Ioan-Vasile Leb (coord.), Bisericã si multiculturalitate în Europa sfîrsitului de mileniu Editura Presa Universitarã Clujeanã, Cluj-Napoca, 2001, 461p.

Ioan Vasile Leb, Biserica în actiune, Ed. Limes, Cluj-Napoca, 2001.

Petru Moldovan, Moshe Idel. Dinamica misticii iudaice Provopress, Cluj, 2005.

Mihai Ralea was a university professor and prominent representative of the Romanian interwar literary intelligentsia. M. Ralea taught psychology, sociology and aesthetics, and was at the same time the director of a reputed literary magazine (Viaţa românească-Romanian Life). Ralea was also a politician, initially an important member of the National Peasant Party, representing its centre left wing. In his case, one may notice the contradiction between his moral arguments in public and his deeds after he reached positions of power (Minister (...) of Labour under the royal dictatorship, Minister of Arts under the pro-communist Petru Groza government, etc.). Ralea was also called “the moralist without morals”, and the compromises he made – manifested through his adherence to anti-democratic regimes – can be documented by numerous archival documents. Due to strong political connections, Ralea survived in the high ranks of cultural bureaucracy even during cultural Stalinism. He maintained important positions both at the University of Bucharest and with humanities research institutes of the post-1948 Soviet-style Romanian Academy of Sciences. In the late 1950s and early 1960s, he also gained posi-tions of international cultural representation with the Romanian branch of the United Nations Educational, Scientific and Cultural Organisation (UNES-CO) and the Romanian Institute for the Cultural Relations with Foreign Countries (IRRCS, the Romanian VOKS). His survival (as a professor of psychology after 1948) had a significant price – Ralea’s collaboration with the Stalinist regime. Using open sources and also newly declassified archival documents, the article is an attempt to approach M. Ralea’s case of survival in the high cultural bureaucracy in the East European context. (shrink)

The paper is the final, fifth part of a series of studies introducing the new conceptions of “Hilbert mathematics” and “ontomathematics”. The specific subject of the present investigation is the proper philosophical sense of both, including philosophy of mathematics and philosophy of physics not less than the traditional “first philosophy” (as far as ontomathematics is a conservative generalization of ontology as well as of Heidegger’s “fundamental ontology” though in a sense) and history of philosophy (deepening Heidegger’s destruction of it from (...) the pre-Socratics to the Pythagoreans). Husserl’s phenomenology and Heidegger’s derivative “fundamental ontology” as well as his later doctrine after the “turn” are the starting point of the research as established and well known approaches relative to the newly introduced conception of ontomathematics, even more so that Husserl himself started criticizing his “Philosophy of arithmetic” as too naturalistic and psychological turning to “Logical investigations” and the foundations of phenomenology. Heidegger’s “Aletheia” is also interpreted ontomathematically: as a relation of locality and nonlocality, respectively as a motion from nonlocality to locality if both are physically considered. Aristotle’s ontological revision of Plato’s doctrine is “destructed” further from the pre-Socratics' “Logos” or Heideger’s “Language” (after the “turn”) to the Pythagoreans “Numbers” or “Arithmetics” as an inherent and fundamental philosophical doctrine. Then, a leap to contemporary physics elucidates the essence of ontomathematics overcoming the Cartesian abyss inherited from Plato’s opposition of “ideas” versus “things”, and now unifying physics and mathematics, particularly allowing for the “creation from nothing” instead of the quasi-scientific myth of the “Big Bang”. Furthermore, ontomathematics needs another interpretation of arithmetic, propositional logic and set theory in the foundations of mathematics, where the latter two ones are both identified with Boolean algebra, and the former is considered to be a “half of Boolean algebra” in the exact meaning to be equated to it after doubling by a dual anti-isometric counterpart of Peano arithmetic. That unified algebraic realization of the foundations of mathematics is related to Hilbert mathematics in both “narrow and wide senses” where the latter is isomorphic to the qubit Hilbert space, thus underlying all the physical world by the newly introduced substance of quantum information being physically dimensionless and generalizing classical information measured in bits. The substance of information, whether classical or quantum, visualizes the way of the unification of physics and mathematics by merging their foundations in Hilbert arithmetic and Hilbert mathematics: thus how ontomathetics is a “first philosophy”. The relation of ontomathematics to the Socratic “human problematics”, furthermore being fundamental for Western philosophy in Modernity, is discussed. Ontomathematics implies its “substitution” by abstract information (or by “subjectless choice” relevant to it), thus “obliterating the human outline on the ocean beach sand” (by Michel Foucault’s metaphor). A reflection back from the viewpoint of mathematic to Western philosophy as the philosophy of locality ends the study. (shrink)

