Neste artigo, Bar-Hillel e Carnap apresentam pela primeira vez as ideias básicas de uma teoria da informação semântica. O conceito de informação, baseado em sentença declarativa em uma dada linguagem, é definido pelo conteúdo descritivo expresso pelas sentenças. A quantidade de informação é calculada com base em um conjunto de funções lógicas probabilísticas sobre conjuntos de conteúdos descritíveis. Esta teoria tem aplicabilidade dedutiva e indutiva, significando um marco para o desenvolvimento das teorias filosóficas da informação.

Bibliography of A. A. Fraenkel (p. ix-x)--Axiomatic set theory. Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre, von P. Bernays.--On some problems involving inaccessible cardinals, by P. Erdös and A. Tarski.--Comparing the axioms of local and universal choice, by A. Lévy.--Frankel's addition to the axioms of Zermelo, by R. Mantague.--More on the axiom of extensionality, by D. Scott.--The problem of predicativity, by J. R. Shoenfield.--Mathematical logic. Grundgedanken einer typenfreien Logik, von W. Ackermann.--On the use of Hilbert's [epsilon]-operator in scientific theories, (...) by R. Carnap.--Basic verifiability in the combinatory theory of restricted generality, by H. B. Curry.--Uniqueness ordinals in constructive number classes, by H. Putnam.--On the construction of models, by A. Robinson.--Interpretation of mathematical theories in the first order predicate calculus, by T. Skolem.--The elementary character of two notions from general algebra, by R. Vaught.--Foundations of arithmetic and analysis. Axiomatic method and intuitionism, by A. Heyting.--On rank-decreasing functions, by G. Kurepa.--On non-standard models for number theory, by E. Mendelson.--Concerning the problem of axiomatizability of the field of real numbers in the weak second order logic, by A. Mostowski.--Non-standard models and independence of the induction axiom, by M. O. Rabin.--Sur les ensembles raréfiés de nombres naturels, par W. Sierpinski.--Philosophy of logic and mathematics. Remarks on the paradoxes of logic and set theory, by E. W. Beth.--Logique formalisée et raisonnement juridique, par R. Feys.--Im Umkreis der sogenannten Raumprobleme, von H. Freudenthal.--Process and existence in mathematics, by H. Wang. (shrink)

One of the tasks with which communication engineers are presented is that of devising a mechanism by which a significant sequence of words, a message, produced by somebody, the sender of the message, is reproduced at some other place, with the shortest practical time lag. The reproduction must be such that the receiver of the message will be able to understand what the sender meant by his message, at least, if he knows the sender's language. The following illustration is typical: (...) A writes on a sheet of paper “I love you” and wishes that B, 3000 miles away, should become aware of the full content of this message, with little delay and at a low cost. There will be institutions, in a capitalistic society, which will compete with each other in providing A, for a price, with the required service. Those companies which perform these services most satisfactorily, i.e., with an overall better combination of faithfulness, time lag, and cost, will get the job. The executives of these companies will hire engineers and put them to work on improving this overall combination. (shrink)

We offer a case-study in irrationality, showing that even in a high stakes context, intelligent and well trained professionals may adopt dominated practices. In multiple-choice tests one cannot distinguish lucky guesses from answers based on knowledge. Test-makers have dealt with this problem by lowering the incentive to guess, through penalizing errors (called formula scoring), and by eliminating various cues for outperforming random guessing (e.g., a preponderance of correct answers in middle positions), through key balancing. These policies, though widespread and intuitively (...) appealing, are in fact ‘‘irrational’’, and are dominated by alternative solutions. Number-right scoring is superior to formula scoring, and key randomization is superior to key balancing. We suggest that these policies have persisted since all stake-holders – test-makers, test-takers and test-coaches – share the same faulty intuitions. (shrink)

Esta apresentação identifica os principais conceitos envolvidos na teoria semântica da informação na obra An Outline of a Semantic Theory of Information de Bar-Hillel e Carnap. Inicio indicando as influências e desdobramentos sobre a elaboração desta teoria, seguido dos principais conceitos que os autores usarão para tratar o conteúdo semânticodas sentenças. O ponto de partida são operações conjunto-teoréticas, inicialmente através das funções In e Cont. Mas a dificuldade com a adição os leva a especificar o conceito de informatividade (...) semântica por meio das funções cont e m, que avaliam o espaço lógico-probabilístico sentencial. Sendo inversamente definíveis, onde a altaprobabilidade de verdade de uma sentença implica em seu escasso conteúdo informacional. Com isto, os autores introduzem a função inf como a contribuição de uma sentença na identificação de qual descrição-de-estado possível é o caso. A partir disto, eles ajustam a teoria para tratar probabilidades experimental-indutivas entre hipótesese evidências. (shrink)

Neste artigo defendo que a Teoria da Informação Fortemente Semântica de Floridi – TIFS – está correta ao assumir a Tese da Veracidade, que por sua vez orienta a definição de informação semântica como “p é informação se e somente se p é constituído por dados bem-formados, com significado e verdadeiros”. Argumento que a teoria não é arbitrária, pois dá conta do desembaraço de conundrums filosóficos importantes, principalmente por evitar o paradoxo de Bar-Hillel e Carnap, que é gerado (...) a partir da teoria clássica da informação semântica. Primeiro é discutido um dos principais resultados da teoria clássica, o de produzir “sentenças muito informativas para serem verdadeiras”. Depois são resumidas as motivações para a elaboração de uma “lógica de estar informado” e é mostrado como o sistema KTB-IL é montado e modelado mantendo-se entre os seus axiomas o da veracidade – K ou A4. Finalmente, a TIFS é examinada e defendida ao mostrar que ela restringe aleticamente a extensão do conceito clássico de informação para evitar problemas com tautologias e contradições. A TIFS oferece uma solução original ao capturar nossas intuições modais a respeito da informatividade como noção básica. (shrink)

In this article I defend that Floridi’s Theory of Strongly Semantic Information – TSSI – is correct while encompassing the Veracity Thesis, which guides the semantic information definition as “p is information if and only if p is constituted by meaningful, truth well-formed data”. I argue that the theory is not arbitrary because it deals with important philosophical conundrums, mainly by avoiding the Bar-Hillel and Carnap paradox (1953) generated from the classical theory of semantic information. First, one of (...) the classic theory’s main result is discussed: the production of “too much informative sentences to be true”. Then the motivations to elaborate a “logic of being informed” are summarized and it is shown how the KTB-IL system is built and modelled keeping the veracity axiom among its axioms – K or A4. Finally the TSSI is examined and defended by showing that it aletically restricts the extension of the classic concept of information, avoiding problems with tautologies and contradictions. The TSSI offers an original solution by capturing our modal intuitions concerning informativeness as a basic notion. (shrink)

Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of (...) the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians. (shrink)