In a seriesof papers beginning in 1944, the Dutch mathematician and philosopherGeorge Francois Cornelis Griss proposed that constructivemathematics should be developedwithout the use of the intuitionistic negation1 and,moreover, without any use of a nullpredicate.In the present work, we give formalized versions of intuitionisticarithmetic, analysis,and higher-order arithmetic in the spirit ofGriss' ``negationless intuitionistic mathematics''and then consider their relation to thecurrent formalizations of thesetheories.

The present work contains an axiomatic treatment of some parts of the restricted version of intuitionistic mathematics advocated by G. F. C. Griss, also known as negationless intuitionistic mathematics.Formal systems NPC, NA, and FIMN for negationless predicate logic, arithmetic, and analysis are proposed. Our Theorem 4 in Section 2 asserts the translatability of Heyting's arithmetic HAinto NA. The result can in fact be extended to a large class of intuitionistic theories based on HAand their negationless counterparts. For instance, in Section (...) 3 this is shown for Kleene's system of intuitionistic analysis FIMand our FIMN. (shrink)

This paper presents an intuitionistic proof of a statement which under a classical reading is logically equivalent to Gödel's completeness theorem for classical predicate logic.

The present work contains an axiomatic treatment of some parts of the restricted version of intuitionistic mathematics advocated by G. F. C. Griss, also known as negationless intuitionistic mathematics.Formal systems NPC, NA, and FIMN for negationless predicate logic, arithmetic, and analysis are proposed. Our Theorem 4 in Section 2 asserts the translatability of Heyting's arithmetic HAinto NA. The result can in fact be extended to a large class of intuitionistic theories based on HAand their negationless counterparts. For instance, in Section (...) 3 this is shown for Kleene's system of intuitionistic analysis FIMand our FIMN. (shrink)

This work is a sequel to our [16]. It is shown how Theorem 4 of [16], dealing with the translatability of HA(Heyting's arithmetic) into negationless arithmetic NA, can be extended to the case of intuitionistic arithmetic in higher types.

This work is a sequel to our [16]. It is shown how Theorem 4 of [16], dealing with the translatability of HA(Heyting's arithmetic) into negationless arithmetic NA, can be extended to the case of intuitionistic arithmetic in higher types.

In a seriesof papers beginning in 1944, the Dutch mathematician and philosopherGeorge Francois Cornelis Griss proposed that constructivemathematics should be developedwithout the use of the intuitionistic negation1 and,moreover, without any use of a nullpredicate.In the present work, we give formalized versions of intuitionisticarithmetic, analysis,and higher-order arithmetic in the spirit ofGriss' ``negationless intuitionistic mathematics''and then consider their relation to thecurrent formalizations of thesetheories.

Let HA be Heyting's arithmetic, and let CS denote the conjunction of Kreisel's axioms for the creative subject: \begin{eqnarray*} {\rm CS}_1.&&\quad \,\forall\, x (\qed_x A \vee \; \neg \qed_x A)\; ,\nn {\rm CS}_2. &&\quad \,\forall\, x (\qed_x A\to A)\; ,\nn {\rm CS}_3^{\rm S}. &&\quad A\to\,\exists\, x \qed_x A\; ,\nn {\rm CS}_4.&&\quad \,\forall\, x\,\forall\, y (\qed_x A & y \ge x\to\qed_y A)\; .\nn \end{eqnarray*} It is shown that the theory HA + CS with the induction schema restricted to arithmetical (i.e. not (...) containing $\qed$ ) formulas is conservative over HA. (shrink)

Within a weak system \ of intuitionistic analysis one may prove, using the Weak Fan Theorem as an additional axiom, a completeness theorem for intuitionistic first-order predicate logic relative to validity in generalized Beth models as well as a completeness theorem for classical first-order predicate logic relative to validity in intuitionistic structures. Conversely, each of these theorems implies over \ the Weak Fan Theorem.

The study examines a problematic hypothesis of possible approaches to identifying the quantum physical foundations of the functioning of consciousness. The authors proceed from the fact that in modern conditions, not a single science, nor all sciences taken together, gives a final answer to the question of the “mechanism” of the origin of thought. However, this does not mean at all that research in this direction needs to be stopped. The authors express confidence that modern and subsequent research into the (...) “quantum concept of consciousness” will lead to the identification of previously unknown patterns, opening the way to the formation of new principles and approaches. As an example, the corresponding Penrose - Hameroff concept is considered. Quantum mechanics complements the tools of neurobiology and other branches of neuroscience, which together form an interdisciplinary field of knowledge that is dynamically growing and developing. The authors are not apologists for the omnipotence of quantum physics. Quantum correlates of consciousness actually mean that it is not today’s quantum mechanics itself that explains the emergence of mental states, but the fact that in the birth of these states it is essential that in the very process of the formation of neurodynamic impulses in the neurons of the cerebral cortex that generate mental states, there are processes of quantum nature. It should also be recognized that the quantum-molecular level (nanolevel) of processes in the neurons of the brain really exists and it is this that is the source of proto-consciousness. Science strives to move forward, new research programs are emerging within the framework of quantum biology, quantum psychology, quantum information science, which in turn can shed light on the hypothesis of the “quantum concept of consciousness.”. (shrink)

