scholarly journals Metaphysics and mathematics: Perspectives on reality

2017 ◽  
Vol 73 (3) ◽  
Author(s):  
Gideon J. Kühn
Keyword(s):  
Mathematical Proof ◽  
Number System ◽  
Natural Numbers ◽  
Theoretical Computer ◽  
Root Cause ◽  
Computer Scientists ◽  
Depth Study ◽  
And Mathematics ◽  
The 19Th Century ◽  
The Universe

The essence of number was regarded by the ancient Greeks as the root cause of the existence of the universe, but it was only towards the end of the 19th century that mathematicians initiated an in-depth study of the nature of numbers. The resulting unavoidable actuality of infinities in the number system led mathematicians to rigorously investigate the foundations of mathematics. The formalist approach to establish mathematical proof was found to be inconclusive: Gödel showed that there existed true propositions that could not be proved to be true within the natural number universe. This result weighed heavily on proposals in the mid-20th century for digital models of the universe, inspired by the emergence of the programmable digital computer, giving rise to the branch of philosophy recognised as digital philosophy. In this article, the models of the universe presented by physicists, mathematicians and theoretical computer scientists are reviewed and their relation to the natural numbers is investigated. A quantum theory view that at the deepest level time and space may be discrete suggests a profound relation between natural numbers and reality of the cosmos. The conclusion is that our perception of reality may ultimately be traced to the ontology and epistemology of the natural numbers.

scholarly journals The notion of Natural Numbers among Germanic Mathematicians during the Second Half of the 18th Century

2020 ◽  
Vol 19 (37) ◽  
pp. 01-23
Author(s):  
Elías Fuentes Guillén
Keyword(s):  
19Th Century ◽  
18Th Century ◽  
Number System ◽  
Natural Numbers ◽  
The 19Th Century ◽  
Positive Integers

While the idea of the naturalness of the positive integers is ancient, the idea of the naturals as the foundation of our number system is not. This latter idea, along with other factors, eventually led to the abstract definitions of natural numbers at the end of the 19th century. But, what led to such an idea that was already present among Germanic mathematicians in the first third of the 19th century? This article examines the tensions around the notion of number among the Germanic mathematicians of the second half of the 18th century with the aim of contributing to a better understanding of some of the factors that explain theemergence of such a different approach to naturals.

scholarly journals A New Set Theory for Analysis

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 31
Author(s):  
Juan Ramírez
Keyword(s):  
Real Number ◽  
Number System ◽  
Order Structure ◽  
Natural Numbers ◽  
Real Numbers ◽  
The Real ◽  
Power Set ◽  
Universe Of Sets ◽  
The Universe ◽  
Real Number System

We provide a canonical construction of the natural numbers in the universe of sets. Then, the power set of the natural numbers is given the structure of the real number system. For this, we prove the co-finite topology, C o f ( N ) , is isomorphic to the natural numbers. Then, we prove the power set of integers, 2 Z , contains a subset isomorphic to the non-negative real numbers, with all its defining structures of operations and order. We use these results to give the power set, 2 N , the structure of the real number system. We give simple rules for calculating addition, multiplication, subtraction, division, powers and rational powers of real numbers, and logarithms. Supremum and infimum functions are explicitly constructed, also. Section 6 contains the main results. We propose a new axiomatic basis for analysis, which represents real numbers as sets of natural numbers. We answer Benacerraf’s identification problem by giving a canonical representation of natural numbers, and then real numbers, in the universe of sets. In the last section, we provide a series of graphic representations and physical models of the real number system. We conclude that the system of real numbers is completely defined by the order structure of natural numbers and the operations in the universe of sets.

"Marketocentric" Economics Is Obsolete

2004 ◽  
pp. 36-49 ◽  
Author(s):  
A. Buzgalin ◽  
A. Kolganov
Keyword(s):  
Economic Theory ◽  
Middle Ages ◽  
Modern Science ◽  
Economic Systems ◽  
Main Mode ◽  
Post Market ◽  
Market Relations ◽  
Post Industrial ◽  
The 19Th Century ◽  
The Universe

The "marketocentric" economic theory is now dominating in modern science (similar to Ptolemeus geocentric model of the Universe in the Middle Ages). But market economy is only one of different types of economic systems which became the main mode of resources allocation and motivation only in the end of the 19th century. Authors point to the necessity of the analysis of both pre-market and post-market relations. Transition towards the post-industrial neoeconomy requires "Copernical revolution" in economic theory, rejection of marketocentric orientation, which has become now not only less fruitful, but also dogmatically dangerous, leading to the conservation and reproduction of "market fundamentalism".

