On the Development of the Notion of a Cardinal Number

Deiser, Oliver

doi:10.1080/01445340903545904

Cited by 15 publications

(10 citation statements)

References 31 publications

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“…220-226]. Frege's context was instructive: an attack on Georg Cantor's method of making set theory omnipresent in mathematics by forming any set and abstracting from it the nature of its members and then their order-type so as to lay bare its cardinal number, and thus claim arithmetic as a part of his 'general set theory' [46]. …”

Section: Abstractionmentioning

confidence: 99%

Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics

Grattan‐Guinness

2011

Log. Univers.

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A prized property of theories of all kinds is that of generality, of applicability or least relevance to a wide range of circumstances and situations. The purpose of this article is to present a pair of distinctions that suggest that three kinds of generality are to be found in mathematics and logics, not only at some particular period but especially in developments that take place over time: 'omnipresent' and 'multipresent' theories, and 'ubiquitous' notions that form dependent parts, or moments, of theories. The category of 'facets' is also introduced, primarily to assess the roles of diagrams and notations in these two disciplines. Various consequences are explored, starting with means of developing applied mathematics, and then reconsidering several established ways of elaborating or appraising theories, such as analogising, revolutions, abstraction, unification, reduction and axiomatisation. The influence of theories already in place upon theory-building is emphasised. The roles in both mathematics and logics of set theory, abstract algebras, metamathematics, and model theory are assessed, along with the different relationships between the two disciplines adopted in algebraic logic and in mathematical logic. Finally, the issue of monism versus pluralism in these two disciplines is rehearsed, and some suggestions are made about the special character of mathematical and logical knowledge, and also the differences between them. Since the article is basically an exercise in historiography, historical examples and case studies are described or noted throughout. Mathematics Subject Classification (2000). Primary 00A30, 01A55, 01A60, 01A85, 03-03, 03-99; Secondary 00A35, 00A69, 00A71, 00A79, 03B10, 03C55, 03G05, 30-03, 31-03.Keywords. History and philosophy of pure and applied mathematics, history and philosophy of symbolic logics, parts and moments, generality of theories, theory change, monism and pluralism, sets and multisets, abstract algebras, metamathematics, model theory.

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Section: Abstractionmentioning

confidence: 99%

Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics

Grattan‐Guinness

2011

Log. Univers.

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“…We first need to calculate the sum of non-repeated combinations for each class of ASC structures through the so-called Cardinal Number defined by Deiser (2010). The individual classes are determined by number of initial nodes denoted by i.…”

Section: Generating Of Asc Structuresmentioning

confidence: 99%

Configuration complexity assessment of convergent supply chain systems

Modrák

Márton

2014

International Journal of General Systems

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System designers usually generate alternative configurations of supply chains (SCs) by varying especially fixed assets to satisfy a desired production scope and rate. Such alternatives often vary in associated costs and other facets including degrees of complexity. Hence, a measure of configuration complexity can be a tool for comparison and decisionmaking. This paper presents three approaches to assessment of configuration complexity and their applications to designing convergent SC systems. Presented approaches are conceptually distinct ways of measuring structural complexity parameters based on different preconditions and circumstances of assembly systems which are typical representatives of convergent SCs. There are applied two similar approaches based on different preconditions that are related to demand shares. Third approach does not consider any special condition relating to character of final product demand. Subsequently, we propose a framework for modeling of assembly SC models, which are dividing to classes.

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“…El número natural como concepto matemático no fue formalizado, desde la matemática sabia, hasta el siglo XIX (Deiser, 2010). La formalización propuesta por Cantor, Frege y Russell se fundamenta en la teoría de conjuntos.…”

Section: Propuesta De Un Modelo Epistemológico De Referencia Del Númeunclassified

La enseñanza del número en la escuela infantil: un estudio exploratorio del logos de la profesión

Muñoz

García

Delgado

2017

REDIMAT

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On the Development of the Notion of a Cardinal Number

Cited by 15 publications

References 31 publications

Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics

Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics

Configuration complexity assessment of convergent supply chain systems

La enseñanza del número en la escuela infantil: un estudio exploratorio del logos de la profesión

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