Idea Of Infinity Research Articles

The concept of infinity and the development of set theory solutions

The concept of infinity is intricately connected to and comprehended via the framework of cardinal and ordinal numbers. Cardinal and ordinal numbers are fundamental mathematical ideas within the field of set theory. The cardinal number is used to denote the quantity of items inside a given set while ordinal defines basic algorithms. This article demonstrates how the discipline of set theory may be used as a tool to investigate the nature of infinity, or at the very least give some insights into the subject. The idea of infinity may be better understood by looking at it through the lens of set theory and the commutative property. In addition to that, this research presents the connection and compatibility examination of Cohens operation upon the Zermelo Freankel axiomatic framework. These accomplishments are discussed in this article as illuminating insights for readers to consider while imagining the ultimate solution to the problems posed by the Continuum Hypothesis and the nature of infinity. Through the use of examples from contemporary researchers, the multiverse and indeterminism are introduced as potential approaches to the problem of how to solve Cantors legacy in the future.

Metaphysics as Prayer: Introducing Ferdinand Ulrich

AbstractAdapting Hegel's division of poetry into the three modes, epic, lyric, and drama, Hans Urs von Balthasar characterized his own distinctive approach to theology as “dramatic,” indicating by that term an integration of the objective, conceptual dimension of the epic mode and the subjective, existential dimension of the lyric mode. This essay proposes that the German thinker Ferdinand Ulrich (1931‐2020), friend of Balthasar, achieves something analogous in philosophy: an “onto‐drama,” which integrates metaphysics and prayer. The principal aim of this essay is to introduce Ulrich to a wider audience by presenting the basic themes of his 1973 book, Prayer as the Fundamental Act of the Creature. Using Emmanuel Levinas's text “Philosophy and the Idea of Infinity” as a foil in order to bring out the distinctive features of Ulrich's thought, this essay argues for the essential interdependence of the encounter with God and meditative reflection on the question of being, an interdependence that is played out as a drama right at the heart of personal identity.

FRIEDRICH HÖLDERLIN's AESTHETICS BETWEEN PLATO AND KANT (TO THE QUESTION OF FORMATION OF THE CATEGORIES OF THE BEAUTIFUL AND SUBLIME)

The article analyzes the aesthetic views of Friedrich Hölderlin, and, first, his understanding of the categories of the Beautiful and Sublime. Particular attention is paid to the comparison of Hölderlin's views with the aesthetic teachings of Plato and Immanuel Kant, who had a great influence on the German poet. The author of the article concludes that Hölderlin sought to unite the Platonian and Kantian understanding of beauty, seeing the similarity between the concepts of Plato and Kant in the question of the source of the beautiful. The central for aesthetics of Hölderlin was the problem of combining the spheres of aesthetic and ethical, to solve which he relied on the idea of Kant about beautiful as a symbol of the moral good and the Teaching of Plato on the climbing of the soul to the Good. Hölderlin pays less attention to the theoretical development of the category of the Sublime than to the comprehension of the category of the Beautiful, however, in his writings, the Sublime is present implicitly, and Hölderlin's understanding of this category is close, on the one hand, to Platonian, bringing together the Beautiful and the Sublime, and, on the other, to Kantian understanding, which brings the Sublime together with the idea of infinity, God and the sphere of morality. The conclusions to which Hölderlin comes, are far from Platonism, and from Kantianism. The poet concludes about the central and leading role of poetry and poetic gift in the knowledge of the world, which should be aesthetic. This indicates a romantic way to interpret Hölderlin's aesthetic concepts of Plato and Kant.