This book explores three worlds shared by the humans in their collective experiences. It identifies and explores the world of commonsense, the world of religion, and the world of science as three essential dimensions of human experience. The book helps understand that humans can gain comfort and pleasure in commonsense, achieve meaning and purpose from religion, and attain truth and rationality through science. It actively applies theories to and develops theoretical explanations from different domains or situations of human existence. This (...) book is of interest to theorists, researchers, instructors, and students across major academic disciplines in the humanities and social sciences. (shrink)

In the present paper, these authors argue on actual reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed completely. An outline of plausible resolution of this problem is given here, based on: a) Gödel’s incompleteness theorem, b) Newton’s aether stream model. And in another paper we will present our calculation of receding Moon from Earth based on such a matter creation hypothesis. More experiments and observations are called to verify this new hypothesis, albeit it is inspired from (...) Newton’s theory himself. (shrink)

In the same spirit with the theme of last issue of this SGJ journal (“Ongoing creation”), this paper shortly reviews a plausible mechanism from Aether to become ordinary matter from the perspective of Neutrosophic Logic. We also discuss two other possible applications of Neutrosophic Logic, including a resolution of conflicting paradigms in medicine. We hope that some ideas as outlined herein will be proved useful in the near future.

In the present paper we discuss: a) how Hilbert’s unification program failed completely, and b) we outline a new electron model based on Helmholtz’s electron vortex and Kolmogorov theory of turbulence. Novelty aspect: we discuss among other things, electron capture event, and von Karman vortex street. We also discuss a new model of origination of charge and matter. This paper is a sequel to a preceding paper on similar theme.

In a recent paper, we describe how a model of quantum communication based on combining consciousness experiment and entanglement can serve as impetus to stop 5G-caused diseases. Therefore, in this paper we will discuss how entanglement can be explained in terms of quantum theory. This short review may be considered as an effort to bring QM into real problem solving, i.e. telecommunication.

Smarandache Hypothesis states that there is no speed limit of anything, including light and particles. While the idea is quite simple and based on known hypothesis of quantum mechanics, called Einstein-Podolski-Rosen paradox, in reality such a superluminal physics seems still hard to accept by majority of physicists. Here we review some experiments to support superluminal physics and also findings to explain Smarandache Quantum Paradoxes and Quantum Sorites Paradox. We also touch briefly on new experiment on magneton, supporting SubQuantum Kinetic Model (...) of Electron. (shrink)

Recently, a friend of one of these writers told her story of using one of a healthcare product to activate her stem cells as part of regenerative medicine. Regenerative medicine is a field of medicine that seeks to repair or replace damaged or diseased tissues and organs. This can be done through a variety of methods, including stem cell therapy, tissue engineering, and gene therapy. This is a short review article on this rapid field called regenerative medicine, in particular via (...) a new method called photobiomodulation, especially by virtue of low-intensity laser pen treatment. Hopefully it will attract more research in this interesting direction, both for laser/photobiomodulation to boost plant growth as well as in healthcare (see also: Christianto & Smarandache, 2022; Christianto, 2023). (shrink)

Biblical interpretation and/or hermeneutics is largely influenced by context and prevailing events and/or issues. This is attested by many scholars in the field. Previous pandemics have influenced the way biblical hermeneutics is conducted during the period. The situation is not too different from the emergence of COVID-19. The pandemic has been scripturalised to argue that it is the fulfilment of scriptural signs for the second coming of Jesus. Others assert that it is the result of human sins and 5G technology. (...) Amid these propositions, biblical narratives concerning miracles/healing, eschatology, and hope were handled uniquely. This study employs narrative research criticism to analyse various propositions concerning COVID-19 and how biblical texts were engaged to propound an epideictic rhetorical theory of biblical interpretation during the emergence of COVID-19. The main finding is that although there are many assigned eschatological interpretations to the pandemic, there is an epideictic interpretation of miracle narratives of Jesus to minister healing to persons affected and infected by COVID-19.Contribution: This study emphasises the problem-solving approach to biblical interpretation in the African context. It proposes the application of this approach in response to the impact of the COVID-19 pandemic. (shrink)

The European Commission’s proposal to address antimicrobial resistance using transferable exclusivity vouchers (TEVs) is fundamentally flawed. European policymakers and regulators should consider alternatives, such as better funding for basic and clinical research, use of advance market commitments funded by a pay-or-play tax, or enacting an EU Fund for Antibiotic Development.

