Infinity Exists Research Papers - Academia.edu (original) (raw)

2025

Le désir ne se laisse pas réduire à un simple manque comblable, contrairement au besoin. Il s’éprouve comme un mouvement infini, creusé par sa propre insatisfaction, et trouve un écho dans l’expérience esthétique. À travers les analyses... more

2025

# Mathematical Formalization of the Unified Framework ## 1. Core Operators and Functions ### The Sign Field Tensor (SFT) \text{SFT}(Q) = \sum_{i \in \{r,i,j,k\}} (\pm 1)_i \cdot Q_i$$ Where: - QQQ is a quaternion... more

2025

This work explores the foundational conditions from which dimensions, consciousness, and realities may emerge. It offers a modular framework for rethinking existence-not as a fixed order, but as an unfolding architecture of possibility.

2025

Prima di indagare gli scritti matematici, è opportuno tener conto di alcune coordinate di fondo della filosofia della matematica elaborata da Cusano nei suoi scritti. Nel primo capitolo del De docta ignorantia, Cusano, analizzando il modo in cui pro cede la conoscenza razionale 1 , afferma che ogni ricerca consiste nell'istituire un confronto tra due cose, di cui una è nota e l'altra è ciò che si intende conoscere. Mediante tale com paratio si giunge a individuare un rapporto (proportio), che permette di conoscere ciò che è ignoto 2 . Avendo carattere comparativo, la nostra conoscenza si basa fondamentale sulla misurazione, la quale non può realizzarsi senza il numero, che, afferma Cusano, costitui sce la condizione necessaria di ogni comparazione 3 e, in quanto tale, è il principio formale di ogni atto conoscitivo della ragione 4 . Da ciò Cusano trae due conseguenze fondamentali. La prima è che l'infinito è per l'uomo inconoscibile, in quanto si sottrae a ogni propor tio e a ogni comparatio 5 : «finiti ad infinitum nulla est proportio». 6 La seconda è che la «precisa veritas est incomprehensibilis» 7 , ossia che è impossibile conoscere perfettamente (adaequate) le cose, il che conferisce alla nostra conoscenza un carattere strutturalmente congetturale 8 . Misurando, inoltre, l'uomo diventa consapevole dei limiti della propria conoscen za e, facendo esperienza dell'impossibilità di raggiungere la conoscenza dell'ab-solutum, acquisisce la saggezza della consapevolezza della propria ignoranza, la docta ignorantia 9 . E, poiché il processo attraverso il quale comprendiamo è lo stesso che blocca l'accesso all'infinito e ci separa abissalmente da esso, alla mente non resta che vedere l'infinito prospettivamente, nella miriade di modi in cui si manifesta nel mondo finito, ossia nella 1

2025

Humanity Accepts the Idea of Infinity but Struggles to Conceive of a World Without a Beginning
It is commonly asserted that an atheist is someone who has rejected belief in the existence of a divine entity. The prefix “a-” denotes negation or removal—thus, an atheist is one who has severed their personal connection to theos (god). It is therefore evident that one can only reject what is perceived as existing. The atheist does not subscribe to the notion that God created the world, but rather maintains that it is humanity that created the concept of God.
It would be futile to deny that, throughout history, humankind has needed a deity—once out of fear of death and the unknown, today due to the anxiety provoked by chaos, the absence of reassuring natural laws, and the desire for a metaphysical register that is at once mystical, miraculous, and rational. Even the rational scholar, guided by empirical principles, is troubled by the question of the universe’s origins: they may accept the notion of infinity, yet struggle to conceive of a reality with no beginning. Could this difficulty be the very source of the Big Bang theory?
In antiquity, the term “religion” did not exist in its modern sense. Worship was not a private act but primarily a political practice aimed at forging a collective identity around a shared pantheon. In the Greco-Roman world, cultic practice was predominantly public and civic, serving to unify the subjects of the empire around a common symbolic system that ensured imperial stability. Cultic revolution, then, preceded agriculture, writing, and perhaps even the domestication of fire. Was it also linked to belief in a deity? All evidence suggests so.

