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

Characteristica Designata I

This series of posts will focus a an old theme in philosophy, the idea that there can be a characteristics capable of expressing that of which we can say that it is a property of all things. My interest is to consider a shift in how we can relate to such universality which took place … Continue reading

Algebraic Concepts Characterized / Distinguishing the General from the Generic / Little Dramas Staged / Plotting from History / Pre-specificity / Projective Theory of Technology / Thinking as an Algebraic Mechanist

Continuing the Dedekind Legacy – Computing within the open totality of what can be the object of thought

abstract The paper presents an architectonic notion of computation in the philosophical sense, which depart from the genuinely algebraic ideas in number theory that have been articulated a.o. by Richard Dedekind. Such a perspective interprets the idea of singularity (Ray Kurzweil) as a hubris in the Fregean positivist tradition relying on some „third empire of … Continue reading

Algebraic Concepts Characterized / Gilles Deleuze / Little Dramas Staged / Plotting from History / Projective Theory of Technology / Thinking as an Algebraic Mechanist

The idea of a Characteristica Universalis between Leibniz and Russell, and its relevancy today

Abstract In this post I will investigate the Leibnizian idea of a Characteristica Universalis from a comparative point of view on two diverging paradigms on computation that can be distinguished, as I will argue, to have emerged since the end of the 19th century. While algebraists like Augustus de Morgan, George Boole, Charles Sanders Peirce … Continue reading

Neo-baroque Articulation of Columns: Modules, Solids, Units
Algebraic Concepts Characterized / architectonic articulations - the stanzaic structure of genuinely procedural forms / Projective Theory of Technology / Thinking as an Algebraic Mechanist

Neo-baroque Articulation of Columns: Modules, Solids, Units

We are familiar with the use of generative grammars, L-systems or other recursive procedural frameworks, similar to the subdivision generally applied here in the work of Michael Hansmeyer, mainly from the analysis of natural process and organic structures. What is extraordinary about these examples here is the fact that Hansmeyer does not seek to reference … Continue reading

Algebraic Concepts Characterized / Little Dramas Staged / Plotting from History / Projective Theory of Technology / Thinking as an Algebraic Mechanist

Within the Republic of Things – what architectonic form would the Roman Capitol have if it were transformable today into a philosophical school?

“All algebraic inquiries, sooner or later, end at the Capitol of modern algebra over whose shining portal is inscribed the Theory of Invariants.” This writes Arthur Cayley in a letter, around 1850, to his friend James Joseph Sylvester [1]. It strangely resonates, as a statement, with another very famous saying, namely every road leads to Rome. … 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

Algebraic Concepts Characterized

Deleuze’s notion of the Differential

“Just as we oppose difference in itself to negativity, so we oppose dx to not-A, the symbol of difference [Differenzphilosophie] to that of contradiction. It is true that contradiction seeks its Idea on the side of the greatest difference, whereas the differential risks falling into the abyss of the infinitely small. This, however, is not … Continue reading