Excerpt from Les Sceptiques Grecs Enfin le doute lui-meme n'est pas le scepticisme. C'est du doute seulement qu'on pourrait dire qu'il est a peu pres contem porain de la pensee humaine; car, pour un esprit qui reflechit, la decouverte de la premiere erreur suffit a inspirer une certaine defiance de soi; et combien de temps a-t-il fallu a des esprits un peu attentifs pour s'apercevoir qu'ils s'etaient plus d'une fois trompee? About the Publisher Forgotten Books publishes hundreds of thousands of (...) rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Ces etudes debordent le probleme du temps chez les Stoiciens et se proposent d'etablir que cette question, en apparence modeste, permet d'eclairer, et en meme temps commande l'ensemble du systeme. Au premier abord en effet, la theorie du temps se presente comme une simple section d'un chapitre de la Physique, celui qui traite des Incorporels. Mais deja la simple interpretation des textes transmis fait voir que cette theorie tient etroitement a d'autres theories, comme celle des incorporels en general, des categories, (...) de la substance. Abordant ensuite les theses majeures de la logique et de l'ethique, on s'apercoit qu'a leur tour elles sont solidaires de la conception du temps qui, dans bien des cas, fait evanouir leur apparence de paradoxe. A cela meme, il n'y a rien d'etrange, si l'on se souvient que le stoicisme, plus que tout autre philosophie antique, constitue un systeme coherent. Mais plus particulierement, le probleme du temps a du former comme le noeud de la reflexion stoicienne qui vise, contre les lourdes autorites de Platon et d'Aristote, a retablir dans sa realite et dans sa dignite, le concret, le sensible, disqualifie comme sujet a la generation et a la corruption, c'est-a-dire, en un mot, comme l'etre dans le temps. (shrink)

In his opening address at a discussion of the book: V. V. Bychkov, N. B. Mankovskaya, and V. V. Ivanov, Trialogue: Living Aesthetics and the Contemporary Philosophy of Art , held on 27 February 2012 at the S. Gerasimov All-Russia State University of Cinematography , the author shows that Trialogue came into existence as a result of interpretation, polemical debate, and further development of ideas formulated in his early fundamental work. The Artistic Apocalypse of Culture . The key idea of (...) both books is V. Bychkov's hypothesis of Culture -post- culture drawn from radical processes that take place in art, aesthetics, and the culture of the last century. (shrink)

As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1,. 2, 2022), Our universe is but one page in a large book [4]. For example, things and Beings can travel between Universes, intentionally or unintentionally. In this short remark, we revisit and offer short remark to Neil’s ideas and trying to connect them with geometrization of musical chords as presented by D. Tymoczko and others, then to Escher staircase and then to Jacob’s (...) ladder which seems to point to possibility to interpret Jacob’s vision as described in the ancient book of Genesis as inter dimensional or heavenly staircase, e.g. an inter dimensional bridge between heaven and earth (see also classic book: Hofstadter, Godel, Escher, Bach). Jacob’s vision of angels going down to earth from that staircase has been depicted for instance in William Blake art etc. In our communication with others via physics literature and discussions etc, we came to several conclusions as follows: Firstly, possibility of quantum wormhole effect to mirror particle universe, which sometimes it is termed non-orientable wormhole. While such mirror particles effect have been more than 50 years predicted with the so-called parity violation (cf. Lee & Yang, 1950s), and that is called symmetry breaking. Secondly, a series of extended experiments on laser irradiated cold water may suggest possible transition from a phase of water to be at least partially fourth phase of water, which may be composed of crystalline water (see e.g. Gerald Pollack, and also Harold Aspden on liquid crystalline). If we can imagine laser cooling effect can be done in protracted time, then we can achieve a physical representation of Aspden’s liquid crystalline. Therefore, in subsequent article (Part II) we outlined simple model of such an effect of tunneling via quantum liquid crystalline Universe, which may likely be modeled with iced-water. It is interesting to remark here that certain experiments by Stockholm University scientists have shown that X-ray triggered water can exhibit properties just like liquid crystal (cf. PRL, 2020). That is why we consider it possible that there can be quantum phase transition where liquid water (comprised of iced cubes and water) can exhibit effects such as tunneling in quantum liquid crystalline Universe. Last but not least, we admit that what we outlined here is just an initial phase; and if you wish, perhaps we can call such experiments as “wormhole-at-lab” experiments (abbreviated: WHALE). (shrink)

GESCHÉ, Adolphe. Deus para pensar o ser humano. Victor René Villavicencio Matienzo GALANTINO, Nunzio. Dizer o homem hoje: novos caminhos da antropologia filosófica. Victor René Villavicencio Matienzo LIBÂNIO, J. B. Qual o caminho entre o crer e o amar? Victor René Villavicencio Matienzo IBARRONDO, Xabier Pikaza. Monoteísmo e globalização: Moisés, Jesus, Muhammad. Wellington Teodoro da Silva MARTINS, Iris Mesquita. Felicidade na velhice. Iris Mesquita Martins.

