Jan Wolenski

Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of an effectively computable function defined in natural numbers with the notion of a recursive function. Despite the many efforts of prominent scientists, Church's Thesis has never been disproven. There exists a vast literature concerning the thesis. The aim of this book is to provide a one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics, CT and physics, the epistemic status of CT, CT and philosophy of mind, provability of CT and CT and functional programming. Adam Olszewski, is assistant professor of the philosophy of mathematics and mathematical logic at the Department of Philosophy of Pontifical Academy of Theology, Cracow (Poland). Jan Wolenski is professor of philosophy, Institute of Philosphy, Jagiellonian University, Cracow (Poland). He is one of the most distinguished logicians in Poland. Robert Janusz is assistant professor in the Department of Philosophy of Ignatius College, Cracow (Poland).

There are many versions of the Liar Paradox. J. Agassi names 13 of them. But the most important one is related to Tarski’s theorem that the truth predicate is non-definable for systems that are sufficient for the formalisation of elementary arithmetic of natural numbers. Let S be such a system. We assume that S is consistent and that the syntax of S has been arithmetized as understood by G¨odel. Let E be any sentence of S. E ∗ is the symbol of the G¨odel number of E. If formula A belongs to the language of system S, then formula E is a constant point for formula A if and only if S ⊢ E → A. It can be proved that every formula A ∈ S has a constant point in S.

The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical problems.

This book presents the heritage of the Lvov-Warsaw School from both the historical and the philosophical perspective. The historical view focuses on the beginnings and the dramatic end of the School brought about by the outbreak of World War II. The philosophical view, on the other hand, encompasses a broad spectrum of issues, including logical, epistemological, axiological, and psychological problems, revealing the interdisciplinary nature of studies carried out by Kazimierz Twardowski and his students. With thirteen diverse and original essays this volume is split into three parts: History, Culture and Axiology; Psychology; and Logic and Methodology. Exploring not only the history of philosophy represented by the Lvov-Warsaw school, the book also reflects on the condition of contemporary philosophy from the perspective of concepts developed by its representatives. Furthermore, the studies presented in this book delve into problems of contemporary science and its distinctive interdisciplinary character. This volume is, therefore, not only a collection of analyses of the Lvov-Warsaw School philosophy, but also an investigation into the interdisciplinarity of science and philosophy itself.

The paper discusses some logical problems concerning analogy. The traditional understanding of analogy as _proportion_ (proportion) is inadequate, at least if proportionality is taken in mathematical sense. This situation is clear if we considered various special cases of analogy for instance _analogia legis_ and _analogia juris._ Since analogy assumes a similarity of analogata (items being or investigated) as analogical, a general analysis of analogical relation must begin with the concept of similarity. It can be defined as possessing a common property. This idea is formalized by devices borrowed from logic and set theory.

This paper is inspired by Marcin Tkaczyk’s works and discusses the problem of the necessity of the past (is the past determined?) and its role in the analysis of future contingents. The discussion centers on the statements (accepted by Tkaczyk, but slightly paraphrased)) firstly, that every past state of affairs is determined, and, secondly, that at least some some future states of affairs are contingent. The paper argues that because the first assertion is not justified, the antinomy of future contingents does not arise. The argument uses modal and metalogical devices.

Les débats qui ont eu lieu, lors du Congrès de philosophie scientifique de 1935, sur la sémantique et sa portée philosophique présentent un grand intérêt historique pour deux raisons. Tout d’abord, on s’accorde à y reconnaître un des évènements majeurs du congrès. En second lieu, et de façon plus substantielle, ils ont joué un rôle décisif dans le développement de la sémantique comme discipline philosophique. C’est Carnap qui en a pris l’initiative en invitant Tarski à donner deux conférences. Ce sont eux qui, avec Kokoszyńska, deviendront les porte-parole de la sémantique. Neurath, qui a préparé le résumé de la discussion, avait plusieurs objections contre la sémantique à la Tarski. En particulier, il craignait que la sémantique n’introduise la métaphysique dans la philosophie. La suite a montré que les partisans de la sémantique ont gagné.