2025

I. Il concetto polivalente di potenza alle origini della metafisica occidentale 1. «Analogia di potenza» Tesi centrale di ogni teologia politica è che il problema teologico della poten-za divina si costruisca in modo da valere come schema di interpretazione del fenomeno "secolare" della potenza umana: che la potenza di dio agisca da crite-rio ermeneutico in relazione al "quantitativo di potenza" espresso dal singolo in-dividuo (o soggetto collettivo) nel mondo umano. Si potrebbe parlare propriamente, in questo caso, di una analogia di po-tenza tra l'uomo e dio, e il criterio analogico potrebbe funzionare anche in senso inverso: dall'uomo a dio, per cui le stesse regole-le stesse leggi di movimento della potenza umana-dovrebbero valere (stante l'unità ontologica dell'Essere, e fatta salva la proporzione finito/infinito) per l'onnipotenza divina, ricostruita dal sapere teologico. Secondo gli schemi della teologia politica ebraico-cristiana il ra...

2025, OpenELAB

It's fascinating to delve into the history of Arduino, as it represents a significant democratization of electronics and programming. Here's a structured approach to writing a paper on the history of Arduino, incorporating key points:

2025

N icholas of Cusa (1401-64) was a philosopher and theologian whose writings influenced the development of Renaissance mathematics and science. The first part of this article traces the historical development in the West of thought about the Infinite prior to the time of Nicholas of Cusa. The second part of the article discusses his philosophy as presented in his major work, On Learned Ignorance. The third part of the article then examines the subsequent development of thought about the Infinite and the ways in which Nicholas of Cusa influenced mathematics and science.

2025

A study published in PLOS ONE found that papers uploaded to Academia receive a 69% boost in citations over 5 years. Vediamo se questa è la volta buona, che la mia teoria sull'nfinito venga approvata. In ogni modo è scritta nel Web dove... more

A study published in PLOS ONE found that papers uploaded to Academia receive a 69% boost in citations over 5 years.
Vediamo se questa è la volta buona, che la mia teoria sull'nfinito venga approvata. In ogni modo è scritta nel Web dove rimarrà per secula seculorum. Amen...

2025, International Journal of Philosophical Studies

This essay is concerned with a passage from §24 of Hegel’s Encyclopaedia, in which Hegel characterises the concepts or ‘thoughts’ developed in the discipline of metaphysics by saying that they ‘used to count as expressing the essentialities of things’. I begin by drawing attention to Hegel’s use of the past tense in this passage and suggest that it looks problematic for conceptual realist interpreters of Hegel’s idealism, who want, roughly, to attribute to him the view that thoughts or ‘thought-determinations’ express the essentialities of things. I then develop this challenge with help from Robert Pippin, who takes Hegel, in this passage, to be rejecting the metaphysical projects of pre-Kantian European rationalism. If Pippin is right, then in this passage Hegel is in fact distancing himself from the view that conceptual realist accounts attribute to him. In the final part of the article, I re-examine some of Hegel’s remarks concerning the history of European metaphysics and offer an alternative, better explanation of Hegel’s use of the past tense in the passage in question, one which neutralises the objection to conceptual realist accounts of Hegel’s idealism.

2024, In book: Divined Explanations. The Theological and Philosophical Context for the Development of the Sciences (1600-2000)

Until the first half of the nineteenth century, mathematicians considered only the potential infinite, maintaining the tradition of the refusal of the actual infinite. Bolzano’s concept of infinite allows the treatment of paradoxical situations. His proof for the existence of an infinite set, based on mathematical induction, is well known. Less known are his arguments about the actual existence of infinite entities presented in his work Paradoxes of the Infinite. According to Bolzano, God is infinite in knowledge, volition, and action ad extra. Our purpose is to discuss his brief explanation by expanding it to understand its theological presuppositions.

