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 in 19th century algebra: Then, developments in mathematics have for the first time, it seems, related the question of the universal not to that which remains constant, to substances, primary or secondary, to a ‘nature of the object’s generality’, but inversely, to that which remains invariant, to that which conserves. Michel Serres has drawn the explicit consequences of this shift when he pointed out in a recent lecture before the Académie Française that between all objects of the world, what is common is a fourfold activity: to store, to expand, to emit and to receive information.
“I do not know any living being, cell, tissue, organ, individual, or perhaps even species, of which we cannot say that they store information, that they expand information, that they emit it and they receive information. […] I know of no object in the world, atom, crystal, mountain, planet, star, galaxy, of which one could not say again that it stores information, it deals with information, it emits and it receives information. So there’s this quadruple characteristic in common between all the objects of the world, living or inert.”
Michel Serres 2010
The implications of revisiting the topos of a universal characteristics in this manner affects the ‘nature’ of the algebraic symbolic, and all the philosophical issues involved in ‘naming’ by ‘articulating’ ‘terms’ while bringing polynomials into formulaic constellations.
At stake,thereby, is rendering the symbolic quantity-notion distinguishable from that of physical quantity as well as from that of semantic content. I will argue along fourfold axes :
- The indexed-linearity in the logistic order we experience emerging today is in the philosophical sense amphibolic. The symbolic nature of its terms allows their ‘existence’ (in the sense of logical quantification) in a plurality of manners.
- Because of the structural amphiboly of such orders, thinking about them in terms of seriality and the exchange of positive values is insufficient.
- A characterization of indexed-linearity as algebraic polynominality is more adequate because its terms rely on definitions that are conceived.
- With the emphasis the Leibniz’ian idea of a universal characteristics puts on the application of synthetic procedures as encodings that render assessable what would remain transparent otherwise, it bears a crucial philosophical legacy for dealing with amphibolic structures.
My points of departure – what I try to formulate as a problem – in a nutshell:
Symbolic numbers are counting magnitudes – yet there are many forms such ‘governance’ can take. Such forms can be seen as providing the imaginary horizon of political thought in the Welt Zeit (the Planetary Era of Globalization).
The aporetic anchor point to consider thereby seems to be that to learn something means to master as subject-matter.
This post in context: