Similar reading experiences

A similar reading experience when reading the Modes of Existence book and when reading the account of categorical logic and new Axiomatization of Mathematics in Rodin’s book

Axiomatic Method and Category Theory (http://arxiv.org/pdf/1210.1478v1.pdf)

As a reader when I read MOE I have the feeling that I am called to peal out layers of my subjectivity that get externalized into ways of discourse-movement that follow their own specifications (the modes of existence with their own specification) while “me” is left with quite a little “Equipment”.  Perhaps with just dispositions.

Me, a Thomas-Anderson-like figure,  wanting to wake up from the dream  “the  World of the Western Moderns” and wandering in what body I will find what self.

Similarly when I read in Rodin’s book the presentation of how in Categorical Logic in Mathematics , a general “universal” logic is abandoned in favor of  local logics connected to the matter at hand, I have this feeling that “my” logic has stopped being in my head but it now runs “in front of my eyes”,  being projected in perceptible inscriptions.

“Today one has a choice between different ready-made logical tools and a freedom to construct new logical tools appropriate to the given task. Thus one is no longer in a position allowing for relying on logic as something given; the epistemic requirement according to which one must “reason logically” in the new context means that one must pay attention to logical issues like truth and rules of inference but not that one must stick to some particular logical rules.” (Rodin)

If I understand well what the mathematician has in front of his/her eyes are  inscriptions that can take both geometrical and logical interpretation so that the same “movement” can both be a movement of inferencing and a movement in meaning related to specific mathematical content. It is as if, thought in its most abstract (as in mathematical logic) takes its leave from the airy mind and takes on an inscriptional body.

Perhaps mathematics can flow in a sense similar to how the modes flow in front of a much “lighter” subjective apparatus

In MOE: Experiencing the “beings that bare relationships” in front of my eyes. That is: through words, in front of my eyes, the content and logic of my experience are represented at the same time.

The person that Latour  addresses at the last chapter of MOE is one that can leave aside quite a lot: to become a sensitive ear listening to tonalities of distinct networks while at the same time his usual means of monitoring his own subjectivity (learned through long engagement with everyday life) are turned into ruins. Then he is asked “to entrust  himself exclusively to the often fragile guidance of these discontinuous trajectories”. Himself who is torn into pieces, perhaps to turn  towards a different way of connectedness, of selfdom-through-“some new way of harmony” (a problem of composition) in a way that leaves talk about substance behind while giving attention to subsistence .

Once more a resonance with Categorical Logic:

“Instead of looking for a core invariant structure shared by all geometrical spaces one studies maps between these spaces (i.e., objects in the sense of 8.8) and organizes the universe of these maps/objects into a category”

“These squares represent not some invariant structures surviving through changes but certain coherences between different changes, which make these diagrams to commute. This coherence of transformation in mathematics is called functoriality. Unless the relevant functors are invertible functoriality does not imply invariance. The tendency of thinking of functoriality as generalized invariance is the same tendency by which people think of homomorphisms as imperfect isomorphisms. This tendency can be described as a case of conceptual inertia, which prevents one from making the full justice of a new concept.”