2024

Comparison between the Mathematics of God and Mathematica Ad Infinitum within the field of Transreal Mathematics. Seguo il confronto fra la matematica di Dio di Massimo Melli e la mia Mathematica Ad Infinitum (MAI)
Vito Ceravolo rivela di essere un matematico classico, che considera i tachioni e i logoni: Anatemi fisici. Nonostante la bocciatura, la mia matematica però sopravvive nel mondo iperuraneo delle idee, dove tutto si muove a velocità infinita, perchè il Tempo è zero.

2024, Ontology of Divinity, ed. M. Szatkowski, De Gruyter, Berlin

This historical essay compares the views of Nicholas of Cusa ('Cusanus') and Georg Cantor on the topics of infinity, divinity, and mathematical knowledge. Echoing Nicholas and neo-Platonism, Cantor says in his Grundlagen (1883) that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, which can only be acknowledged but never known. Moreover, Cantor envisions his transfinite set theory as providing the analytical methods and techniques necessary for a complete philosophy of nature. Cantor's novel mathematics is presented as part of a long tradition, to which Cusanus, Bruno, Spinoza, Leibniz and others belong, in which the infinite character of organic life forms is appreciated and is taken to be in some sense a mirror and symbol of the divine. The doctrine of symbolism present in both Cusanus and Cantor enables these thinkers to articulate a transcendental apophatic approach to divinity.

2024, Academia Dot EDU

The Laws of Form (LoF), as introduced by George Spencer-Brown, provides a conceptual framework rooted in the notion of distinction. By focusing on the act of distinction and its recursive application, LoF offers a novel way to approach transfinite set theory. This article explores how LoF recasts the traditional framework of transfinite mathematics into a simpler and more intuitive system, emphasizing the role of boundaries, distinctions, and recursion. We demonstrate that the hierarchy of infinities can be reinterpreted in terms of discrete distinctions, and the continuum can be redefined as a web of nested boundaries. This reinterpretation bridges the conceptual gap between discrete and continuous systems and provides fresh insights into cardinality, ordinal numbers, and the nature of irrationality.

2024, Aracne

via Raffaele Garofalo, 133/A-B 00173 Roma (06) 93781065 isbn 978-88-548-3021-9 I diritti di traduzione, di memorizzazione elettronica, di riproduzione e di adattamento anche parziale, con qualsiasi mezzo, sono riservati per tutti i Paesi. Non sono assolutamente consentite le fotocopie senza il permesso scritto dell'Editore. I edizione: gennaio 2010 Indice Introduzione Esposizione dell'argomento La dialettica Forma e materia logica in Aristotele

2024, ISSN 2282-5711

We address Zeno's paradoxes on motion, in the search for the coherence of becoming, defining step by step a becoming-theory.

2024, Boston College Center for Christian and Jewish Learning

This is the "Welcome Presentation" I offered as 2024-2025 Boston College Corcoran Visiting Chair in Christian-Jewish Relations. The purpose is to introduce my research project for the year: Reasoning for Repair: Studies of Reparative Reasoning in Jewish and Catholic Traditions. I examine efforts by Jewish and Christian theologians to address moments of crisis in human reasoning: when, for example, thinkers contradict themselves when trying to measure the infinite or comprehend God within the limits of finite reasoning. He will examine Scripture- and tradition-based reasoning as resources for repairing such crises, utilizing insights from quantum science and transcendental reasoning.

2024, Academia.edu

This paper shows how an infinite series yields both an infinite solution and a finite solution and how to determine which one is correct and which one is just plain crazy!

