The Case for the Irreducibility of Geometry to Algebra

Victor Pambuccian, Celia Schacht

Research output: Contribution to journalArticlepeer-review

Abstract

This paper provides a definitive answer, based on considerations derived from first-order logic, to the question regarding the status of elementary geometry, whether elementary geometry can be reduced to algebra. The answer we arrive at is negative, and is based on a series of structural questions that can be asked only inside the geometric formal theory, as well as the consideration of reverse geometry, which is the art of finding minimal axiom systems strong enough to prove certain geometrical theorems, given that there are no algebraic structures that one could associate with those minimal axiom systems.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalPhilosophia Mathematica
Volume30
Issue number1
DOIs
StatePublished - Feb 1 2022

ASJC Scopus subject areas

  • Mathematics(all)
  • Philosophy

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