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The introduction of the concept of the field of rationality and its correlates (the field of potentiality and the formal field) by Józef Życiński and Michał (Michael) Heller opened up space for the philosophical explanation of the unreasonable effectiveness of mathematics in capturing regularities built into the physical reality. The presented study is a response to the clear incentive of these authors towards the development of the understanding and applicability of these concepts. It is argued that identifying symmetries within the field of rationality not only helps to articulate the fundamental role of symmetries in physics but also provides a better grasp on the issue of potentialities for the emergence of complexity in the Universe. Additionally, some global properties of this field can be more deeply comprehended. By indicating the drawbacks and limitations of this approach, perspectives for further inquiry into the meaning and usefulness are suggested.

Apophatic theology is an approach in theology that emphasizes the limitation of human language and concepts in describing the nature of the Divine. Rooted in ancient religious traditions, apophatic theology has gained attention in contemporary discourse for its potential convergence with the scientific method. This paper expands on a novel application of this approach in which the formal methods of science such as logic and mathematics are engaged to inquire into how God thinks and to what degree the modes of human reasoning can be projected on the nature of the Divine mind. This application has been proposed by Michał Heller and is referred to as the logical apophatism. In the course of the analysis carried out in this paper more in-depth understanding of the logical apophatism has been obtained by contrasting it with classical approaches to negative theology such as the Triplex Via and supplementing with recent advances within the cognitive sciences. It is concluded that Heller’s use of the apophatic approach is manifestly non-standard and its novelty consists in the shift of emphasis from the negative character of the language of theology to the logic of the Divine mind and the logic that underpins the workings of the Universe.

The unusual applicability of mathematics to the description of the physical reality still remains a major investigative task for philosophers, physicists, mathematicians and cognitive scientists. The presented article offers a critical analysis of the philosophical motivations and development of a major attempt to resolve this task put forward by two prominent Polish philosophers: Józef Życiński and Michał Heller. In order to explain this particular property of mathematics Życiński has first introduced the concept of the field of rationality together with the field of potentiality to be followed by Heller’s formal field and the field of categories. It turns out that these concepts are fully intelligible once located within philosophical stances on the relations between mathematics and physical reality. It will be argued that in order to achieve more extended conceptual clarification of the precise meaning of the field of rationality, further advancements in the understanding of the nature of the human mind are required.

The purpose of the article is to investigate the philosophical and theological validity and coherence of the classical concept of a miracle within the contemporary scientific world view. The main tool in this process will be the cognitive standard model of the formation of religious beliefs operative in the cognitive science of religion. The application of this model shows why an intentional agent is assigned as responsible for the occurrence of events with no visible cause such as a miracle: miracles are events that violate the intuitively expected behaviors observable in the physical reality. It will become evident that much of the conceptual content of the classical understanding of miracles can be retained despite of the ontological and epistemological challenges of the contemporary science. In particular, this concerns the semantic view of miracles in which a miracle does not occur as an objective Divine intervention but qualifies as religious interpretation of the natural course of events always in reference to a cultural and personal context that is unique to those who directly experience these events either as direct recipients or as observers.

The evolutionary theology is a new branch of theology in which the dynamic picture of the origin and development of life in Universe by means of the adaptive processes governed by the natural selection is considered to be the adequate ontological foundation. The presented paper surveys the challenges that the implementation of the evolutionary ontology presses upon selected basic theological issues: methodology of theology, natural theology, the doctrine of the original sin and the problem of suffering and evil. It will be argued that the large extent of the expected modifications within the theological expression as the dynamic ontology is introduced qualifies as the change of the theological paradigm similarly to how the changes of the paradigms in sciences lead to the scientific revolutions. Finally, a novel model of the rationality of the development of the theological doctrine will be proposed where the hermeneutics of continuity and the hermeneutics of rupture are not in opposition but they contribute to the overall rationality as its complementary constitutive principles.

The current 50th issue of Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) summarizes the efforts of both philosophers and scientists to understand how a broader philosophical context sets the stage for the development of scientific research, with physics playing a leading role. In particular, the paper reviews the content of the last twenty-five issues of the journal with an emphasis on the philosophical problems that arise in the practice of physics. The overview reveals that these problems reflect the main conceptual division in physics between the treatment of the micro-world described by quantum mechanics and the macro-world governed by the general theory of relativity. Both of these theories, taken separately, generate a host of philosophical concerns such as their proper interpretation (Bell’s Theorem and its consequences) or the meaning and the eventual validity of the notions of space and time. Other philosophical problems in physics, such as chaos and determinism, are also considered. The authors are well aware that the formulation of the future theory of quantum gravity will be a demanding task requiring profound philosophical reflection.

