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)
There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (1999); (...) Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper. (shrink)
An explanation is given of why, after adding to a model M of ZFC first a Solovay real r and next a Cohen real c, in M[ r][ c] a Cohen real over M[ c] is produced. It is also shown that a Solovay algebra iterated with a Cohen algebra can be embedded into a Cohen algebra iterated with a Solovay algebra.
We introduce a new cardinal characteristic r*, related to the reaping number r, and show that posets of size $ r* which add reals add unbounded reals; posets of size $ r which add unbounded reals add Cohen reals. We also show that add(M) ≤ min(r, r*). It follows that posets of size < add(M) which add reals add Cohen reals. This improves results of Roslanowski and Shelah [RS] and of Zapletal [Z].
By an algebraic semantics we shall mean a class K of matrices M = for a propositional language L such that D is a singleton, D = fdg. A logic has an algebraic semantics i C =6 ; and there exists an algebraic semantics K strongly adequate for C, i.e., C = CnK. Proposition. If a logic has an algebraic semantics, then every factorial matrix M 2 M atr has the following properties: M is of the form, where 1A 2 (...) A each formula 2 C denes the constant 1A in A, that is, A[a1; : : : ; an] = 1A for any a1; : : : ; an 2 A. (shrink)
In the present note we continue the investigations undertaken in . A full version of the paper has been submitted to Studia Logica. x1 Our goal is to give a characterization of the so called factorial matrices for a logic. A matrix M = is factorial i the greatest congruence M of M coincides with the diagonal of A. Recall that is a congruence of a matrix M = i is a congruence of the algebra A and for any a; (...) b 2 A, if ab then a 2 D i b 2 D. (shrink)
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)
In Branden Thornhill-Miller and Peter Millican’s challenging and provocative essay, we hear a considerably longer, more scholarly and less melodic rendition of John Lennon’s catchy tune—without religion, or at least without first-order supernaturalisms, there’d be significantly less intra-group violence. First-order supernaturalist beliefs, as defined by Thornhill-Miller and Peter Millican, are “beliefs that claim unique authority for some particular religious tradition in preference to all others”. According to M&M, first-order supernaturalist beliefs are exclusivist, dogmatic, empirically unsupported, and irrational. Moreover, again according (...) to M&M, we have perfectly natural explanations of the causes that underlie such beliefs. They then make a case for second-order supernaturalism, “which maintains that the universe in general, and the religious sensitivities of humanity in particular, have been formed by supernatural powers working through natural processes”. Second-order supernaturalism is a kind of theism, more closely akin to deism than, say, Christianity or Buddhism. It is, as such, universal, empirically supported, and beneficial. With respect to its pragmatic value, second-order supernaturalism, according to M&M, gets the good of religion without its bad. Second-order supernaturalism is thus rational and inconducive to violence. In this paper, I will examine just one small but important part of M&M’s argument: the claim that religion is a primary motivator of violence and that its elimination would eliminate or curtail a great deal of violence in the world. Imagine, they say, no religion, too. Janusz Salamon offers a friendly extension or clarification of M&M’s second-order theism, one that I think, with emendations, has promise. He argues that the core of first-order religions, the belief that Ultimate Reality is the Ultimate Good, is rational and, if widely conceded and endorsed by adherents of first-order religions, would reduce conflict in the world. While I favor the virtue of intellectual humility endorsed in both papers, I will argue contra M&M that belief in first-order religion is not a primary motivator of conflict and violence. Second, partly contra Salamon, who I think is half right, I will argue that the religious resources for compassion can and should come from within both the particular and the universal aspects of religious beliefs. Finally, I will argue that both are guilty, as I am, of the philosopher’s obsession with belief. (shrink)
This article attempts to answer the question: what has the current migration crisis revealed in relations between Christianity and Islam, two religions with common Abrahamic roots? What conclusions can be drawn about the state of these relations, particularly with regard to ordinary members of the two religions? How should we assess the reaction of Christians in Europe to the inflow of refugees from Muslim countries in the light of the Gospel, the Second Vatican Council and the teaching of Pope Francis?The (...) article consists of four parts. Part I briefly presents Christian-Muslim relationships over the centuries. Part II focuses on the sense of danger occurring in European societies in connection with the influx of Muslims during the migration crisis. Part III presents the teachings of the Second Vatican Council about Islam and Part IV describes Pope Francis’s attitude towards refugees from Muslim countries. (shrink)