Art à la the Occult: The Literary Esotericism of James Joyce’s Ulysses

Abstract Widely considered a hermetic text of avant-garde modernism for its inaccessibility to the “common reader,” James Joyce’s magnum opus Ulysses is literally esoteric with allusions to Kabbalistic concepts, terms of Hindu cosmology, Trinitarian heresies, and Continental mystics; quasi-ironic references to Dublin Theosophists; the protagonist Leopold Bloom’s Freemasonry; and structural use of Platonic/Aristotelian metaphysics. However, the esotericism of Ulysses is not confined to the text’s cavalier allusiveness. Nor is the religious origin of Joyce’s art merely part of the personal mythology of the author, a relapsed Catholic, whose Eucharistic aesthetic endeavors to “transmut[e] the daily bread of experience into the radiant body of everliving life.” This article argues that esotericism is a fundamental principle underlying the composition of Ulysses, its envisaged relationship with the “implied reader,” and its larger socio-cultural ramifications. It explores the literary esotericism of Ulysses as analogous to religious esotericism with reference to: the idea of the book as cosmos with the chaotic “word” as its prima materia; its archetypal/symbolic consciousness; the idea of infinity as a hermeneutic principle; manifestation of the ideas of initiation and secrecy as hermeneutic challenges; the self-imposed antithetical character of avant-garde modernism vis-à-vis the mainstream; and the possibility of deciphering a Joycean “vision.”

O Infinito Atual em Or Hashem de Hasdai Crescas (1340 -1411)

Este artigo enfoca a concepção de infinito atual do filósofo judeu medieval Hasdai Crescas (1340–1411), formuladas no livro Or Hashem (1410) às três primeiras proposições de Maimônides, tal como são enunciadas na segunda parte do Guia dos Perplexos. As teses de Maimônides têm como objetivo negar a possibilidade do infinito atual como magnitude imaterial ou material, como conjunto infinito de seres finitos e como série infinita de causa e efeito. Após uma breve exposição da trajetória dos conceitos de infinito nas diversas tradições sapienciais judaicas recebidas na Idade Média, indicamos como a argumentação em prol da ideia de infinito atual em Crescas dialoga com elas. Desse diálogo, emerge o conceito de infinito como singularidade atualizada paralelamente no real como vácuo infinito, lugar de coexistência de infinitos universos, e como infinito atual divino como Kavod, Glória, que preenche o universo infinito e como causa imanente da série infinita de causa e efeito que constitui a existência eterna dos seres contingentes. Na crítica à terceira proposição maimonidiana, a causa primeira é descrita como causa ontológica e imanente da série infinita de causas e efeitos. Nessa discussão, Crescas aponta para uma ideia de Deus muito diferente daquela elaborada por Maimônides. Temos aqui o debate judaico medieval entre os defensores da transcendência divina e os defensores da imanência. Esse tema é importante para a compreensão da recepção da obra de Hasdai Crescas por Picco Della Mirandolla, Bruno e Espinosa.

Die Welt und ihr Unendliches. László Tengelyi über das Problem phänomenologischer Metaphysik. Transl. from German Elfir Sagetdinov

László Tengelyi has published in his last book "World and Infinity. On the problem of phenomenological metaphysics" a perspective is presented which is characterized by two main traits. On the one hand, he advocates the thesis that phenomenology enables a new type of metaphysics that does not connect with any ontotheology. He thus approaches a diagnosis of time formulated in the field of the more recent French metaphysical history, for example when Courtine speaks of the end of the "end of metaphysics. On the other hand, Tengelyi explicitly assigns his approach to what he calls a "Wuppertal tradition": the tradition founded by Klaus Held, in which phenomenology as such is understood as a phenomenology of the world. However, Tengelyi deviates from a "hero’s principle": while Held prioritizes a phenomenology of the finiteness of the world inspired by Heidegger, Tengelyi is concerned with the rehabilitation of Husserl’s idea of infinity. In Tengelyi’s work, these two main traits combine to form a phenomenology of the world and its infinite, which sees itself as a renewal of metaphysics with originally phenomenological means. Tengelyi finds the sources of her elaboration primarily in Husserl and Heidegger, in addition in the French phenomenology, with Sartre and Levinas, but also with Richir and Marion, and beyond the phenomenological tradition, he relies on Aristotle and Duns Scotus as well as on Kant, Schelling and Rickert.