Scientists, who have made significant contributions to the deepening of knowledge in their area of research, often engage in discussions concerning the ultimate explanations of the Universe. This is particularly visible in cosmology for the theories presented directly refer to the major questions raised by the philosophers such as the origin and the fate of the Universe, the nature of the physical laws and the existence of God. Stephen Hawking has made himself known as one of the most vocal speakers in this regard by insisting that the no-boundary Hartle-Hawking model can be used to explain away the need for any external agent in the creation of the Universe. In his recent popular book entitled The Grand Design written together with Leonard Mlodinow, Hawking declared the death of philosophy on the grounds that it did not stood up to the challenges of science by not answering the ultimate questions the way science is now capable of doing. The article aims at demonstrating that Hawking’s and Mlodinow’s radical claims rest on very strong and ill-justified philosophical assumptions of the model dependent realism. Although it is a philosophically legitimate standpoint, its reductive character does not permit the extent of generalization as suggested in The Grand Design.

The common sense conviction that rationality is based on the classical logic requires major revision since the essential assumption of many standpoints in the cognitive science, concerning the non-contradictory character of mind, seems to be no longer tenable. Firstly, the non-algorithmic models of mind proposed by John Lucas and Roger Penrose are presented. In the context of these models, the importance of the Gödel incompleteness theorems for the philosophy of mind and artificial intelligence is debated. Secondly, several specific difficulties in applying the ‘Gödelian arguments’ in the modeling of mind are pointed out. As the main thesis of the article, it is stipulated that mind operates according to a wrong algorithm that is functionally equivalent to a contradictory formal system. The examples of the contradictory contents of mental states, evidenced in the phenomenon of self-deception and the mediaeval double truth theory in science, are discussed. Some consequences of the model of an inconsistent mind, based on the revision of the classical logic, are surveyed.

Unlike in the classical regime, the measurement performed on a quantum system perturbs the state of the system and its properties remain unknown between measurements. Several early interpretations of quantum mechanics suggested that the reduction of the wave vector that occurs in a measurement is effected by a conscious act of an observer. For example, London and Bauer fostered the conviction that it is the act of observation that decides on the fate of the Schrodinger cat. Later developments of quantum mechanical formalism, e.g., decoherence, indicated that there was no need to causally link the mental states of an observer with the purely physical process of a quantum measurement. In particular, the novel quantum models of human brain put forward by Roger Penrose suggest that it is the reduction of the wave vector that causes conscious act of the observer. Although this reversal does not clarify the specifics of the quantum measurement process directly, it illustrates the principle of methodological naturalism whereby externally introduced heuristic postulates are replaced by well justified scientific explanations.

Inasmuch as mathematical platonism can be clearly matched with the radical realism, there exists a possibility to point out an approach, promoted by a French physicist, Roland Omnés, that is equivalent to the Aristotelian position of moderate realism. This standpoint denies the existence of an independent universum of mathematical entities and claims that mathematics is encoded in the laws of physics. In analogy to logicism, where mathematics is considered to be reducible to logic, Omnés' position is called by him 'physism' to stress the reducibility of mathematics to the laws of physics. The goal of Roland Omnés is to construct a common philosophy of mathematics and physics where the realities of these two disciplines converge. The first part of the analysis aims at the description and critical evaluation of physism from the point of view of the adequacy of the consistent histories interpretation of quantum mechanics to provide physical basis of the abstraction of the mathematical structures from the physical reality.

Recenzja książki: Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, Alfred A. Knopf, New York 2005, ss. 1049.

The Schrödinger's Cat paradox was proposed in 1935 by Edwin Schrodinger, one of the founders of quantum mechanics, as an attempt to visualize the macroscopic realization of a quantum superposition state. A cat is placed in a sealed box together with a vial of poison. A two-state particle (e.g. an electron) is sent into a detector in the box resulting either in a broken or an intact vial and a dead or live cat, respectively. The main problem consists in whether the superposition state of a microscopic particle can be transferred upon the macroscopic cat, that is, whether the cat can exist in a superposition state, being simultaneously dead and alive. Since the standard Copenhagen interpretation is unable to assign any reality to the quantum superposition state, the paradox finds no resolution within the regime of this interpretation. Von Neumann's insistence on the uniform treatment of both microscopic (quantum) and macroscopic (classical) objects according to the laws of quantum mechanics provides a more consistent framework for the resolution of the paradox. In particular, the discovery of the phenomenon of decoherence, whereby the disappearance of the quantum interferences at the macro level is accounted for, suggests the onset of an extremely efficient interference relaxation process (10-23 s) upon the interaction of the two state particle with the detector. As a result, Schrodinger's cat can exist macroscopically either as dead or alive and never as a combination of both. Decoherence not only aids the resolution of the Schrodinger's Cat paradox but also sheds light upon the mechanisms by which the macro-world emerges from the microscopic quantum realm.

Recenzja książki: Roland Omnes, Quantum Philosophy: Understanding and Interpreting Contemporary Science (Filozofia kwantowa: rozumienie i interpretacja współczesnej nauki), tłum. z języka francuskiego Arturo Sangalli, Princeton and Oxford: Princeton University Press, 1999, ss. 296.

Recenzja książki: Anna Brożek, Symetria w muzyce, czyli o pierwiastku racjonalnym w komponowaniu dzieł muzycznych, OBI — Kraków, Biblos — Tarnów 2004, ss. 147.