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The Growth of Mathematical Knowledge

The Growth of Mathematical Knowledge

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"The Growth of Mathematical Knowledge" by Emily Grosholz, Herbert Breger is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.

Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics.

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Best For: Students and scholars interested in the philosophical and historical aspects of mathematics.
Focus: Exploring the development and significance of mathematical knowledge from a philosophical perspective.
Covers: The role of mathematics as a bridge between humanities and sciences, its educational importance, and its place in classical philosophy.
Why It Matters: It highlights how mathematics serves as a foundational element in understanding knowledge and intelligibility across disciplines.

"The Growth of Mathematical Knowledge" by Emily Grosholz, Herbert Breger is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.

Topic: Core Mathematics

Author: Emily Grosholz, Herbert Breger

Who this is for:

  • Teachers and classroom instructors
  • Students building subject mastery
  • Readers looking for practical learning support

Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.

Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics.

AuthorEmily Grosholz, Herbert Breger
PublisherSpringer
Published2010-12-09
ISBN-139789048153916
BindingPaperback
LanguageEnglish
SubjectsPhilosophy
TopicCore Mathematics
SeriesSynthese Library

Format: Paperback

Language: English

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