Do círculo ao quadrado, um estudo sobre a convergência de uma sequência de curvas

Neste trabalho apresentamos aplicações dos conceitos de convergência de sequências numéricas e de funções a um problema geométrico, o qual surgiu a partir de uma análise utilizando-se do GeoGebra. Tal questão envolve o comportamento de uma família de traços de curvas planas, cujo traço da curva inicial é dado por um círculo de raio k e cujo os demais, se aproximam, intuitivamente, de um quadrado de lado medindo 2k. É feita uma prova desta convergência, bem como, uma demonstração de que as áreas subentendidas pelos traços das curvas e os comprimentos de arco destas, convergem respectivamente para a área e comprimento de arco do quadrado limite. Também apresentamos uma breve ambientação histórica dos conceitos de convergência e das ideias de infinito por trás destes conceitos. Com o objetivo de ser desenvolvido ao nível de graduação, tal artigo vai de certa forma, de encontro ao que historicamente foi feito para se determinar características de figuras curvas através de aproximações por figuras retilíneas.

A Cultural overview on the concept of infinity

Abstract: The human being meets the idea of infinity very early, still a child, when he realises that he can go on counting using natural numbers until it is impossible to continue to count. The idea of infinity attracts and rejects, sometimes becomes an object of desire and sometimes of study and systematic research. Infinity is the testimony that intellect, even starting from experience, can overcome limits and boundaries. Our own limited experience on the Earth suggests the existence of something beyond it. Scientists, artists, philosophers, musicians, writers, mathematicians have often assumed towards this concept positions and opinions sensitively different. Infinity would be, by its etymology and nature, what escapes all possible classification and measurement, while mathematics tends to classify and measure every object it examines, and has been able to measure it. Infinity follows us from primary school until university, but often remains a misunderstood concept in the mathematical sense.

The Idea of Infinity in Its Physical and Spiritual Meanings

This article compares the physical meaning of infinity with the spiritual meaning. It notes that infinity remains somewhat of a mystery in a physical world in which our comprehension is largely framed around the concept of boundaries. But our sense of the scope and nature of our understanding of finiteness has been gradually expanding with the development of human civilization, and is now expanding at an even greater rate than ever before, both at the micro level and the macro level. The article suggests that if we are ever to understand infinity, we have to move outside the dimensions of this physical universe as we perceive it, moving to that other and higher reality, to the metaphysical, or, as some would describe it, the spiritual. It has long been thought that the spiritual realm was the realm of the infinite, just as the material world was thought to be the world of the finite. Viewed in this light, there is no difficulty for many in associating the concept of infinity with the greater spiritual realm, that is, that realm that exists beyond the dimensions applicable to humanity in this physical world. But if the spiritual realm is infinite, and if the physical world is merely a sub-set of the higher spiritual realm, then arguably infinity also applies to the various dimensions of the physical world of existence through its ongoing evolution. The search for boundaries within those various dimensions may be merely a reflection of our limited perception as humans. The reality of the physical universe may be one of infinity in time, space etc., even though we may have difficulty comprehending this. Once we move beyond the finite physical perspective, then science and religion can come together, being different aspects of the total infinite reality.

Muzyka jako teofania? Pytania do George’a Steinera

Music occupies a special place in George Steiner’s thinking: “Three areas: the essence and name of God, higher mathematics and music (what is the connection between them?) are located at the limits of language” (Steiner, Errata). The seemingly rhetorical question in parentheses turns out to be a source of deep controversy, the essence of which is revealed in historical-genealogical reflection. Steiner attempts to incorporate Romantic metaphysics within the traditional scholastic symbiosis of Biblical creationism and Pythagoreanism, which reveals his philosophy of music to be entangled in a range of contradictions. On the one hand, a critical reading of Steiner's works uncovers the difficulties posed by the attempt to reconcile pre- and post-Enlightenment culture; on the other hand, the still unused opportunities offered by Romanticism and its modernist continuations are clearly visible. Musical aesthetics, rooted in the idea of infinity, plays a crucial role in these divagations.

