The main goal of this paper is to present the Marian Smoluchowski’s work on thermal and primordial fluctuations which are the main cause of Brownian motion and one of the first empirical evidences for molecular structure of matter.

All physical processes are deterministic de iure. Physicists speak about different types of determinism of physical processes, depending on the degree with which their course can be anticipated. Usually, the course of ergodic processes can be predicted with less certainty than the non-ergodic ones, the latter being integrable. Recent measurements of motions of single particles in composite systems, especially in living biological cells, show that such motions are, in most cases, breaking the Boltzmann’s ergodic hypothesis. On the other hand, their (...) trajectories are random, i.e., one cannot know a priori where the particle will be even in near future. This leads to conclusion that many existing in nature processes are nonergodic but not integrable, therefore predictable only in the mean, representing still other type of determinism. (shrink)

The time of mechanics is the eternal and unchangeable time of Parmenides, it is Plato’s idea of time, whereas the time of thermodynamics is Heraclitus’ flowing time, Thomas Aquinas’ time measured by various phenomena. I once wrote [2] that people who are not used to a physicist’s way of thinking are (at best) confused by the idea of a symmetrical time of mechanics. Physicists on the other hand often believe that the time of thermodynamics (irreversibility) does not really exist, and (...) is merely an illusion. It seems therefore that both of these aspects of time, the time of mechanics and the time of thermodynamics, should be treated as complementary, in anticipation of a future “theory of everything” which will somehow reconcile them. (shrink)

This paper analyzes selected issues related to the philosophy of the Krakow physicist Andrzej Fuliński. Since the 1970s, Fuliński has been strongly associated with the interdisciplinary milieu gathered around Heller and Życiński. His activity can therefore be considered within the context of the broader phenomenon known as the Krakow School of Philosophy in Science, which was founded by Heller and Życiński. This paper proposes the thesis that Fuliński’s style of philosophy is connected with the concept of (...) philosophy in science and tries to justify the thesis that Fuliński, due to his cooperation with the interdisciplinary milieu in Krakow and the specificity of his philosophical works, deserves to be regarded as a representative of the Krakow School of Philosophy in Science. (shrink)

The famous theory of undecidable sentences created by Kurt Godel in 1931 is presented as clearly and as rigorously as possible. Introductory explanations beginning with the necessary facts of arithmetic of integers and progressing to the theory of representability of arithmetical functions and relations in the system (S) prepare the reader for the systematic exposition of the theory of Godel which is taken up in the final chapter and the appendix.

This review pertains to the book _Evolutionary Theology (Teologia ewolucyjna)_ written by Wojciech P. Grygiel and Damian Wąsek. The book presents a distinct and modern viewpoint on theology by offering a comprehensive analysis of the characteristics of theological language and utilizing it to reevaluate certain theological beliefs, such as the concept of original sin, within the framework of the ever-changing understanding of the Universe. This approach contributes significantly to the restoration of theology’s credibility in modern culture by bridging the gap (...) between science and theology. (shrink)

In this paper, the concept of structural information is presented. The mathematical foundation of the concept is put forward, and the nature of information encoded in a structure is studied. A method for calculating the amount of structural information is introduced. An application to the analysis of cognitive maps is also presented and discussed.

During the global financial crisis of 2007–2009 and the currentCovid-19 debacle, central banks acted quickly, boldly, and effectively. The paper argues that they did so thanks to the lessons learned from the past financial crises, which provided them with opportunities to reconsider their previous beliefs. A case in point is the banking crisis in the United States during the Great Depression of the 1930s that taught central banks to act rapidly and decisively in order to prevent an initial liquidity crisis (...) from escalating into a solvency crisis leading to bankruptcies of banks with potentially disastrous consequences for the entire economy. The paper revisits the consequences of the currency crises of the 1990s, which transformed exchange rate regimes across the world: the EMS one of 1992–1993 that accelerated the launch of the euro, and the Asian one of 1997–1998 resulted in the proliferation of floating exchange rates in emerging economies. (shrink)