2024, Medioevo. Rivista di storia della filosofia medievale

This article examines the possible origin of a mangled Greek sentence – anthropos necten, with the meaning of ‘the man comes/walks’ – that is to be found in Dominicus Gundissalinus’ Latin translation of the Arabic-speaking theologian Abū... more

2024, The Ontology of Divinity, edited by M.Szatkowski, Berlin

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. Moreover, Cantor envisioned his transfinite set theory (Mengenlehre) as providing the analytical methods and techniques necessary for a comprehensive, organic, nonreductive description of nature, a Naturphilosophie. Thus Cantor's novel mathematics is presented as part of a long tradition, to which Cusanus, Bruno, Spinoza, Leibniz and others belong, in which the infinity and infinite character of organic life forms is appreciated, and is in some sense a mirror or symbol of the divine. The doctrine of symbolism and the different commitments to the laws of logic present in both the work of Cusanus and Cantor enables these thinkers to articulate a transcendental apophatic approach to divinity.

2024, The Ontology of Divinity, edited by M. Szatkowski

2024, Pi Repeats

Irrational numbers are infinite and chaotic; never repeating. However, their lack of repetition is an incorrect assumption and can be logically deduced by two methods. The first, is an explanation of why Pi (as well as other irrational numbers) ultimately repeat, and the second, a more precise method of how. I wish to stress, this assertion is not just for Pi, but for all irrational numbers.

2024

Purtroppo a pagina 147 Berlinski rivela di essere un conservatore della scuola matematica francese di Cauchy, che essendo una scuola conservatrice, è eretica verso l'eresia della divisione per zero, che per me è invece l'ortodossia.

2024

La retta, come il punto, fa parte di quelle entità geometriche impossibili da spiegare con definizioni specifiche, perché, è costituita da elementi immateriali senza dimensione, i Logoni, che sono gli atomi della Mente di Dio, cioè gli atomi del Pensiero. E come Dio non si riesce a spiegare, se non con analogie e perifrasi basate sulla fede, così la retta è inspiegabile, tranne che con analogie basate sulla logica matematica.
Una semplice linea retta, che tende all’infinito in due direzioni, secondo Berlinski è un oggetto antico dell’esperienza umana, la prima delle grandi astrazioni della vita sensitiva.

2024, International Journal for Philosophy of Religion

Cantor argued that absolute infinity is beyond mathematical comprehension. His arguments imply that the domain of mathematics cannot be grasped by mathematical means. We argue that this inability constitutes a foundational problem. For Cantor, however, the domain of mathematics does not belong to mathematics, but to theology. We thus discuss the theological significance of Cantor's treatment of absolute infinity and show that it can be interpreted in terms of negative theology. Proceeding from this interpretation, we refer to the recent debate on absolute generality and argue that the method of diagonalization constitutes a modern version of the via negativa. On our reading, negative theology can evoke an attitude of humility with respect to the boundedness of the human condition. Along these lines, we think that the foundational problem of mathematics concerning its domain can be addressed through a methodological attitude of humility.

2024

The proof for God's existence provided by John Duns Scotus is presented and analysed. The main source is the treatise De primo principio. Connections of the Scotus's proof to those of Anselm of Canterbury and Thomas Aquinas are carefully examined. The important role of the theory of modality and logical modal rules in the proof is emphasized. The logical structure and suppositions of the proof in question are discussed in detail.

2024, Philosophia Christi

'exist in reality', 'have extra-mental existence', 'be instantiated in the real world'. We are contending, then, that an actual infinite cannot exist in the real world ... What I shall argue is that while the actual infinite may be a fruitful and consistent concept in the mathematical realm, it cannot be translated from the mathematical world into the real world, for this would involve counter-intuitive absurdities. 4 364 PHILOSOPHIA CHRISTI

2024

Il segno di infinito ha una duplice risonanza. Combina l'attrattiva mistica dell'ignoto e dell'inconoscibile in tutta la sua vastità con la fredda precisione della matematica e con il desiderio di descrivere l'inimmaginabile. Il nastro a forma di otto sdraiato sul fianco è un simbolo le cui origini si perdono nella notte dei tempi, un'ombra dell'antico uroboro, il serpente che si morde la coda.

