The aim of this paper is to prove how what is apparently a mistake made by Plutarch, wheter deliberate or not, in his reference to the arson attack of Caesar´s soldiers in Alexandria as the end of the famous Library, show us the common sense of the term “bibliotheke” from that time up to now. Coming to this conclusion has required a detailed analysis of the Library of Alexandria since its birth applying Aristotelian doctrine to its configuration not only as (...) an organized space for books but also as an imaginary reading room from which the helenistic world of relations is established. In a second approach, we focus the attention on the change occurred in this collection with the introduction of alphabetical order and, then, with the philological activity of Callimachus. As a result of his Pinakes, the platonic concept of daimon, “guide”, became the first characteristic o a philologist or librarian. Using the information ordered in the Pinakes anybody could be a librarian and find a library anywhere. The old megále bibliotheke of Alexandría remains only with the idea of the conservation of original papyrus. This is de reason of the enigmatic sentence of Plutarch announcing the end of this situation caused by the action of the fire. (shrink)

A conservative extension of first order logic, suitable for circumscriptive inference, is introduced.

The article analyzes three different cases of clinical research in which children are asked to participate. Participation of children in researches is one of the major challenges for Bioethics and societies nowadays due to the tensions and issues concerning the guarantee of rights in clinical research, the responsibilities of the different actors involved, and the purpose of improving the quality of life without affecting scientific freedom and new knowledge production. The aim of the article is to establish the way in (...) which autonomy is exercised, considering ethical and regulative aspects within clinical research involving children. In order to achieve such a purpose, case study research methodology is employed, revealing the tensions and ethical issues involved in this particular kind of clinical research as well as considering international documents and the national regulation regarding this particular problem. (shrink)

The propositional calculus AoC, “Algebra of Classes”,and the extended propositional calculus EAC, “Extended Algebra ofClasses” are introduced in this paper. They are extensions, by additionalpropositional functions which are not invariant under the biconditional,of the corresponding classical propositional systems. Theirorigin lies in an analysis, motivated by Cantor’s concept of the cardinalnumbers, of A. P. Morse’s impredicative, polysynthetic set theory.

An extension of the Quantified Propositional Calculus1 obtained by the addition of two binary propositional functions is put forward as an inheritor of E. Schröder's “Algebra der Logik”. The formal system is itself not new, in fact it forms part of A. P. Morse's “A Theory of Sets”; although the latter is considered as a first-order system. Since the additional propositional functions are not invariant under the logical biconditional, this system–and many others naturally obtained from it–give us a collection of (...) examples of non-standard, but mathematically meaningful, propositional systems. (shrink)

In Logical Forms Part II, Chateaubriand begins the Chapter on “Propositional Logic” by considering the reading of the ‘conditional’ by ‘implies’; in fact he states that:There is a confusion, as a matter of fact, and it runs deep, but it is a confusion in propositional logic itself, and the mathematician’s reading is a rather sensible one.After a careful, erudite analysis of various philosophical viewpoints of logic, Chateaubriand comes to the conclusion that:Pure propositional logic, as just characterized, belongs to ontological logic, (...) and it does not include a theory of deduction as a human activity. This is a part of epistemological logic, and is more closely connected to the applications of pure propositional logic.An implicit assumption in Chateaubriand’s reasoning appears to be that propositions have a timeless status. I will present arguments for the opposite viewpoint which leads to an analysis of Propositional Logic not covered under Chateaubriand’s monograph and perhaps resolves some conflicts therein; much as the conflict between the Intuitionist and Classical Mathematician on whether every function on the Reals is continuous is resolved by the realization that they are talking about different “entities”.Em Logical Forms II, Chateaubriand inicia o capítulo “Lógica Proposi-cional” considerando a leitura do ‘condicional’ como ‘implica’. De fato, ele diz o seguinte:Na verdade, existe uma confusão, e ela é profunda, mas é uma confusão na lógica proposicional ela mesma, e a leitura de um matemático é bastante sensível.Depois de uma análise cuidadosa e erudita dos vários pontos de vista filosóficos da lógica , Chateaubriand chega à conclusão que:A lógica proposicional pura, tal como aqui caracterizada, pertence à lógica ontológica, e não inclui uma teoria da dedução como atividade humana. Isto é parte da lógica epistemológica, e é mais intimamente conectada às aplicações da lógica proposicional.Uma premissa implícita no raciocínio de Chateaubriand parece ser a de que proposições têm um estatuto atemporal. Eu argumentarei em favor da visão oposta, que leva a uma análise da Lógica Proposicional não abordada no texto de Chateaubriand e que talvez resolva alguns conflitos. Muito do conflito entre Intuicionistas e Matemáticos Clássicos sobre se toda função sobre os números reais é contínua é resolvido pela compreensão de que eles estão falando de “entidades” diferentes. (shrink)

A reduction algebra is defined as a set with a collection of partial unary functions (called reduction operators). Motivated by the lambda calculus, the Church-Rosser property is defined for a reduction algebra and a characterization is given for those reduction algebras satisfying CRP and having a measure respecting the reductions. The characterization is used to give (with 20/20 hindsight) a more direct proof of the strong normalization theorem for the impredicative second order intuitionistic propositional calculus.