Conference Proceedings (ASPLF Conference “Le Beau” in Iaşi, Romania, August 23-27, 2016). -/- Sections: 1. Le beau dans l'histoire de la philosophie; 2. Le beau à travers les cultures; 3. Beauté de la pensée et beauté du langage; 4. Ontologie et métaphysique du beau; 5. Le beau dans la nature et dans la société; 6. Beauté, éthique, politique; 7. Les catégories esthétiques; 8. L'esthétique et la vie quotidienne; 9. Renouvellement et perspectives de l'esthétique. -/- Conference sections: 1. The Beautiful in (...) the History of Philosophy; 2. The Beautiful across Cultures; 3. Beauty in Thought and Beauty in Language; 4. Ontology and Metaphysics of the Beautiful; 5. The Beautiful in Nature and in Society; 6. Beauty, Ethics, Politics; 7. Aesthetic Categories; 8. Aesthetics and Everyday-Life; 9. New Perspectives in Aesthetics. (shrink)

The paper is one of the first empirical attempts that builds on the moral dilemmas and group rationality literature to explore the way in which group composition with respect to group members’ individual choices in moral dilemmas and social influence processes impact on group moral choices. First individually and then, in small groups, 221 participants were asked to decide on 10 moral dilemmas. Our results show that emergent group level utilitarianism is higher than the average individual utilitarianism, yet, lower than (...) the highest individual utilitarianism within groups. We also show that average individual utilitarianism positively predicts group utilitarianism while group fragmentation in individual utilitarianism has a negative effect on group utilitarianism. Next to group composition, minority influence processes explain additional variance in group utilitarianism, cognitive dissent having a positive influence, while normative deviance a negative influence on group utilitarianism. Majority influence has no significant influence on group utilitarianism. Finally, our results show that the relationship between group fragmentation in individual utilitarianism and emergent group utilitarianism is mediated by the two forms of minority influence. (shrink)

This study emphasises the cosmic dimensions of the Church understood as the Throne of God, analysing its understanding in this way by the great writers and thinkers of the ancient world, for example, Philo the Alexandrine, Saint Dionysius the Areopagite and Saint Irene of Lyon. The reconstitution of all the cosmological contexts and understanding of the Throne of God inspired by the texts of the ancient authors is opening a very interesting perspective over the existence of the Church as a (...) cosmic Throne of God and reassembling of all the heavenly and intelligible creations sustained and vivified by the primal light of God transmitted in this way towards the lower degrees of the heavenly angelic and churchly hierarchy. Thus, the real source of primacy in the Church is originated, as Saint Dionysius pointed out, in the primal light of God poured over the Church. The Church as the Throne of God helps to discover the real cosmic and heavenly perspective over the heavenly power and authority, the bishops of the Churches are called frankly by God from the beginning (Rv 3:21). (shrink)

Bryan Rennie (ed.), Changing Religious Worlds. The Meaning and End of Mircea Eliade State University of New York Press, Albany, 2001.