2024, Mediaevalia. Textos e Estudos

Una finzione feconda per la filosofia della natura: Francisco Suarez e l'annihilatio mundi (A fruitful fiction for the philosophy of nature: Francisco Suarez and the 'annihilatio mundi' )
Abstract This contribution focus on the fiction of the suppression of bodies by God (annihilatio mundi) and its implications for the philosophy of nature, namely within the development of the concepts of place and space. Recalling how some medieval thinkers formulate such an hypothesis, this study proposes a first analysis of its treatment by Francisco Suarez (in particular in the treatise De angelis). Indeed, in the wake of scholastic reflexions arisen in the XIIIth and XIVth centuries, Francisco Suarez made an abundant use of the fiction of the annihilatio mundi to support his thesis of the independence of spatial relationships with regard to the presence or absence of bodies, thus making the idea of emptiness (vacuum) philosophically plausible. This hypothetical treatment of the annihilatio mundi ultimately leads to a significant theoretical move beyond the Aristotelian conception of place.

2024

Nel capitolo Teologi e Filosofi ci sono dozzine di interpretazioni del concetto di Dio e del suo equivalente matematico, l'Infinito. Tutti i teologi e tutti i filosofi però, non hanno il coraggio di dire la verità su come stanno le cose e si limitano a "leccare il culo a Dio", per paura della Sua giusta punizione. L'unico che ha il coraggio di dire la verità è Jean-Paul Sartre, il quale dice: " L'assenza di Dio non è una chiusura: è l'apertura dell'infinito. L'assenza di Dio è più grande e più divina di Dio.

2024

WE ARE THE GODS OF CREATION, NOT ONLY IN THIS UNIVERSE, BUT IN ALL OF THE REST OF THE MULTIVERSE – THUS, WE DO EXIST IN EVERY REALM OF CREATION.

2024

The article discusses the mutual influence of science, religion and metaphysics in the history of the creation of Georg Cantor's set theory

2024

PRAXIS scuola di filosofia. X edizione: «Che cosa significa pensare? Mente Macchina Natura». 20-21-22 luglio 2023

2024

I diritti di traduzione, di memorizzazione elettronica, di riproduzione e di adat tamento totale o parziale, con qualsiasi mezzo (compresi i microfilm), sono ri servati per tutti i Paesi. Fotocopie per uso personale del lettore possono essere effettuate nei limiti del 15% di ciascun volume dietro pagamento alla SIAE del compenso previsto dall'art.

2024

Primo di una serie di tre articoli – in pubblicazione sulla rivista ufficiale della Provincia Picena San Giacomo della Marca dei Frati Minori – dedicati ad illustrare, in modo sintetico e con carattere divulgativo, la vita, le opere e i capisaldi del pensiero del filosofo francescano Ruggero Bacone.
Questo primo contributo, in particolare, dopo una presentazione generale del personaggio, intende ripercorrere le principali tappe della sua vita e fornire una panoramica delle sue opere maggiori.
In: “La Marca francescana”, anno VIII, n. 5, settembre/ottobre 2023, pp. 24-27.

2023

This paper will offer a defence of the Kalam cosmological argument for the existence of God, originally proposed by al-Ghazâlî (c.1056-1111), and reiterated and defended in our own time by W.L. Craig, together with a robust defence of its necessary concomitant, causal finitism, arguing that time and space must be finite. It will also argue that attempts to combine the Kalam argument with the teleological one, whether in its 'fine-tuning' or design forms, fail. It will conclude that creation was not ex nihilo, but from the infinite substance of God.

2023, «Saepe mihi cogitanti…». Studi di filosofia tardo-antica, medievale e umanistica offerti a Giulio d’Onofrio, a cura di A. Bisogno, L. Catalani, A. Cavallini, R. de Filippis, Roma: Città Nuova (Institutiones)

The essay analyses section 4 of Augustine's letter 14, in which the author answers a question from his friend Nebridius about the existence of divine ideas of individuals.

