu de la problématique de la négation en régime néoplatonicien a moins été de dépasser la définition aristotélicienne de la négation que de rompre avec le primat supposé de l’affirmation, en démontrant qu'il n'est pas ontologiquement fondé, lorsque l'on a affaire à la pensée de l'Un. Mais aussi et surtout, on retrouve dans la théologie dionysienne, une réhabilitation de la positivité des attributs divins révélés dans l’Ecriture, ouvre la pensée du néant suressentiel à la non-opposition. L’entrée ici du concept de révélation est d’une importance capitale, car, désormais en régime chrétien, s’il faut préserver le secret, l’obscurité et faut aussi la concilier avec la révélation, bref, il faut maintenir transcendance, il ne faut pas négliger l’immanence. Ce geste de l'Aréopagite s'avère être d'une grande fertilité au Moyen Age. (shrink)