Mathematical, Philosophical and Semantic Considerations on Infinity (I): General Concepts

Usó-Doménech, J. L.; Nescolarde-Selva, Josué Antonio; Requena, Mónica Belmonte

doi:10.1007/s10699-015-9428-9

Cited by 6 publications

(4 citation statements)

References 9 publications

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“…These two forms of infinity essentially cover all possible instances of infinity that one could intuitively understand or conceive. There seems to be, intuitively, no infinity that metaphysical conceivable and fits intuition can not be categorized into one of these two typical forms or both [3,4]. But why does our intuition only possess these two ways to construct or categorized infinity?…”

Section: Metaphysical Infinitymentioning

confidence: 96%

The Set Theory and the Description of Infinity: the Nature of Infinity Perceived from Metaphysics and Ontology

Wu¹

2023

EHSS

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Infinity is possibly one of the most complicated conceptions confronting mathematics and philosophy. People could always conceive it via intuition, but find it hard to describe in the logical realm. In the 19th century, German mathematician Cantor proposed the set theory, for the first time, people could use mathematical tools to explain the nature of infinity. However, such an explanation still lies on the axiomatic foundation, which does not directly fit our intuition about infinity. Therefore, this study will attempt to establish a 'bridge' between the infinity that fits intuition and the infinity that is described by set theory, hence arguing why the set theory could describe infinity universally in the senses of metaphysics and ontology.

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Section: Metaphysical Infinitymentioning

confidence: 96%

The Set Theory and the Description of Infinity: the Nature of Infinity Perceived from Metaphysics and Ontology

Wu¹

2023

EHSS

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“…Generally speaking, the cardinality of the power set of a set A, such that CardA = n, is 2 n (i.e., CardA = n → CardP (A) = 2 n ). Cantor was interested in the generalization of this result to transfinite numbers [6][7][8]. If a cardinality that can be assigned to the set of natural numbers, that is, CardN = ℵ 0 , then immediately a power set of the set of all natural numbers can be defined, with cardinality equivalent to CardP (N) = 2 ℵ 0 = ℵ 1 .…”

Section: Definitionmentioning

confidence: 99%

Cantor Paradoxes, Possible Worlds and Set Theory

et al. 2019

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In this paper, we illustrate the paradox concerning maximally consistent sets of propositions, which is contrary to set theory. It has been shown that Cantor paradoxes do not offer particular advantages for any modal theories. The paradox is therefore not a specific difficulty for modal concepts, and it also neither grants advantages nor disadvantages for any modal theory. The underlying problem is quite general, and affects anyone who intends to use the notion of “world” in its ontology.

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“…Philosophers have identified it with Reality and Truth. Mystics have called it God, YHVE, Brahman and Tao (Graham and Kantor, 2009;Restivo, 1983;Sabán, 2018;Us o-Doménech et al, 2015a, 2016a, 2018a). On the one hand, the Infinite inspires a sense of a potential for limitless expansion beyond any finite boundary.…”

Section: The Infinite In Cusanus' Thoughtmentioning

confidence: 99%

Dialectical logic for mythical and mystical superstructural systems (ii)

Doménech

Nescolarde-Selva

Gash

et al. 2019

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Purpose The distinction between essence and existence cannot be a distinction in God: in the actual infinite, essence and existence coincide and are one. In it, maximum and minimum coincide. Coincidentia oppositorum is a Latin phrase meaning coincidence of opposites. It is a neo-Platonic term, attributed to the fifteenth-century German scholar Nicholas of Cusa in his essay, Docta Ignorantia. God (coincidentia oppositorum) is the synthesis of opposites in a unique and absolutely infinite being. God transcends all distinctions and oppositions that are found in creatures. The purpose of this paper is to study Cusanus’s thought in respect to infinity (actual and potential), Spinoza’s relationship with Cusanus, and present a mathematical theory of coincidentia oppositorum based on complex numbers. Design/methodology/approach Mathematical development of a dialectical logic is carried out with truth values in a complex field. Findings The conclusion is the same as has been made by thinkers and mystics throughout time: the inability to know and understand the idea of God. Originality/value The history of the Infinite thus reveals in both mathematics and philosophy a development of increasingly subtle thought in the form of a dialectical dance around the ineffable and incomprehensible Infinite. First, the authors step toward it, reaching with their intuition beyond the limits of rationality and thought into the realm of the paradoxical. Then, they step back, struggling to express their insight within the limited scope of reason. But the Absolute Infinite remains, at the border of comprehensibility, inviting them with its paradoxes, to once again step forward and transcend the apparent division between finite and Infinite.

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Mathematical, Philosophical and Semantic Considerations on Infinity (I): General Concepts

Cited by 6 publications

References 9 publications

The Set Theory and the Description of Infinity: the Nature of Infinity Perceived from Metaphysics and Ontology

The Set Theory and the Description of Infinity: the Nature of Infinity Perceived from Metaphysics and Ontology

Cantor Paradoxes, Possible Worlds and Set Theory

Dialectical logic for mythical and mystical superstructural systems (ii)

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