The main aim of the present paper is to explain a nature of relationships exist between Nelson and Heyting algebras. In the realization, a topological duality theory of Heyting and Nelson algebras based on the topological duality theory of Priestley for bounded distributive lattices are applied. The general method of construction of spaces dual to Nelson algebras from a given dual space to Heyting algebra is described. The algebraic counterpart of this construction being a generalization of the Fidel-Vakarelov construction is (...) also given. These results are applied to compare the equational category N of Nelson algebras and some its subcategories with the equational category H of Heyting algebras. It is proved that the category N is topological over the category H. (shrink)

In this article, the author notes that Thomas Aquinas, in his brief work entitled De Ente et Essentia, proved that at the base of understanding the world, the human being, and God in particular, there is our understanding of being and its essence. When we make a small mistake at the beginning in our understanding of being and its essence, it will turn to be a big one in the end. And what is “at the end” of our knowledge is (...) the discovery of the First and Ultimate Cause of all things, known as: Ipsum Esse, God, the Absolute, The Most Perfect Substance, on whom everything depends, and who depends not on anything else. These present inquiries about the proper understanding of being and its essence are aimed at formulating proof of the necessity of existence of a Being that is the First Cause, and which, existing as Ipsum Esse, is the source and reason of existence of all beings. Without these inquiries, the proof itself would be incomprehensible, and more importantly it would be a purely a priori one. Furthermore, without the existential conception of being, which Thomas first formulated, one could not discover the First Cause which, as Ipsum Esse, is the source of the existence of every being. This issue seems to have escaped the attention of the author of the book Aquinas’s Way to God. The Proof in “De Ente et Essentia.”. (shrink)

Natural Deduction Natural Deduction is a common name for the class of proof systems composed of simple and self-evident inference rules based upon methods of proof and traditional ways of reasoning that have been applied since antiquity in deductive practice. The first formal ND systems were independently constructed in the 1930s by G. Gentzen and S. Jaśkowski and … Continue reading Natural Deduction →.

This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

This summary was delivered at the closing session of the “Korczak: A New Anthropology of Education” conference on September 21, 2002 in the Polish Culture Institute of Warsaw University’s Polish Studies Faculty. Author points that the primary goal of the conference was to set Korczak’s work against modern-day thought trends and cultural dilemmas. Summing up the result of the conference author notices that the deepest roots of the Korczak’s work lies in the Judaic and Christian traditions but it also draws (...) on European enlightenment, Polish romanticism, and positivism. (shrink)

A new type of formalization of classical first-order logic with equality is introduced on the basis of the sequent calculus. It serves to justify the claim that equality is a logical constant characterised by well-behaved rules satisfying properties usually regarded as essential. The main feature of this approach is the application of sequents built not only from formulae but also from terms. Two variants of sequent calculus are examined, a structural and a logical one. The former is defined in accordance (...) with Dos̆en’s criteria for logical constants. The latter is a standard Gentzen’s sequent calculus and satisfies Hacking’s criteria for logicality, including cut elimination. It is also shown that provided rules are harmonious in the sense advocated by Gratzl and Orlandelli. (shrink)

The paper presents a uniform proof-theoretic treatment of several kinds of free logic, including the logics of existence and definedness applied in constructive mathematics and computer science, and called here quasi-free logics. All free and quasi-free logics considered are formalised in the framework of sequent calculus, the latter for the first time. It is shown that in all cases remarkable simplifications of the starting systems are possible due to the special rule dealing with identity and existence predicate. Cut elimination is (...) proved in a constructive way for sequent calculi adequate for all logics under consideration. (shrink)

