Algebraic Concepts Characterized / Projective Theory of Technology

Projective theory on technology: an emphatic plan

something like an inverted manifesto (evocatio). 

A projective theory on technology is interested in equipping and furnishing a realm for considering technology as intellectual, not as rational or materialist. Our interest is to enrich the operational and generic understanding of technical principles with world. This perspective allows us to engage in a kind of inverse grammaticality, which departs from generalizations and seeks to articulate the origins of artefacts in the intellectual worlds where they have been engendered. Every object, product, article realized, conceptually or in manifest form, indexes the symbolical dispositions that are to make it what it will be for the people to whom they are meaningful. A house, a chair, a cushion, a piece of paper, a brick, a metal joint, a steam engine, a refridgerator, a pump, a cogwheel, a number, a needle, a toothbrush, a bra, a saddle, any thing rendered into general form engenders and modifies the range of activities we can engage in. We want to view every instance of a general thing as the offspring of a conceptual masterpiece – and not as a replication of a prototype. While prototypes are supposed to be reasonable-reductions-of-concretions-stripped-to-the-essential, masterpieces are singular coagulations of abounding mutual impacts in medias res, that cannot not replicated or reproduced in any other way than by challenging them. Enriching the operational and generic understanding of technical principles with world means to start with tautology: a house is a house. How can we challenge this generic predication with the world in the manifold ways we value it?

We wish to inverse the more common perspective on technology which views in the generic an abstract extraction, a functional purification of the totality of the concretely given. A projective theory of technology on the other hand is interested in these dispositions as carefully crafted, manifest expressions that refer to the totality of what can be thought rigorously, by manipulating symbols.

We want to understand theory not in a primarily reflective, explanatory, legitimative or applicative sense, but rather in a sense which continues the tradition of epoché, a term from ancient sceptics who related with it an abstention from the act of deciding. Yet the dynamics we wish to evoke thereby is not one driven by doubt. It is not the postulate of an unresolvable uncertainty of „being of two minds“ (lat. dubitare) which we make our theorem. And neither would it be well conceived along the phenomenological line of suspension, which seeks a hygienic reduction of bias by making the temporary barring-out of the functions or priviledges of judgements-all too-little-considered its method.

Our methodical hypothesis is this: while Descartes was able to turn doubt into a method by orientating thought within the formal representations possible in the coordinate space of analytic geometry, and while Husserl seeked to infinitesimalize this method by phenomenalizing the constitutive element of this method, namely the ratio, through making suspension the key element of his method, we can today go one step further by integrating computational tools in a conceptual way.

If we affirm the algebraic factorizability of terms, we can reconsider Husserl‘s method of suspension in terms of acts of restraint: Restraint literally means to draw back, confine, concentrate and limit. If we replace the structural rôle of decomposition into elementary units, which was guiding notions of judgement and decision for more than 2 millennia, by the algebraic factorizability of terms, we need not be threatened by foundational questions regarding the existence of limits. Like this, we might be able to develop a generalized notion of quantity, to be gained by extending into symbolically (algebraically) controllable ideality. George Boole, Richard Dedekind and Emmy Noether may count as the pioneers of such a method. While algebra was conceived as allowing to analytically deal with unknown quantities, it turns into a means for dealing synthetically with unknown quantities. The rigorous conception of the so-called Dedekind continuity is synthetic. It is rigorous without being representational – it is rigorous while being genuinely operational.

Hence it dismisses the ontological question regarding the existence of continuity in favor of a categorical perspective regarding how we may speak about it such that its meaning can be determined (and judgement may be enabled). Such an operational approach, however, looses any relation to an absolute, no matter wheter it is assumed positively or of negatively.

Continuing the tradition of philosophical epoché in terms of restraint, rather than doubt or suspension, does not provide us a means for depriving or releasing reason to make up ones mind. It is not a hygienic procedure aimed at cleansing and purifying. Rather, it is an extensional procedure capable of teaching us to articulate a wealth of opportunities that are all, on reasonable grounds, feasible. It is in this way that we envisage an architectonics as capable of furnishing an intellectual space of considerateness. We see in it an fertile means for learning to cultivate the wealth and welfares of civilizations, and hence a way out of the uniformizing dogmas of functionalism, relative positivism, and the accelerating speed they impact towards impasses in the developments of globalization.

Key terms for it would have to give criteria for distinguish domains, fields, groups, rings, and the operational procedures  applicable to them as the symbolic forms of the phenomena these domains engender. By departing form a generalized notion of quantity, we can form numerical species that can be conceived according to the ways of how they bound the general notion of quantity piecewise.

Also compare my earlier post on an algebraic understanding of architectonic interpretation.

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