Infinity, infinite processes and limit concepts

This article seeks to recover a neglected chapter in the historical and theoretical background of social theory in general and critical theory in particular with a view to refining the understanding of the presuppositions of a cognitively enhanced critical social science appropriate to our troubled times. For this purpose, it offers a brief reconstruction of the mathematical-philosophical tradition from ancient to modern times by extrapolating that part of it that is marked by the ideas of infinity, infinite processes and limit concepts. It gives suggestive indications not only of how these ideas relate to extant social-theoretical thought, but especially also of the two related cognitive directions – the weak-naturalistic and the socio-cultural – in which such thought is currently challenged to go.

Theology and An-Archy: Deep Incarnation Christology following Emmanuel Lévinas and the New Materialism

In this article, I explore deep incarnation Christology. I posit that many of these christological models offered today, while a welcome development in theology, are grounded in metaphysical anthropocentrism. Insofar as such theologies normalize the human and ground theology within a humanist, conceptualist horizon, the idea of divine infinity is circumscribed, and the human becomes divinized and self-positioned as a transcendent species. Likewise, such a framework, identifying God within strict, dogmatic boundaries, posits divinity as the alter ego of the human. To the contrary, I suggest that theology cannot be grounded within human intentionality. Although theology unfolds in representational thought, it is grounded instead in passivity, revealed outside of the subject's time, in an an-archic past and a pure future, wherein divinity is encountered within but ultimately beyond human corporeity in affective encounters with cosmos and Earth. As such, the idea of infinity is grounded in a time and space beyond the beginning of human consciousness. Such a model invites us to consider a God who comes to mind from beyond an impassable chasm, and thus irreducible to the human imagination. Thus, while this article embraces the idea of deep incarnation, it reimagines the doctrine along lines that are different from what is prominent today.

В поисках возвышенного: «Хождение по водам» И. К. Айвазовского (1849) из Государственного художественного собрания Королевского дворца в Сербии.

The indescribable idea of the sublime fascinated and challenged the famous nineteenth century artist Ivan Konstantinovich Aivazovsky, whose dwelling upon this concept gave rise to countless visual responses. In this paper, we examine the earliest known version of his piece known as Walking upon the Sea, dated 1849, from the State Art Collection of the Royal Compound in Serbia. This particular image is a peculiar combination of the stormy sea at night and religious theme that embodies the artist’s inner self- observations, thoughts, worldview, and the perceptive power of the years to come. Aivazovsky was a man of Romanticism and a visionary genius as well. He was occupied with the ideas of infinity, great drama and of the divine that challenges viewers’ senses of space and time. Walking upon the Sea, the art piece of its time, is a manifest reflection of skepticism of the era, groundbreaking experiments, innovations, and discoveries.

Egoism, Labour, and Possession: A reading of “Interiority and Economy,” Section II of Lévinas' Totality of Infinity

