Distinguishing the General from the Generic / Lectures / Pre-specificity / Thinking as an Algebraic Mechanist

Abstract: Serious stories around the fantastic dream of a mathesis universalis and the inception of Universal Algebra in the late 19th century

Proposal for The Common Denominator Conference, Universität Leipzig, March 2014. Keywords: Critical Reasoning; Symbolic Reasoning; Amphiboly, Reflection and Projection; Computability In 1898 Alfred North Whitehead published A Treatise on Universal Algebra in order to present “a comparative study of the various Systems of Symbolic Reasoning“ that had been allied to ordinary Algebra since mid 19th … Continue reading

Algebraic Concepts Characterized / Little Dramas Staged

A “Lobachevsky-like” revolution in arithmetics

“I have not yet any clear view as to the extent to which we are at liberty arbitrarily to create imaginaries, and to endow them with supernatural properties” declared John Graves in reaction to his mathematician friend’s invention of the quaternions (Hamilton 1843). Henri Poincaré held it as: “a revolution in arithmetic which is entirely … Continue reading