scholarly journals The Theme of Death and Eternity in Emily Dickenson’s Poetry

2008 ◽  
Vol 4 (1-2 (5)) ◽  
pp. 112-119
Author(s):  
Gayane Petrosyan
Keyword(s):  
Human Brain ◽  
19Th Century ◽  
American Poetry ◽  
Dark Side ◽  
Surrounding World ◽  
The People ◽  
The World ◽  
The 19Th Century ◽  
The Universe

The poetry of the world-renowned poetess Emily Dickenson received general acclaim in the fifties of the previous century, 70 years after her death. This country-dwelling lady who had locked herself from the surrounding world, created one of the most precious examples of the 19th century American poetry and became one of the most celebrated poets of all time without leaving her own garden.Her soul was her universe and the mission of Dickenson’s sole was to open the universe to let the people see it. Interestingly, most of her poems lack a title, are short and symbolic. The poetess managed to disclose the dark side of the human brain which symbolizes death and eternity.

scholarly journals Le Corbusier: architecture, music, mathematics: longing for classicism?

2015 ◽  
Author(s):  
Clara Germana Gonçalves ◽  
Maria João Dos Reis Moreira Soares
Keyword(s):  
Seventeenth Century ◽  
Le Corbusier ◽  
Palabras Clave ◽  
The Will ◽  
Music And Mathematics ◽  
And Mathematics ◽  
Universal Order ◽  
Siglo Xx ◽  
The Universe

Abstract: This paper aims to study the role of the relationships between architecture, music and mathematics in Le Corbusier's thought and work and their relevance in his reinterpretation of classical thinking. It seeks to understand to what extent working with this triad – a foundational and, up until the seventeenth century, dogmatic aspect of architecture in general and of its aesthetics in particular – expresses a will not to break with the fundamental and defining aspects of what could be considered as architectural thought rooted in classical tradition: that which is governed by the will to follow the universal order in the work of art; building a microcosmos according to the macrocosmos; linking, in proportion to one another, the universe, man and architecture. The Modulor presents itself as a manifestation of that will, synthesizing these aspects while proposing itself as an instrument for interdisciplinary thought and practice in which the aforementioned aspects of classical thought are present, clearly and pronouncedly. Le Corbusier’s thought and work presents itself as a twentieth century memory of an ancient and ever present tradition conscious of its struggle for “humanity”. Resumen: Este artículo pretende estudiar el papel de la relación entre arquitectura, música y matemática en el pensamiento y la obra de Le Cobusier y su significado en su reinterpretación del pensamiento clásico. Intenta entender en qué medida con esta triada – aspecto fundacional y hasta el siglo XVII dogmático de la arquitectura, en general, y de su estética, en particular – Le Corbusier expresa su recusa por cortar el vínculo con los aspectos fundamentales y definidores de lo que puede considerarse un pensamiento de tradición clásica en arquitectura: aquel tutelado por la voluntad de seguir el orden universal en la obra de arte – construyendo un microcosmos según un macrocosmos – para así vincular, a través de la proporción, universo, Hombre y arquitectura. El Modulor se presenta como manifestación de esa voluntad, sintetizando estos aspectos y presentándose como un instrumento para un pensamiento y una práctica interdisciplinares en los cuales el pensamiento clásico se encuentra clara y marcadamente presente. El pensamiento de Le Corbusier, través su mirada hacia la relación arquitectura-música-matemática, se presenta, en el siglo XX, como una memoria de una antigua y siempre presente tradición, consciente de su busca por “humanidad”.  Keywords: Le Corbusier; Architecture, music and mathematics; classical thought; Modulor. Palabras clave: Le Corbusier; Arquitectura, música y mathematica; pensamiento clásico; Modulor. DOI: http://dx.doi.org/10.4995/LC2015.2015.791

scholarly journals Evolution of teaching the probability theory based on textbook by V. P. Ermakov

2021 ◽  
Vol 11 (2) ◽  
pp. 300-314
Author(s):  
Tetiana Malovichko
Keyword(s):  
Probability Theory ◽  
19Th Century ◽  
Mathematical Expectation ◽  
Random Variable ◽  
Total Probability ◽  
Creative Development ◽  
Educational Literature ◽  
And Mathematics ◽  
Kyiv Polytechnic Institute ◽  
The 19Th Century