Israel Knohl Mesia dinainte de Iisus. Slujitorul pãtimitor de la Marea Moartã Traducere de Ana-Elena Ilinca, Ed. Dacia, Cluj-Napoca, 2001.

Moshe Halbertal, Ezoterism si exoterism. Restrictiile misterului in traditia iudaica Ed. Limes, Cluj-Napoca, 2004, traducere din limba engleza de Roxana Havrici.

Moshe Idel, Hasidism între extaz si magie Ed. Hasefer, Bucuresti, 2001.

Moshe Idel, Maimonides and the Jewish Mystic, Dacia Publishing House, Cluj-Napoca, 2001.

Moshe Idel, Perfectiuni care absorb: Cabala si interpretare Ed. Polirom, Iasi, 2004, prefata de Harold Bloom, traducere de Horia Popescu.

G. E. Moore’s critical analysis of right action in utilitarian ethics and his consequentialist concept of right action is a starting point for a theory of moral/right action in ethics of social consequences. The terms right and wrong have different meanings in these theories. The author explores different aspects of right and wrong actions in ethics of social consequences and compares them with Moore’s ideas. He positively evaluates Moore’s contributions to the development his theory of moral/right action.

En examinant l’oeuvre de Descartes et en en découvrant les éléments sociologiques, il nous devient possible de déduire l’horizon social de son système. Descartes mentionne les conditions, les manifestations et les unités sociales. Pour lui, l’individu est partie d’un tout. L’amitié et la générosité sont des sentiments profondément sociaux. Mais la raison met la vie sociale en valeur et c’est elle aussi qui décide, en cas de conflit entre l’individu et la société, lequel des deux a le bon droit de (...) son côté et si c’est l’individu qui doit se sacrifier à la société. Le Souverain Bien est le critère suprême. La société à laquelle aspire Descartes doit être dirigée par une aristocratie intellectuelle, créée sur des bases démocratiques et ayant à sa tête, peut-être, un roi-philosophe, législateur unique et prévoyant. L’homme cartésien est une synthèse de la sagesse antique, de Partisan moderne et de l’homme créateur qui, par la science et la raison, cherche à rapprocher la Société du Bien souverain. (shrink)

Moshe Idel considers that the emergence of Hasidism is not the result of the confrontation between ancient and modern orientations. In M. Idel’s interpretation of the Hasidic phenomenon, a central point is ascribed to the inevitable encounter of the Hasidim masters with a variety of mystic literature. I have chosen to analyze three extremely complex and very important concepts regarding Jewish mystic phenomenon: mitzvoth, worlds, and community. In discussing these concepts I have tried to emphasize their practical and very important (...) nature. I have also described the relations that bring them together, in order to identify the special role of the Hasidic mystic in the process of influencing the superior and inferior worlds. This depends on the manner in which he respects and carries out the commandments. I would like to emphasize the blurred line between mystic and magic in the Hasidism of Southeastern Europe. (shrink)

The philosophy of the modern age begins with two enigmatic figures—Descartes and Bacon. They are steeped in the common spirit of philosophical reform, but view the tasks and the place of metaphysics differently. Bacon thinks that metaphysics should be constructed on the basis of physics and has an applied and empirical character. Descartes believes that physics grows out of a priori metaphysics.

Are causal explanations (e.g., “she switched careers because of the COVID pandemic”) treated differently from the corresponding claims that one factor caused another (e.g., “the COVID pandemic caused her to switch careers”)? We examined whether explanatory and causal claims diverge in their responsiveness to two different types of information: covariation strength and mechanism information. We report five experiments with 1,730 participants total, showing that compared to judgments of causal strength, explanatory judgments tend to bemoresensitive to mechanism andlesssensitive to covariation – (...) even though explanatory judgments respond to both types of information. We also report exploratory comparisons to judgments of understanding, and discuss implications of our findings for theories of explanation, understanding, and causal attribution. These findings shed light on the potentially unique role of explanation in cognition. (shrink)