2023, DOAJ (DOAJ: Directory of Open Access Journals)

dal 2005. Le sue ricerche hanno il loro perno nelle idee elaborate nel Medioevo (particolarmente nei secoli XIII e XIV) sulla natura e i requisiti del sapere scientifico.

2023, Cybernetics and Systems

I heap up monstrous numbers, Pile millions upon millions, I put aeon upon aeon and world upon world, And when from that awful height Reeling, again I seek thee, All the might of number increased a thousand fold Is still not a fragment of... more

2023

In a well-known Berlin aphorism, Hegel notes that a great man condemns people to explicate him (see GW 22, 476). However, before we can explicate we must understand.

2023, Vivens Homo

This article intends to show how the distinction between the category of aevum and angelic time in Thomas Aquinas's system reveals the theorisation of a difference between a real order and a gno-seological/logical order in the consideration of being. This difference highlights the Angelic Doc-tor's ontology as profoundly metaphysical and precisely for this reason dynamic and relational. Aquinas' doctrine proves to be an indispensable resource to draw on for a contemporary reflection on time in the dialogue between humanistic knowledge and scientific research.

2023, Understanding the infinite nature of fractals in an ethical future

Science without Art is unethical, and Art without science is illogical. Fractals In the beauty of fractals, we can see the equal and opposite moving balance of the two. It's been quite a long time since I explored the beauty and magic of fractals. My first encounter was Arthur C Clarke's "Colours of Infinity" video which showed the extraordinary properties of fractals. Fractals are shapes of unlimited life growth. They are inter-dimensional, undetermined, infinite-form patterns, mathematically, based on partial fractionshence their name. Although I did not know it then, colours of infinity referred to the dark light energy released from the photon once it had split and, more importantly, how this repulsive force goes to infinity. At the beginning of the 21st century splitting the photon was only a theory. However, two quantum engineers, Moody and Maylor, have successfully broken the photon, bringing their experiments to fruition. Their results show black light fractal patterning. Dark matter pulls galaxies together, while dark energy pushes them apart. Astronomers measure the universe's expansion using the explosions of white dwarfs, called type Ia supernovas, which led to the discovery of dark energy in 1998.

2023

Secondo l'amico Corrado, la Poesia è un infinito immenso che oltre a contenere la Logica del pensiero Matematico, contiene tutto l'inatteso mondo della fisica quantistica, che ci sorprende sempre con la sua illogica profondità. Quindi la... more

2023, Milano University Press

2023

Hilbert's Grand Hotel shows that a fully occupied hotel with infinitely many rooms can accommodate additional guests. But our analyze finds that this is not true.

2023

La supposizione che l'origine della cultura europea nasconda nel suo ven-tre convulso una verità non ancora scoperta dalla critica tradizionale, ma che si ripresenta costantemente ai nostri occhi in qualità di arcano inviolabile, è stata probabilmente il pungolo che ha spinto Giovanni Semerano 1 a credere nell'effettiva possibilità che ci possa essere qualcos'altro da cui partire alla ri-cerca delle radici più nascoste della nostra cultura. E così, controcorrente, questi si incammina nel cháos concettuale dell'inizio dell'Occidente dove rin-traccia nell'antico accadico 2 il comune denominatore delle nostre origini lingui-stiche, tesi questa che ribalta le teorie dell'ortodossia filologica e filosofica. L'opera di Semerano, si badi bene, non è quella di un eccentrico linguista solitario, la sua non è mera congettura; è un'analisi costante, uno scavo meti-coloso alla ricerca del senso originario delle parole. Da buon archeologo dei suoni e dei simbo...

2023

In the beginning God created the heavens and the earth. (Genesis 1:1) I beseech thee, my son, look upon heaven and earth, and all that is in them: and consider that God made them out of nothing, and mankind also. (2 Maccabees 7:28) He was in the beginning with God; all things were made through him, and without him was not anything made that was made. (John 1:2-3) By faith we understand that the world was created by the word of God, so that what is seen was made out of things which do not appear.