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)
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.
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)
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)
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].
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)
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 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)
For more than fifty years, Sterling M. McMurrin served as one of the preeminent intellectual voices of the LDS community. From his beginnings as an Institute of Religion instructor to U.S. Commissioner of Education, and from a professor of philosophy to U.S. Envoy to Iran, he showed by example how personal and institutional morality can be defended.In a series of candid discussions with Jack Newell, McMurrin reveals his ability to reconcile freedom and conscience. In a spirit of repartee and friendship, (...) writes Boyer Jarvis in the foreword, Newell probes, challenges, and constantly draws McMurrin out as he... reflects upon his wide-ranging ideas and experiences. Rich in insight and humor, this remarkable dialogue captures the sweep and depth of McMurrin's thoughts as Newell engages him in discussing his approaches to philosophy, education, and religion.Among the qualities that characterized McMurrin's life and mind, explains Newell, perhaps the most notable is the freedom with which he has spoken his views on both the sacred and the profane. His intellectual integrity -- coupled as it almost always is with his humane instincts and innate fairness -- has simultaneously confounded and earned the respect of critics. (shrink)
This is the first of a series of commentaries on the works of the latest Heidegger; all of Heidegger's works published by Neske of Pfullingen since 1954 will be presented and interpreted in the series. The expository plan announced in the editor's preface calls for three-part commentaries, with the first part summarizing the work in question, the second presenting glosses of lines or paragraphs as required by their respective importance, and the third giving philological exegesis of texts also as required (...) in the judgment of the editors. The interpretative inspiration is generally traditional, with more emphasis given to themes with echoes in medieval and modern rationalism and in Italian and French ontologism. The editors adopt Heidegger's characteristic attitude in his latter period, his relinquishing of all objective or subjective idealistic presuppositions. Ontology thus becomes the unveiling of the conditions of possibility of Dasein's speech as truth-making. In Being and Time these conditions of possibility were given in the fundamental ontology and reached their existential expression in resolve. In Gelassenheit Dasein has become a mere instrumentality for the ultimate sense of Being to come to pass. The conditions of possibility of the new Dasein are well understood and highlighted by Landolt. Their existential expression is a new temporal tension within the Dasein, that of Warten or attending. If resolve was the modal intentionality of authentic Dasein, attending is the modal intentionality of poetic symbolic Dasein. Landolt does not seem to have been sufficiently critical of the reflective character of this new intentionality. Can it adequately ground essence, fact and freedom? The techniques of this commentary often depart from hermeneutical respect for the text.--A. M. (shrink)