The author studies the Magyar and Slovak ideas of common good that concerned the inhabitants of Hungary in the first half of the 19th century. The Magyar model was based on the rights of an individual, their civic duties, and virtues. Its realisation, however, lay in preferring the interests of the Magyar nation and required the adoption of full Magyar national identity, i.e. assimilation and ethnocide of the non-Magyar inhabitants of Hungary. The author characterises this model as exclusive, chauvinist, and (...) nationalist-Messianic, masquerading as liberal values. On the other hand, the Slovak model of common good was based on the presumption of equal rights and duties for all citizens of Hungary while preserving the possibility of the growth, development, and cultivation of each individual, including the opportunity to gain education in one’s own mother tongue. The author perceives the Slovak model as inclusive, pluralist, and humanist; he considers it as a better alternative for the future of Hungary, which, however, could not be pursued. That means there were two incompatible approaches to the common good of the inhabitants of Hungary, which resulted in the downfall of Hungary. (shrink)

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

The paper questions the scientific rather than ideological problem of an eventual biological successor of the mankind. The concept of superhumans is usually linked to Nietzsche or to Heidegger’s criticism or even to the ideology of Nazism. However, the superhuman can be also viewed as that biological species who will originate from humans eventually in the course of evolution.While the society is reached a natural limitation of globalism, technics depends on the amount of utilized energy, and the mind is restricted (...) by its carrier, i.e. by the brain, it is language which seems to be the frontier of any future development of humans or superhumans. Language is a symbolization of the world and thus doubling in an ideal or virtual world fruitful for creativity and the modeling of the former. Consequently, the gap between the material and the ideal world is both produced by and productive for language. (shrink)

“Negative probability” in practice. Quantum Communication: Very small phase space regions turn out to be thermodynamically analogical to those of superconductors. Macro-bodies or signals might exist in coherent or entangled state. Such physical objects having unusual properties could be the basis of quantum communication channels or even normal physical ones … Questions and a few answers about negative probability: Why does it appear in quantum mechanics? It appears in phase-space formulated quantum mechanics; next, in quantum correlations … and for wave-particle (...) dualism. Its meaning:- mathematically: a ratio of two measures (of sets), which are not collinear; physically: the ratio of the measurements of two physical quantities, which are not simultaneously measurable. The main innovation is in the mapping between phase and Hilbert space, since both are sums. Phase space is a sum of cells, and Hilbert space is a sum of qubits. The mapping is reduced to the mapping of a cell into a qubit and vice versa. Negative probability helps quantum mechanics to be represented quasi-statistically by quasi-probabilistic distributions. Pure states of negative probability cannot exist, but they, where the conditions for their expression exists, decrease the sum probability of the integrally positive regions of the distributions. They reflect the immediate interaction (interference) of probabilities common in quantum mechanics. (shrink)

The paper discusses this year’s Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum information (...) science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by this year’s Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview. (shrink)

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...) mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

The ethics of social consequences is a means of satisficing non-utilitarian consequentialism that can be used to approach disaster issues. The primary values in the ethics of social consequences are humanity, human dignity and moral rights, and these are developed and realized to achieve positive social consequences. The secondary values found in the ethics of social consequences include justice, responsibility, moral duty and tolerance. Their role and purpose is given by their ability to help achieve and realize moral good. Fair (...) treatment within moral issues stems from applying primary as well as secondary values. The nature of these values cannot be determined exclusively in ordinary circumstances. However, in extraordinary circumstances (disasters), not all the requirements relating to the value structure of the ethics of social consequences need be considered in its entirety. In extraordinary circumstances, values are prioritised and realized. Primary values are realized prior to secondary ones. When prioritizing primary values, the realization of positive social consequences, or at least minimizing the negative social consequences, takes priority over other primary values. In disaster bioethics especially, it is often necessary to find a way to minimize the negative social consequences; thus, actions where positive social consequences are prevalent are preferred. (shrink)