The present article was partly inspired by G. Pollack’s book, and also Dadoloff, Saxena & Jensen (2010). As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1, No. 2, 2022), for example, things and Beings can travel between Universes, intentionally or unintentionally [4]. In this short remark, we revisit and offer short remark to Neil Boyd’s ideas and trying to connect them with geometry of musical chords as presented by D. Tymoczko and (...) others, then to Escherian staircase and then to Jacob’s ladder which seems to pointto possibility to interpret Jacob’s vision as described in the ancient book of Genesis as interdimensional staircase, e.g. an interdimensional bridge between heaven and earth (cf. classic book: Hofstadter, Godel, Escher, Bach). Jacob’s vision of angels going down to earth from that staircase has been depicted for instance in William Blake art etc. In our communication with others via physics literature and discussions etc, we came to several conclusions as follows: Firstly, possibility of wormhole effect to mirror particle universe, which sometimes it is termed non-orientable wormhole. While such mirror particles effect have been more than 50 years predicted with the so-called parity violation (cf. Lee & Yang, 1950s), and that is called symmetry breaking. Secondly, a series of extended experiments on laser irradiated cold water may suggest possible transition from a phase of water to be at least partially fourth phase of water, which may be composed of crystalline water (see e.g. Gerald Pollack, and also Harold Aspden on liquid crystalline). If we can imagine laser cooling effect can be done in protracted time, then we can achieve a physical representation of Aspden‘s liquid crystalline. Therefore, in this article we outline a series of simple experiments of laser irradiated iced-water along with beryl and selenite crystals in order to see possibility of such a quantum tunneling via quantum liquid crystalline Universe hypothesis, which may likely be modeled with iced-water. It is interesting to remark here that certain experiments by Stockholm University scientists have shown that X-ray triggered water can exhibit properties just like liquid crystal (cf. PRL, 2020). That is why we consider it possible that there can be quantum phase transition where liquid water (comprised of iced cubes and water) can exhibit effects such as tunneling in quantum liquid crystalline Universe. Last but not least, we admit that what we outlined here is just aninitial phase; and if you wish, perhaps we can call such experiments as “wormhole-at-lab” experiments (abbreviated: WHALE). (shrink)

In March 1912 A. N. Whitehead wrote a letter which sheds new and important light on his own view of his mathematical goals. In this article I publish the letter for the first time and relate its contents not only to his mathematical career but also to his scientific, philosophical and educational interests.

Apunte preliminar, por Francisco Romero.--La obra de Sócrates.--Los mitos en la filosofía de Platón.--Sobre el Banquete de Platón.--El devenir en la filosofía de Platón.--La teroía platónica de la particapación según el Parménides y el Sofista.--Las leyes de Platón y la teoria de las ideas.--La moral de Platón.--Traducción de los pasajes griegos.

Le Cours de Philosophie par Mr V. Cousin réunit les leçons du semestre d'hiver 1819-1820, précédées de quelques cours sur l'École sensualiste et sur la Philosophie de Kant. Il s'agit là d'un travail préparatoire en vue de la composition d'une oeuvre "dogmatique" que Cousin n'a jamais écrite.

Two results of elementary number theory, going back to Kürschák and Nagell, stating that the sums $\sum_{i=1}^k \frac{m_i}{n+i}$ (with $k\geq 1$, $(m_i, n+i)=1$, $m_i\lessthan n+i$) and $\sum_{i=0}^k \frac{1}{m+in}$ (with $n, m, k$ positive integers) are never integers, are shown to hold in $\mathrm{PA}^{-}$, a very weak arithmetic, whose axiom system has no induction axiom.

Il est tout à fait possible de soutenir que l’espace de Newton manque d’objectivité physique (ce qui est un corollaire de la théorie einsténienne) et néanmoins prendre tout à fait au sérieux la thèse de l’espace euclidien comme condition de possibilité de l’expérience. Condition de possibilité de l’émergence d’un sujet qui configure son monde en remettant tout point de son environnement à une métrique. Cette métrique ne serait autre que celle qui donne sens à la géométrie que l’on a appris (...) à l´école, c’est à dire, la métrique euclidienne. Tout en manquant de réalité physique, tout en n`étant pas fertile à l’heure de rendre compte de la forme de l’univers, la métrique euclidienne serait la seule modalité sous laquelle il y aurait pour l’homme une prise sur le monde. Qu’on l’appelle ou pas transcendantale, la reconnaissance de la métrique euclidienne comme condition de possibilité de l’expérience nous rapprocherait de Kant sans pour autant répudier Einstein ou Poincaré. (shrink)