Analizy przeprowadzone w artykule pozwalają na wyciągnięcie wniosków, ważnych dla filozofa przyrody. Między filozofią a naukami przyrodniczymi istnieje interakcja, którą można określić jako współprzenikanie się obu tych dziedzin wiedzy. To współoddziaływanie filozofii z nauką podobne jest do niedomykającego się koła. Trudno jest owo współprzenikanie jednoznacznie scharakteryzować, ale można wskazać pewne idee towarzyszące mu. Uświadomienie sobie filozoficznego uwikłania teorii naukowej powoduje często rozszerzenie jej rozumienia oraz ujawnia, jak wiele informacji zawartych jest w teorii naukowej na temat głębokiej struktury świata. Sformułowanie „filozofia (...) w nauce” można by uznać za charakterystyczne dla współczesnego ujmowania związku filozofii z naukami przyrodniczymi. Należy pamiętać, że wspólna droga filozofii i nauk przyrodniczych pozwala osiągać interesujące poznawczo wyniki, ważne dla rozumienia świata zewnętrznego. Współprzenikanie się filozofii z nauk jest procesem dynamicznym i twórczym. Tak filozofia, jak i nauka, ulegają ciągłym zmianom, które w istotny sposób wpływają na rozwijanie się procesu współprzenikania. Trudno jest przewidywać, w którą stronę ten proces będzie ewoluował. Ważne jest jednak, jak twierdzi M. Heller, aby w tym twórczym procesie dostrzec, że największym sukcesem nauk empirycznych, trwającym do dziś, jest coraz lepsze ugruntowanie się przekonania, że Wszechświat stopniowo, choć tylko w przybliżeniu, ujawnia nam tajemnice swojej struktury. -------------- Zgłoszono: 12/09/2020. Zrecenzowano: 10/10/2020. Zaakceptowano do publikacji: 29/10/2020. (shrink)

Recenzja książki: Richard Holmes, Wiek cudów. Jak odkrywano piękno i grozę nauki, tłum. Ewa Morycińska-Dzius, Seria: Wiedza i Życie – Orbity Nauki, Prószyński i S-ka, Warszawa 2010, ss. 656.

We present a short account of the early history of the Center for Interdisciplinary Research in Cracow. These beginnings go back to the inter-war period when the tradition was established of close interactions between philosophers and scientists, especially physicists (Smoluchowski, Natanson). In the post-war period, under the communist regime, this tradition was continued at the Theological Institute (later the Pontifical Academy of Theology) in Cracow, erected by Cardinal Wojtyła, the then archbishop of Cracow, after the Theological Faculty had been removed (...) from the Jagiellonian University by the communists. The collaboration of the Cracow Center with the Catholic University of Lublin and with the Warsaw Academy of Theology is briefly described, and the style of philosophy in Cracow presented. (shrink)

Recenzja książki: John D. Barrow, Książka o niczym, tł. Łukasz Lamża, Copernicus Center Press, Kraków 2015, ss. 460.

The original view of Joseph Życiński, presented in his book _The Structure of the Metascientific Revolution _(1988), boils down to the observation that almost before our eyes a great revolution took place, not in science, but in the philosophy of science, that is the meta-scientific revolution. His concept of the meta-scientific revolution grew out of his fascination with the revolution that took place in the foundations of mathematics in the first decades of the twentieth century. Whether a change in science (...) deserves to be called a revolution is determined by whether the transformations it underwent also reached the meta-level. The set of presuppositions underlying transformations on the meta-level Życiński calls ideata. One of the aims of this article is to critically reconstruct the meaning of this term. The action of Życiński’s book takes place mainly on meta-level, but the meta-level constantly interacts with what is happening in science itself. The book sometimes makes an impression as if it were a study of the history of science, but history of science in a specific sense – something like a “sampling” of history with numerous examples. Among the creations of human thought, it is difficult to point to an area that changes more dynamically than science itself, but looking at it from a meta-perspective allows us to grasp those of its features that operate on a much broader scale. (shrink)

Recenzja książki: Bogdan Dembiński, _Stara Akademia Platona. W początkach epoki hellenistycznej _, Wydawnictwo Marek Derewiecki, Kęty 2018, s. 183.

This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and ...

The class Matr(C) of all matrices for a prepositional logic (, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matr(C) states the following. Assume C to be the consequence operation on a prepositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of C. Then Matr (C) is the least class (...) of matrices containing K and closed under m-reduced products, submatrices, matrix homomorphisms, and matrix homomorphic counter-images. (shrink)

The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued ukasiewicz logic C ) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).

In the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.

The main result of the present paper — Theorem 3 — establishes the equivalence of the interpolation and amalgamation properties for a large family of logics and their associated classes of matrices.

We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) s q.

The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory for non-protoalgebraic logics.

We are facing a crisis of trust in expertise today. Fewer and fewer people trust experts, and more and more politicians openly ignore expert consensus. 'Democracy in the Post-Truth Era' asks what might happen to democracy if we reject the fundamental liberal assumption that people are capable of making informed choices. The book explores the potential impact on society if people, including politicians, never appreciate the relevance of expert opinions. What if people cannot choose between supporters and opponents of key (...) issues such as the causes of climate change, effectiveness of vaccines and ways of combating economic and social crises? Applying social epistemology to these questions, the book considers whether democracy can be defended in the post-truth era. (shrink)

The present paper is thought as a formal study of distributive closure systems which arise in the domain of sentential logics. Special stress is laid on the notion of a C-filter, playing the role analogous to that of a congruence in universal algebra. A sentential logic C is called filter distributive if the lattice of C-filters in every algebra similar to the language of C is distributive. Theorem IV.2 in Section IV gives a method of axiomatization of those filter distributive (...) logics for which the class Matr (C) prime of C-prime matrices (models) is axiomatizable. In Section V, the attention is focused on axiomatic strengthenings of filter distributive logics. The theorems placed there may be regarded, to some extent, as the matrix counterparts of Baker's well-known theorem from universal algebra [9, § 62, Theorem 2]. (shrink)

We examine the notion of primitive satisfaction in logical matrices. Theorem II. 1, being the matrix counterpart of Baker's well-known result for congruently distributive varieties of algebras (cf [1], Thm. 1.5), links the notions of primitive and standard satisfaction. As a corollary we give the matrix version of Jónsson's Lemma, proved earlier in [4]. Then we investigate propositional logics with disjunction. The main result, Theorem III. 2, states a necessary and sufficient condition for such logics to be finitely based.

With each sentential logic C, identified with a structural consequence operation in a sentential language, the class Matr * (C) of factorial matrices which validate C is associated. The paper, which is a continuation of [2], concerns the connection between the purely syntactic property imposed on C, referred to as Maehara Interpolation Property (MIP), and three diagrammatic properties of the class Matr* (C): the Amalgamation Property (AP), the (deductive) Filter Extension Property (FEP) and Injections Transferable (IT). The main theorem of (...) the paper (Theorem 2.2) is analogous to the Wroski's result for equational classes of algebras [13]. It reads that for a large class of logics the conjunction of (AP) and (FEP) is equivalent to (IT) and that the latter property is equivalent to (MIP). (shrink)