The author studies selected fundamental literary records from Great Moravia of the 9th century (The rules of the holy fathers [Zapovědi svatych otcov], Judicial law for laymen [Zakon sudnyj ljudem], Nomocanon [Nomokanon], Adhortation to rulers [Vladykam zemle Božie slovo velit]) presumably compiled, translated or created by Constantine (Cyril) and Methodius, the Thessaloniki brothers. In the context of defining early and medieval Christian ethics, the author concluded that the texts in question contain elements of the Christian code of ethics, by means (...) of which Constantine (Cyril) and Methodius, following the model of the Byzantine Emperors Leo III and Constantine V, wished to form the social morality of Great Moravia. Based on this, the author holds the opinion that the history of Christian ethics in Moravia, Slovakia and Bohemia goes as far back as the activities of Constantine (Cyril) and Methodius and the period of Great Moravia. (shrink)

The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations of (...) energy conservation in a “safe”, maximally remote point in the alleged “beginning of the universe”. On the contrary, an omnipresent and omnitemporal medium obeying quantum information conservation rather than energy conservation permanently generates action and thus the physical world. The utilization of that creation “ex nihilo” is accessible to humankind, at least theoretically, as long as one observes the physical laws, which admit it in their new and wider generalization. One can oppose Hilbert mathematics to Gödel mathematics, which can be identified as all the standard mathematics until now featureable by the Gödel dichotomy of arithmetic to set theory: and then, “dialectic”, “intuitionistic”, and “Gödelian” mathematics within the former, according to a negative, positive, or zero value of the distance between finiteness and infinity. A mapping of Hilbert mathematics into pseudo-Riemannian space corresponds, therefore allowing for gravitation to be interpreted purely mathematically and ontologically in a Pythagorean sense. Information and quantum information can be involved in the foundations of mathematics and linked to the axiom of choice or alternatively, to the field of all rational numbers, from which the pair of both dual and anti-isometric Peano arithmetics featuring Hilbert arithmetic are immediately inferable. Noether’s theorems (1918) imply quantum information conservation as the maximally possible generalization of the pair of the conservation of a physical quantity and the corresponding Lie group of its conjugate. Hilbert mathematics can be interpreted from their viewpoint also after an algebraic generalization of them. Following the ideas of Noether’s theorem (1918), locality and nonlocality can be realized both physically and mathematically. The “light phase of the universe” can be linked to the gap of mathematics and physics in the Cartesian organization of cognition in Modernity and then opposed to its “dark phase”, in which physics and mathematics are merged. All physical quantities can be deduced from only mathematical premises by the mediation of the most fundamental physical constants such as the speed of light in a vacuum, the Planck and gravitational constants once they have been interpreted by the relation of locality and nonlocality. (shrink)

The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...) Thus, the pair of arithmetic and set are to be similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate now, i.e. after replacing it and its negation correspondingly by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. Indeed, the axiom of choice, as far as it is equivalent to the well-ordering “theorem”, transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. So, the Gödel incompleteness statement relies on the logical contradiction of the axiom of induction and the axiom of infinity in the final analysis. Nonetheless, both can be considered as two idempotent versions of the same axiom (analogically to the Fifth postulate) and then unified after logicism and its inherent intensionality since the opposition of finiteness and infinity can be only extensional (i.e., relevant to the elements of any set rather than to the set by itself or its characteristic property being a proposition). So, the pathway for interpreting the Gödel incompleteness statement as an axiom and the originating from that assumption for “Hilbert mathematics” accepting its negation is pioneered. A much wider context relevant to realizing the Gödel incompleteness statement as a metamathematical axiom is consistently built step by step. The horizon of Hilbert mathematics is the proper subject in the third part of the paper, and a reinterpretation of Gödel’s papers (1930; 1931) as an apology of logicism as the only consistent foundations of mathematics is the topic of the next second part. (shrink)