Values are relational properties that can be defined only in relation to a goal-directed system. Biological values originated with living systems and subjective values originated with the origin of vertebrate (and possibly others’) mind through a conversion (subjectivization) of biological values. While this conversion is understandable in adaptive (functional) terms, the evolutionary mechanism whereby positive and negative meanings in the mind were assigned to molecular and/or neuronal configurations in the brain, so far defies our comprehension. Whatever their origin, the primary (...) subjective values are experienced by most if not all vertebrates, and the hominid conceptual values are all ultimately derived from experiential values. (shrink)

DARWIN’s (1859, 1871) discoveries have profound ethical implications that continue to be misrepresented and/or ignored. In contrast to socialdarwinistic misuses of his theory, Darwin was a great humanitarian who paved the way for an integrated scientific and ethical world view. As an ethical doctrine, socialdarwinism is long dead ever since its defeat by E. G. Moore although the socialdarwinistic thought is a hard-die in the biological community. The accusations of sociobiology for being socialdarwinistic are unfounded and stem from the moralistic (...) fallacy that is, a false assumption that morality is good by definition. Both social and developmental psychology demonstrate that the moral agency is a motivational device for executing reciprocity that remains at the core of any morality across all studied societies and throughout the ontogeny of moral judgment. The level of true universalizing ethical reflection (KOHLBERG’s postconvential stages or GIBBS’s existential phase) is achieved by a small minority of humans, thus showing that Homo sapiens is a moral but not an ethical animal. While the origin of reciprocity has been perfectly explained by sociobiology, the evolutionary assembly of affective and cognitive elements that make up the moral agency is being successfully studied by the social/personality/developmental psychology as extended to non-human primates. As DARWIN (1871) expected, the key innovation for the evolution of moral agency was the emergence of empathy that evolved independently at least three times: in elephants, dolphins and primates. Empathy has a motivational power of its own; it is also necessary for moral agency that requires two cognitive abilities: reflective self-consciousness and understanding of causality; the two make possible the attribution of responsibility. All these requirements are met by the chimpanzees whose moral agency operates in dyads. In contrast, the human moral agency allows for a third party intervention that opens up vast opportunities for ideologies, especially religions, to use and misuse the moral agency to enforce a reciprocation that may be harmful to both individuals and the entire group. Also, the moral agency is known to enforce enhanced intragroup cohesion and loyalty in response to conflict and war, which suggests that the two prima facie opposed human universals, morality and warfare, may have coevolved. The most important ethical consequence that follows from the increasing understanding of the primate moral agency is that every received morality is ethically flawed, none can be taken as a paragon of goodness, and each needs corrections by science-informed ethics. In fact, Darwin pioneered the integration of science and ethics, an approach that has come to be appreciated only recently under the heading of consilience. (shrink)

Most Enlightenment thinkers believed that the World’s order (as ultimately based on divine laws) is good and thus every gain of knowledge will have good consequences. Scientific process was assumed to entail moral progress. In fact some moral progress did occur in the Western civilization and science contributed to it, but it is widely incommensurate with the progress of science. The Enlightenment’s concept of a concerted scientific and moral progress proved largely wrong for several reasons. (1) Public morality and science (...) evolve largely independently and may either enhance or inhibit each other. (2) There are no objective values to be read in the World’s order and simply followed. Instead, our real, subjective values and the moral systems they fuel have all been generated and shaped by evolution rather than designed to be universally good, and thus ought to be managed rather than simply followed. (3) Our evolved morality is flawed, deficient, prone to doctrinal manipulation and refractory to progress. (4) The majority of people show metaethical incompetence in failing to take a reasoned critical stand toward the principles and assumptions of received morals. This makes moral progress largely dependent on those who reach metaethical competence by transcending the conventional stages of moral development. (shrink)

This paper is concerned with n-localization property introduced by Newelski and Rosłanowski in [10] and getting it for CS iterations of forcing notions.