Lévinas is the philosopher of the absolutely Other, the thinker of the primacy of the ethical relation, the poet of the face. Against the formalism of Kantian subjectivity, the totality of the Hegelian system, the monism of Husserlian phenomenology and the instrumentalism of Heideggerian ontology, Lévinas develops a phenomenological account of the ethical relation grounded in the idea of infinity, an idea which is concretely produced in the experience with the absolutely other, particularly, in their face. The face of the other, irreducible to any ontological structure of being or any epistemological intentionality of representation, reaches out from on high across the abyss of the isolated ego, commanding respect all the while granting the possibility of murder. This experience overflows the subjective capacity of the separated ego, forcing it “beyond being.” This anarchic relation with the Other is the groundless condition of possibility for ethical life, that is, truly human life. The structure of the ethical relation can then be determined in hindsight as the ground of meaning for what it is to be an I at all.This is a pretty uncontroversial reading of Lévinas' work, especially Totality and Infinity (TI). And yet, there is one small problem. If this is what Lévinas is doing, then why does the largest section of Totality and Infinity – section II, “Interiority and Economy” – have nothing to do with ethics, the other, or the face at all? Why is it devoted to an arduous analysis of what he calls separation, egoism, economy, enjoyment, labour, and possession? In other words, why does Lévinas spend so much energy on writing about the egoist at the heart of his magnum opus, which is supposedly a text devoted to the Other? And furthermore, why is this section one of the least discussed in the secondary literature on Lévinas?These questions motivate the present inquiry, which modestly seeks to understand what Lévinas is up to in this section. Once laying out the basic story, I will focus on the concepts of labour and possession, for I think these are the unrecognized pivots upon which the transition from ego to Other turns. I will also make some slight attempts to interpret Lévinas' direct or indirect comments on Plato, Kant, Hegel, Husserl and Heidegger. For although he distances himself from these giants, he stands on their shoulders as well.

PHENOMENOLOGY OF HAPPINESS AND ETHICS: FROM ARISTOTLE TO DUNS SCOTUS AND E. LÉVINAS / LAIMĖS IR ETIKOS FENOMENOLOGIJA: NUO ARISTOTELIO IKI DUNSO ŠKOTO IR E. LÉVINO

In this paper I focus on the most problematic aspects of Aristotelian notion of happiness and ethics. Aristotelian ethics and the Greek wisdom on the whole strove for being, completeness and totality. Such thinking and its total attempt to achieve being, especialy rational being, that often became ideological violence, nowadays is receiving more and more incredulity and criticism. The schoolman of the 13th century Duns Scotus already stated such notions of happiness and ethics that required otherness with its radical transcendence. Also the phenomenologist of the 20th century Emmanuel Lévinas criticizes the Western view of humanity. The total(itarian) consciousness and any systematization in Lévinas’ alternative thinking are ruptured by the ideas of infinity and the other that enable to think otherwise, and outside of being. Santrauka Šiame straipsnyje, atsispiriant nuo Aristotelio laimės sąvokos, siekiama kritiškai apmąstyti klasikinę graikiškąją etikos sampratą. Aristotelio etika, o ir graikiškojoje ontologijoje įsišaknijusi (iš)mintis visada siekė apimti, išbaigti ir imanentiškai suvokti būties visumą. Toks vyraujančia tradicija tapęs mąstymas, pagrįstas conatus essendi ir dažnai neišvengiantis tapti ideologine prievarta, šiandien sulaukia vis daugiau nepasitikėjimo ir kritikos. Ir ne tik šiandien. Jau XIII a. scholastas Dunsas Škotas mąstė apie minėtos laimės ir etikos sampratos alternatyvą, kuri reikalauja kitybės idėjos, nurodančios į tai, kas absoliučiai transcenduoja mąstantįjį subjektą. Taip pat ir XX a. fenomenologas Emmanuelis Lévinas savo kritiką nukreipia į vakarietiškąją ontocentrinę pasaulėvoką ir iš jos išplaukiančią žmogiškumo sampratą. Totalią, sisteminančią ir neišvengiamai totalitarinę sąmonę Lévino alternatyviojoje fenomenologijoje „praplėšia“ begalybės ir kitybės idėjos, padedančios mąstyti kitaip ir anapus buvimo.

A Flawed Argument Against Actual Infinity in Physics

In “Nonconservation of Energy and loss of Determinism II. Colliding with an Open Set” (2010) Atkinson and Johnson argue in favour of the idea that an actual infinity should be excluded from physics, at least in the sense that physical systems involving an actual infinity of component elements should not be admitted. In this paper I show that the argument Atkinson and Johnson use is erroneous and that an analysis of the situation considered by them is possible without requiring any type of rejection of the idea of infinity.

