Symbolic Algebra as a Semiotic System

Ladislav Kvasz
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Ladislav Kvasz: Czech Academy of Sciences, Institute of Philosophy

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 3101-3133 from Springer

Abstract: Abstract The invention of symbolic algebra in the sixteenth and seventeenth centuries fundamentally changed the way we do mathematics. If we want to understand this change and appreciate its importance, we must analyze it on two levels. One concerns the compositional function of algebraic symbols as tools for representing complexity; the other concerns the referential function of algebraic symbols, which enables their use as tools for describing objects (such as polynomials), properties (such as irreducibility), relations (such as divisibility), and operations (such as factorization). The reconstruction of both the compositional function and the referential function of algebraic symbols requires the use of different analytic tools and the taking of different temporal perspectives. In this chapter, we offer both: a reconstruction of the compositional function of algebraic symbols, and a reconstruction of their referential function.

Keywords: Logical power; Expressive power; Integrative power; Pictorial form; Epistemic subject; Symbolic algebra (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_65

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DOI: 10.1007/978-3-031-40846-5_65

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