Definindo a verdade 1. Aristóteles e Tarski

Este artigo é um trabalho ao mesmo tempo de história da filosofia e de filosofia. Ele constitui a primeira parte de um díptico que levanta a hipótese da possibilidade de definir a verdade. Após a distinção das três grandes acepções da palavra « verdade » (sinceridade, ipseidade, bondade de um julgamento), a individuação da acepção segundo a qual se trataria de definir a verdade (a terceira) e algumas considerações sobre esta última, o autor concentra-se na questão que consiste em saber o que torna verdadeiro um julgamento. O ponto de partida é a concepção aristotélica da verdade à qual são reconduzidas várias concepções concorrentes, principalmente a dita « da verdade como correspondência com a realidade », embora Aristóteles jamais apresente a sua nesses termos. Em um segundo momento, o autor compara essa concepção com a de Alfred Tarski, que supostamente retomaria Aristóteles, afim de mostrar tudo que separa esses dois pensadores. O autor procede, em seguida, a uma defesa da posição de Aristóteles e, enfim, sugere uma resposta provisória à questão posta: o que torna verdadeiro um julgamento é a crença, sendo que crer não é, todavia, ter por verdadeiro.

Carnap and the Members of the Lvov–Warsaw School. Carnap’s Warsaw Lectures (1930) in the Polish context

In March 1930, Alfred Tarski visited Vienna and delivered few lectures which presented the achievements of the logical branch of the Lvov-Warsaw School. Rudolf Carnap was one of the most careful listeners of these lectures. The same year, in November, Carnap, invited by the Warsaw Philosophical Society, visited Warsaw where he gave three lectures. This was an opportunity for him to meet such members the Lvov-Warsaw School as Jan Łukasiewicz, Stanisław Leśniewski, Tadeusz Kotarbiński, and others. Many years later, Carnap reminisced that he left Warsaw “grateful for many stimulating suggestions and the fruitful exchange of ideas”.In the paper, I reconstruct the details of Carnap’s visit in Warsaw based on Carnap’s diaries, reports published in the Polish Journal Ruch Filozoficzny [Philosophical Movement] and some correspondence. I also discuss some problems presented by Carnap in Warsaw lectures and compare his views to the positons of members of the Lvov-Warsaw School. These problems are: the foundations of psychology, the status of metaphysical sentences, and the character of reasoning.

Logic and Biology: The Correspondence Between Alfred Tarski and Joseph H. Woodger

This article makes available some early letters chronicling the relationship between the biologist Joseph H. Woodger and the logician Alfred Tarski. Using twenty-five unpublished letters from Tarski to Woodger preserved in the Woodger Papers at University College, London, I reconstruct their relationship for the period 1935-1950. The scientific aspects of the correspondence concern, among other things, Tarski’s reports on the work he is doing, his interests, and his --- sometimes critical but always well-meaning --- reactions to Woodger’s attempts at axiomatizing and formalizing biology using the system of Principia Mathematica. Perhaps the most interesting letter from a philosophical point of view is a very informative letter on nominalism dated November 21, 1948. But just as fascinating are the personal elements, the dramatic period leading to the second world war, their reaction to the war events, Tarski's anguish for his family stranded back in Poland, the financial worries, and his first reports on life in the East Coast and, as of 1942, at the University of California, Berkeley.

On the ‘Definability of Definable’ Problem of Alfred Tarski

In this paper we prove that for any m≥1 there exists a generic extension of L, the constructible universe, in which it is true that the set of all constructible reals (here subsets of ω) is equal to the set D1m of all reals definable by a parameter free type-theoretic formula with types bounded by m, and hence the Tarski ‘definability of definable’ sentence D1m∈D2m (even in the form D1m∈D21) holds for this particular m. This solves an old problem of Alfred Tarski (1948). Our methods, based on the almost-disjoint forcing of Jensen and Solovay, are significant modifications and further development of the methods presented in our two previous papers in this Journal.

The Mystery of the Fifth Logical Notion (Alice in the Wonderful Land of Logical Notions)

We discuss a theory presented in a posthumous paper by Alfred Tarski entitled “What are logical notions?”. Although the theory of these logical notions is something outside of the main stream of logic, not presented in logic textbooks, it is a very interesting theory and can easily be understood by anybody, especially studying the simplest case of the four basic logical notions. This is what we are doing here, as well as introducing a challenging fifth logical notion. We first recall the context and origin of what are here called Tarski-Lindenbaum logical notions. In the second part, we present these notions in the simple case of a binary relation. In the third part, we examine in which sense these are considered as logical notions contrasting them with an example of a nonlogical relation. In the fourth part, we discuss the formulations of the four logical notions in natural language and in first-order logic without equality, emphasizing the fact that two of the four logical notions cannot be expressed in this formal language. In the fifth part, we discuss the relations between these notions using the theory of the square of opposition. In the sixth part, we introduce the notion of variety corresponding to all non-logical notions and we argue that it can be considered as a logical notion because it is invariant, always referring to the same class of structures. In the seventh part, we present an enigma: is variety formalizable in first-order logic without equality? There follow recollections concerning Jan Woleński. This paper is dedicated to his 80th birthday. We end with the bibliography, giving some precise references for those wanting to know more about the topic.

Judgments and Truth: Essays in Honour of Jan Woleński

It is a Preface to Volume 9:3/4 that has brought a renewed focus to the role of truth conceptions in frameworks of semantics and logic. Jan Woleński is known due to his works on epistemological aspects of logic and his systematization of semantic truth theory. He became the successor and the worthy continuer of prominent Polish logicians: Alfred Tarski and Kazimierz Ajdukiewicz. This volume is collected on the 80th anniversary of Woleński’s birth and draws together new research papers devoted to judgments and truth. These papers take measure of the scope and impact of Woleński’s views on truth conceptions, and present new contributions to the field of philosophy and logic.

How Should One Write about Masters?

The aim of the paper is to answer the question: how should one write about masters? It is a question about the narrative strategies of authors writing about masters. The presented analysis is based on five examples: (1) John A. Hall’s Ernest Gellner: An Intellectual Biography, (2) Anita Burdman Feferman and Solomon Feferman’s Alfred Tarski: Life and Logic, (3) Edmund Leach’s Lévi-Strauss, (4) Andrzej Walicki’s Idee i ludzie. Próba autobiografii [Ideas and People. An Attempt at an Autobiography], and (5) Dialogues by Roman Jakobson and Krystyna Pomorska. Each text presents different rhetorical devices, authorial relations to the master, and academic aims. The paper concludes with a critical comparison of the five examples (with the addition of some other minor cases also discussed in the paper).