scholarly journals NINETEENTH CENTURY ANALYSIS AS PHILOSOPHY OF MATHEMATICS

2008 ◽  
Author(s):  
JEREMY J. GRAY
Keyword(s):  
Nineteenth Century ◽  
Philosophy Of Mathematics

scholarly journals Kant's Mathematical World

2021 ◽  
Author(s):  
Daniel Sutherland
Keyword(s):  
Nineteenth Century ◽  
Philosophy Of Mathematics ◽  
Mathematical Cognition ◽  
Critical Philosophy ◽  
Cognitive Capacities ◽  
Mathematical World ◽  
The World ◽  
Mathematical Tradition ◽  
Euclid’S Elements ◽  
Way Of Thinking

Kant's Mathematical World aims to transform our understanding of Kant's philosophy of mathematics and his account of the mathematical character of the world. Daniel Sutherland reconstructs Kant's project of explaining both mathematical cognition and our cognition of the world in terms of our most basic cognitive capacities. He situates Kant in a long mathematical tradition with roots in Euclid's Elements, and thereby recovers the very different way of thinking about mathematics which existed prior to its 'arithmetization' in the nineteenth century. He shows that Kant thought of mathematics as a science of magnitudes and their measurement, and all objects of experience as extensive magnitudes whose real properties have intensive magnitudes, thus tying mathematics directly to the world. His book will appeal to anyone interested in Kant's critical philosophy -- either his account of the world of experience, or his philosophy of mathematics, or how the two inform each other.

scholarly journals Stanisław Leśniewski: Rethinking the Philosophy of Mathematics

2015 ◽  
Vol 23 (1) ◽  
pp. 125-138
Author(s):  
Rafal Urbaniak
Keyword(s):  
Nineteenth Century ◽  
Set Theory ◽  
Philosophy Of Mathematics ◽  
Foundations Of Mathematics ◽  
Mathematical Research ◽  
Main Candidate

Near the end of the nineteenth century, a part of mathematical research was focused on unification: the goal was to find ‘one sort of thing’ that mathematics is (or could be taken to be) about. Quite quickly sets became the main candidate for this position. While the enterprise hit a rough patch with Frege’s failure and set-theoretic paradoxes, by the 1920s mathematicians (roughly speaking) settled on a promising axiomatization of set theory and considered it foundational. In parallel to this development was the work of Stanislaw Leśniewski (1886–1939), a Polish logician who did not accept the existence of abstract (aspatial, atemporal and acausal) objects such as sets. Leśniewski attempted to find a nominalistically acceptable replacement for set theory in the foundations of mathematics. His candidate was Mereology – a theory which, instead of sets and elements, spoke of wholes and parts. The goal of this paper will be to present Mereology in this context, to evaluate the feasibility of Leśniewski’s project and to briefly comment on its contemporary relevance.

scholarly journals Theological Underpinnings of the Modern Philosophy of Mathematics.

2016 ◽  
Vol 44 (1) ◽  
pp. 31-54
Author(s):  
Vladislav Shaposhnikov
Keyword(s):  
Nineteenth Century ◽  
Modern Philosophy ◽  
Philosophy Of Mathematics ◽  
Main Concern ◽  
Cultural Expectation ◽  
Divine Knowledge ◽  
Pure Mathematics ◽  
And Mathematics ◽  
Modern Mathematics

Abstract The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern is nineteenth-century mathematics. Theology was present in modern mathematics not through its objects or methods, but mainly through popular philosophy, which absolutized mathematics. Moreover, modern pure mathematics was treated as a sort of quasi-theology; a long-standing alliance between theology and mathematics made it habitual to view mathematics as a divine knowledge, so when theology was discarded, mathematics naturally took its place at the top of the system of knowledge. It was that cultural expectation aimed at mathematics that was substantially responsible for a great resonance made by set-theoretic paradoxes, and, finally, the whole picture of modern mathematics.

scholarly journals An Interdisciplinary Reading of Mathematics

2020 ◽  
Vol 11 (1) ◽  
pp. 40-46
Author(s):  
Yogendra Prasad Shah
Keyword(s):  
Nineteenth Century ◽  
Case Studies ◽  
Growth And Development ◽  
Essential Role ◽  
Philosophy Of Mathematics ◽  
History Of Mathematics ◽  
Research Paper ◽  
Integration Theory ◽  
Educational Context ◽  
History Of

This research paper recapitulates the history of mathematics, which occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. However, there is a problem because genuine historical studies necessitate ever-greater particularity whereas mathematics and philosophy require generality and abstraction. The paper offers some methodological reflections about these matters together with two case studies from nineteenth century history of arithmetic and integration theory, respectively, which try to strike a balance between the directly opposed requirements.

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