The paper is devoted to the study of what changes the course of the probability theory has undergone from the end of the 19th century to our time based on the analysis of The Theory of Probabilities textbook by Vasyl P. Ermakov published in 1878. In order to show the competence of the author of this textbook, his biography and creative development of V. P. Ermakov, a famous mathematician, Corresponding Member of the St. Petersburg Academy of Sciences, have been briefly reviewed. He worked at the Department of Pure Mathematics at Kyiv University, where he received the title of Honored Professor, headed the Department of Higher Mathematics at the Kyiv Polytechnic Institute, published the Journal of Elementary Mathematics, and he was one of the founders of the Kyiv Physics and Mathematics Society. The paper contains a comparative analysis of The Probability Theory textbook and modern educational literature. V. P. Ermakov's textbook uses only the classical definition of probability. It does not contain such concepts as a random variable, distribution function, however, it uses mathematical expectation. V. P. Ermakov insists on excluding the concept of moral expectation accepted in the science of that time from the probability theory. The textbook consists of a preface, five chapters, a synopsis containing the statements of the main results, and a collection of tasks with solutions and instructions. The first chapter deals with combinatorics, the presentation of which does not differ much from its modern one. The second chapter introduces the concepts of event and probability. Although operations on events have been not considered at all; the probabilities of intersecting and combining events have been discussed. However, the above rule for calculating the probability of combining events is generally incorrect for compatible events. The third chapter is devoted to events during repeated tests, mathematical expectation and contains Bernoulli's theorem, from which the law of large numbers follows. The next chapter discusses conditional probabilities, the simplest version of the conditional mathematical expectation, the total probability formula and the Bayesian formula (in modern terminology). The last chapter is devoted to the Jordan method and its applications. This method is not found in modern educational literature. From the above, we can conclude that the probability theory has made significant progress since the end of the 19th century. Basic concepts are formulated more rigorously; research methods have developed significantly; new sections have appeared.

scholarly journals Testing Economic Theory

2018 ◽  
pp. 303-313
Author(s):  
Christopher P. Guzelian
Keyword(s):  
A Priori ◽  
Number System ◽  
Physical Reality ◽  
Economic Research ◽  
Economic Knowledge ◽  
Fractional Reserve Banking ◽  
Physical Universe ◽  
And Mathematics ◽  
Reserve Banking ◽  
The One

Two years ago, Bob Mulligan and I empirically tested whether the Bank of Amsterdam, a prototypical central bank, had caused a boom-bust cycle in the Amsterdam commodities markets in the 1780s owing to the bank’s sudden initiation of low-fractional-re-serve banking (Guzelian & Mulligan 2015).1 Widespread criticism came quickly after we presented our data findings at that year’s Austrian Economic Research Conference. Walter Block representa-tively responded: «as an Austrian, I maintain you cannot «test» apodictic theories, you can only illustrate them».2 Non-Austrian, so-called «empirical» economists typically have no problem with data-driven, inductive research. But Austrians have always objected strenuously on ontological and epistemolog-ical grounds that such studies do not produce real knowledge (Mises 1998, 113-115; Mises 2007). Camps of economists are talking past each other in respective uses of the words «testing» and «eco-nomic theory». There is a vital distinction between «testing» (1) an economic proposition, praxeologically derived, and (2) the rele-vance of an economic proposition, praxeologically derived. The former is nonsensical; the latter may be necessary to acquire eco-nomic theory and knowledge. Clearing up this confusion is this note’s goal. Rothbard (1951) represents praxeology as the indispensible method for gaining economic knowledge. Starting with a Aristote-lian/Misesian axiom «humans act» or a Hayekian axiom of «humans think», a voluminous collection of logico-deductive eco-nomic propositions («theorems») follows, including theorems as sophisticated and perhaps unintuitive as the one Mulligan and I examined: low-fractional-reserve banking causes economic cycles. There is an ontological and epistemological analog between Austrian praxeology and mathematics. Much like praxeology, we «know» mathematics to be «true» because it is axiomatic and deductive. By starting with Peano Axioms, mathematicians are able by a long process of creative deduction, to establish the real number system, or that for the equation an + bn = cn, there are no integers a, b, c that satisfy the equation for any integer value of n greater than 2 (Fermat’s Last Theorem). But what do mathematicians mean when they then say they have mathematical knowledge, or that they have proven some-thing «true»? Is there an infinite set of rational numbers floating somewhere in the physical universe? Naturally no. Mathemati-cians mean that they have discovered an apodictic truth — some-thing unchangeably true without reference to physical reality because that truth is a priori.

