Algebraic Concepts Characterized / Distinguishing the General from the Generic / Metalithikum / Pre-specificity / Thinking as an Algebraic Mechanist

Characteristica Designata IV: algebra as an undiscovered continent, and attempts to appropriate it as the symbolic positivity of ‘pure instrumentality’

In his classic textbook The Development of Mathematics (1950), E.T. Bell describes how abstract, symbolical Algebra appeared like an ‘undiscovered continent’ on the horizon.  Those who pushed the application of the symbolic method without dedicated political or economical commitment were ‘adventurers’, whom Bell calls ‘illegitimate Kings’ striving for ‘profit’: masses of young mathematicians were recruited, … Continue reading

Plotting from History

Towards an algebraic understanding of architectonic interpretation (according to J. Vuillemin)

In his Philosophie de l’algèbre (readable at amazon preview), Jules Vuillemin distinguishes 6 dimensions of interpretation in the Cartesian Architectonics, which depend upon a strict distinction between the synthetical and the analytical. Descartes was of the clear opinion that analysis can only treat particular problems, while synthesis can only proceed within the general. In the view … Continue reading