The Spirit of Pythagoreans Against Platonism: From Logos to Alogon, and from Alogon to Logos, in Mathematical Thinking

Arkady Plotnitsky
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Arkady Plotnitsky: Purdue University, Literature, Theory, and Cultural Studies Program, Philosophy and Literature Program

Chapter Chapter 2 in Logos and Alogon, 2022, pp 33-98 from Springer

Abstract: Abstract This chapter serves as a comprehensive outline of the main concepts considered and the argument offered in this study. The chapter will address earlier mathematics, in particular Pythagorean mathematics, and the mathematics (such as algebra, analytic geometry, and calculus) that emerged with the rise of modernity, as a cultural formation, in the sixteenth century and that contained some of the features of modern mathematics. As this study in general, however, the chapter will be primarily concerned with modern mathematics and radical Pythagorean mathematics. After a brief introduction in Sect. 2.1, Sect. 2.2 offers an outline of radical Pythagorean mathematics as part of modern mathematics. Section 2.3 is devoted to the concept of a mathematical concept, which, or the concept of a concept, in the first place, is rarely adequately considered in mathematical or even philosophical literature, but which is central for this study. Section 2.4 considers the relationships between geometry and algebra in modern mathematics and in radical Pythagorean mathematics, defined as Pythagorean by virtue of the relationships between geometry and algebra in it. Section 2.5 discusses the workings of the alogonal in radical Pythagorean mathematics and the ideality-without-idealism (IWI) view, a form of the reality without realism (RWR) applied to mental and thus mathematical reality.

Keywords: Algebra; Alogon; Geometry; Logos; Modern mathematics; Pythagorean mathematics; Radical Pythagorean mathematics; Quantum theory (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/978-3-031-13678-8_2

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