Cooperative Сrediting: Prospects of F.V. Raiffeisen Approaches Application in Ukrainian Agricultural Sector

2021 ◽  
pp. 106-114
Author(s):  
Andrii Panteleimonenko ◽  
◽  
Vladyslav Honcharenko ◽  
Svitlana Kasyan ◽  
◽  
...  
Keyword(s):  
Local Governments ◽  
Agricultural Sector ◽  
Agricultural Producers ◽  
Rural Credit ◽  
Professional Journals ◽  
Credit Cooperatives ◽  
Depth Study ◽  
State And Local ◽  
Rural Producers ◽  
The 19Th Century

It is emphasized that at the beginning of the XXI century application of cooperative lending experience of F.W. Raiffeisen cooperatives model in Ukrainian practice allowed credit unions to abandon collateral as the main form of credit security. For many small agricultural producers, especially farmers, signing of a group agreement on joint and several liability (formation of the so-called loan circle) was almost the only opportunity to obtain loans. The main reason for stopping this practice is indicated. It was caused by the consequences of the global financial and economic crisis, the first appearances of which have been felt in Ukrainian economy since 2008. It is discovered that the content of publications presented in scientific professional journals of Ukraine only to some extent reveals the essence of F.W. Raiffeisen approaches on lending to small rural producers. The need for in-depth study of such experiences is emphasized. It is proposed to establish rural credit societies in Ukraine, which are based on the experience of F.W. Raiffeisen credit cooperatives. The important role of state and local governments in the financial support of this process is emphasized. The external financing mechanism for such cooperatives, especially at the initial stage of their activity, with the use of F.W. Raiffeisen loan circles practice is described. Establishing rural credit societies to finance peasants and farmers are indicated as promising. A model of a rural credit society is proposed. It was successfully functioning in Germany, as well as on the territory of other European countries, including Ukrainian provinces, starting from the end of the 19th century. And provided that appropriate changes are made to current Ukrainian legislation, these rural credit societies can become a source of affordable loans for the development of farming. The expediency of detailing the proposed model of a credit cooperative is indicated, taking into account all the principles typical for cooperatives of F.W. Raiffeisen model.

Buchnąć z futrówy, odpypić z ponsy – about vocabulary from the category „cheating” in student jargon from the turn of the 19th and 20th centuries

2021 ◽  
Vol 37 (2) ◽  
pp. 213-224
Author(s):  
Jarosław Pacuła
Keyword(s):  
20Th Century ◽  
19Th Century ◽  
Lexical Semantic ◽  
Semantic Categories ◽  
Root Cause ◽  
History Of ◽  
The 19Th Century

The article presents the history of the student jargon. The author describes the vocabulary used in the period: second-half the 19th century – first half the 20th century; the lexis belongs to the thematic category „cheating”. In the text the reader gets to know theses: 1) the lexis discussed is the root cause of one of the most extensive lexical-semantic categories of the student jargon in the post-partition period (after the period of the Partitions of Poland); 2) in former student language a shared store of the vocabulary exists – this group is independent of the administrative dependence of schools; 3) we notice much former vocabulary in the contemporary jargon; 4) we will notice jargon words in the general Polish in the 19th century; 7) we can see the participation of criminal jargon from the 19th century.

The World Code

2008 ◽  
pp. 58-75
Author(s):  
Azamat Abdoullaev
Keyword(s):  
Big Bang ◽  
Theoretical Physics ◽  
Formal Ontology ◽  
Knowledge Domain ◽  
The Real ◽  
Black And White ◽  
The World ◽  
Theory Of Everything ◽  
And Mathematics ◽  
The Universe

Formalizing the world in rigorous mathematical terms is no less significant than its fundamental understanding and modeling in terms of ontological constructs. Like black and white, opposite sexes or polarity signs, ontology and mathematics stand complementary to each other, making up the unique and unequaled knowledge domain or knowledge base, which involves two parts: • Ontological (real) mathematics, which defines the real significance for the mathematical entities, so studying the real status of mathematical objects, functions, and relationships in terms of ontological categories and rules. • Mathematical (formal) ontology, which defines the mathematical structures of the real world features, so concerned with a meaningful representation of the universe in terms of mathematical language. The combination of ontology and mathematics and substantial knowledge of sciences is likely the only one true road to reality understanding, modeling and representation. Ontology on its own can’t specify the fabric, design, architecture, and the laws of the universe. Nor theoretical physics with its conceptual tools and models: general relativity, quantum physics, Lagrangians, Hamiltonians, conservation laws, symmetry groups, quantum field theory, string and M theory, twistor theory, loop quantum gravity, the big bang, the standard model, or theory of everything material. Nor mathematics alone with its abstract tools, complex number calculus, differential calculus, differential geometry, analytical continuation, higher algebras, Fourier series and hyperfunctions is the real path to reality (Penrose, 2005).

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