Aside from the local (mostly Western) efforts to subject animal experimentation to public scrutiny, the extent of animal experimentation, the acceptance of alternative methods and the fate of animals in laboratories depend on experimenters’ morality (as defined by social psychology), whose shaping is of crucial importance for the future of animal use in science. Meanwhile, sociological and ethnographic research in laboratories demonstrates that in the matter of animal use the experimenters are unreflective, ethically incompetent, and incapable of taking a critical (...) view of the received morality. This appears to result largely from their higher education which is known to cause a regression in moral development, inculcate a routine exploitation and/or objectification of animals, and ignore both the scientific premises and moral consequences of animal subjectivity. From all we know, it is researchers’ morality rather than pressing needs and expectations of humanity that interferes with a major restriction of invasive animal research in general and a wide, proactive acceptance of alternative methods in particular. (shrink)

True Darwinian Ethics -/- Darwin’s model for the evolution of morality as presented in Descent of Man (1871) is shown to comprise three major stages that are here referred to as empathic premorality, tribal morality, and universalizing morality. Empathy, the key component of Darwin’s “social instincts” that started moral evolution, is here recognized as the principal cognitive device that conveys epistemic credibility to moral agency. The two constitutive elements of the tribal morality are conscience that Darwin conceived of as a (...) conflict between a lasting social motive and an immediate selfish impulse, and true altruism that evolved as a result of group (community) selection. Darwin’s genius recognized the uniqueness of group selection in human evolution as being dependent on mental faculties and speech that facilitated habit formation through praise and blame form other group members, with empathy as a gauge of others’ emotional reactions. Contrary to repeated claims, Darwin did not derive morality from reciprocity that he (and his contemporaries) considered to be “a low motive”, and adduced it only as a mechanism of habit formation. The universalizing morality was brought about by the increasing powers of intellect that led to respecting individual lives (rather than group interests only) and extending humane concerns beyond one’s group, ultimately to all sentient beings, which places Darwin among the spiritual fathers of modern humanitarianism. In terms of substantive ethics, Darwin’s views support moral individualism that requires to treat each subject according to his/her individual characteristics rather than any group membership. Darwin’s moral individualism and universalism have been elaborated by Peter Singer as the principle of equal consideration of interests and the expanding circle of ethics, respectively. Darwin’s model of moral evolution, which starts with intuitive but epistemically reliable moral agency and then allows for its rational improvement, provides a way out of the moral subjectivism of evolutionary ethics that reduces morality to an adaptation to social life. The primary or core morality that relies on empathy and implements reciprocity supports welfare (wellbeing) of a group and its members. Welfare (which has been defined by Darwin) is a basic “terminal” (ultimate) value that constitutes an objective, measurable fact. Since the primary morality supports welfare, it is objectively good, which justifies an ethical reasoning that such morality ought to be extended (with appropriate adjustments) to all sentient beings. Confusion over the status of morality is largely due to the lack of appreciation of its complexity: not only had its motivational apparatus (known as the moral agency) evolved by superposition of many emotional and pure cognitive mechanisms, but it has subsequently been co-opted to implement prudential, religious and possibly other norms that are accidental and sometimes contrary to its original social function. Those secondary morality norms are now enforced by the moral agency but lack moral objectivity and thus may support the perception of moral subjectivism and relativism. In short, true Darwinian ethics is based on the scientific axiology that recognizes evolutionary origins of all values, requires respecting all values that are experienced by each and every subject according to its individual characteristics, and calls for a critical assessment of each and every received morality. (shrink)

Having positive experience is, by defintion, in the interest of every subject. Whether being alive per se, in addition to having positive experiences, is in a subject's interest depends of her/his cognitive development. Only a reflectively self-conscious subject can take and thus have an interest in one's own individual existence and may not want to die regardless of the expected experience. Since most non-human subjects (except for a few mammalian and avian species) are not aware of their subjective existence they (...) cannot take and thus have interest in their lives per se. However, they do have interest in maximizing rewarding experience and minimizing suffering. (shrink)