Charms of evident identity

In this article I seek to rethink the traditional notion of identity. In the tradition of Western thought identity was viewed first and foremost from an ontological point of view. After the turn toward the subject, the I is thought of as the centre, the base and the producer of any identity. Phenomenological analysis deepens the origin of identity to the relation of the I to the world, i.e. to the alterity. Yet the alterity, by becoming the content of consciousness, is not an absolute alterity. The way, in which identity assimilates, possesses the world and annihilates alterity, is representation. Representation seeks evidence. Representation as intentional perceptivity localizes every object in the light of consciousness. Light and vision are paradigmatic metaphors of the traditional Western thought. Hence in this article I seek to show why and how light and evidence do not tolerate absolute alterity. Identity can be sobered from the charms of evidence only by responsible relation to the Other, i.e. by ethics. Here identical subject loses the right of priority in front of the imperative of the other person. Idea of infinity worries total identity from within. Infinity does not permit identity to quiet down and induces to heed transcendence and alterity. Only in this way alterity can escape the violence to become a content of egocentrical identity and the victim of manipulation. Responsibility in the face of the other person precedes evident perception and legitimates the latter.

At the brink of infinity: poetic humility in boundless American space

From popular culture to politics to classic novels, quintessentially American texts take their inspiration from the idea of infinity. In the extraordinary literary century inaugurated by Ralph Waldo Emerson, the lyric too seemed to encounter possibilities as limitless as the U.S. imagination. This raises the question: What happens when boundlessness is more than just a figure of speech? Exploring new horizons is one thing, but actually looking at the horizon itself is something altogether different. In this carefully crafted analysis, James von der Heydt shines a new light on the lyric craft of Emily Dickinson, Robert Frost, Elizabeth Bishop, and James Merrill and considers how their seascape-vision redefines poetry's purpose.Emerson famously freed U.S. literature from its past and opened it up to vastness; in the following century, a succession of brilliant, rigorous poets took the philosophical challenges of such freedom all too seriously. Facing the unmarked horizon, Emersonian poets capture - and are captured by - a stark, astringent version of human beauty. Their uncompromising visions of limitlessness reclaim infinity's proper legacy - and give American poetry its edge. Von der Heydt's book recovers the mystery of their world.

Descartes: God as the Idea of Infinity

Abstract: This article returns to Descartes' texts and correspondence and looks to recent scholarship to reveal three key elements of Descartes' distinctive epistemological structure. It shows that because objectors ignore Descartes' opposition to the ‘order of being’ they are led to a binary and incorrect reading of his argument. However, by correctly following Descartes' own logic, the method of doubt can be used to prove the existence of an infinite God.

The Meaning of Infinity in Sufi and Deconstructive Hermeneutics: When Is an Empty Text an Infinite One?

In this article I examine the role of infinity in the hermeneutics of two very separate thinkers—a thirteenth-century Sufi and a contemporary French poststructuralist. In both cases, the way a certain idea of infinity (be it the inexhaustible mind of an infinite God or the infinite array of different contexts for a text) leads to an infinitizing of the text itself is the subject. Ultimately, the article suggests that deconstruction actually restores a medieval sense of infinity to the text—albeit in a very different way from its mystical predecessors—by emphasizing the endless range of contexts a text can be read in. We may conclude this history of hermeneutics with the following remark. The initial purpose of hermeneutics was to explain the word of God. This purpose was eventually expanded into an attempt to regulate the process of explaining the word of man. In the nineteenth century we learned, first from Hegel and then more effectively from Nietzsche, that God is dead. In the twentieth century, Kojève and his students, like Foucault, have informed us that man is dead, thereby as it were opening the gates into an abyss of postanthropological deconstruction. As the scope of hermeneutics has expanded, then, the two original sources of meaning, God and man, have vanished, taking with them the cosmos or world and leaving us with nothing but our own garrulity, which we choose to call the philosophy of language, linguistic philosophy, or one of their synonyms. If nothing is real, the real is nothing; there is no difference between the written lines of a text and the blank spaces between them. —Stanley Rosen, Hermeneutics as Politics