Versus Laboratory has announced a forthcoming lecture by Colombian mathematician and philosopher Fernando Zalamea to take place at Jan Van Eyck Academie on 29 September, 2011 (details here). While I highly encourage you to attend this seminar, I use this announcement as an opportunity to very briefly introduce Zalamea’s project in the context of a prologue to the future series of introductory posts I intend to write on Zalamea and his universalist project in mathematics and philosophy.

Fernando Zalamea (Bogotà, 1959) belongs to a contemporary and transmodernist renaissance in which science, philosophy, and art enter new synthetic domains. The underlying thesis of Zalamea’s project is simple and can be described — albeit reductively — as follows:

Mathematics is able to map universality and bring the labyrinth of the universal continuum — in its different modalities, global-regional reflexivity, general openness and particular designations — into focus. And it is universality through which (a true-to-the-universe) knowledge can mediate the abyssality or depth of an absolutely open and reflexive universe:

Universality – Knowledge – Abyssality

The triadic commutation above systematically reveals the reflexive web of the universe (from the universe to the universe, or universe-for-itself) which can be traversed by trans-modal, trans-regional and synthetic-analytic passages. The web of the universal and open continuum, thus, illuminates the continuous and reflexive passage Universality Abyssality in terms of real alternatives (Universality / Abyssality). Here, real or true-to-the-universe alternatives should be understood as free transits, transformations, twists, syntheses and relations to the open which simultaneously factor in particularities of local fields and an unrestricted conception of globality inexhaustible by any collection of multitudes or regional horizons. The logic of (real) alternatives, accordingly, is concerned with free expressions of the Universal in all its global-local horizons and through various relational and modal webs. Reflexivity of the universe, therefore, should be thought in terms of free expressions of the Universal, or more accurately, in terms of alternative passages through which the universe traverses back-and-forth between global and local horizons. In other words, reflexivity is the modally and relationally unbound universe-for-itself.

Following the rich legacy of universalism represented by thinkers such as Ramon Llull, Novalis and Charles Sanders Peirce, Zalamea approaches the logic of real alternatives implicit to the triadic universal commutation by way of combinatorial (Llull), compositional (Novalis) and synthetic (Peirce) environments where fusion of modalities, gluing of local fields of knowledge and plastic interweaving of analytical poles can take place. The logic of real alternatives (or free expressions of the Universal) implicit to the abyssal self-reflexivity of the universe is naturally embedded in a true-to-the-universe synthetic landscape that can be systematically approached. This universally synthetic — which by definition means both analytical and synthetic — landscape, therefore, is the topos of (universal) knowledge that highlights and constitutes the reflexive passage Universality – Abyssality.[1] Every true-to-the-universe thought — that is, rational, Copernican and speculative — must pass and work through this synthetic environment, its relational and modal webs, its local filters or perspectives for decanting truth and free global-local dialectics that encompass all nature and culture. Without any prior and systematic observation of this universal synthetic environment, philosophy risks either regional myopias (analytical saturation, local rigidification, over-axiomatization …) or a sort of speculative universal incompetency arising from restricted and often whimsically polarized conceptions of universality (all is synthesis, no particularly exists, …).

Maps and compasses which are required for exploring this synthetic environment or universal web of transits (constituted of integration and differentiation, continuities and obstructions, exact and vague distributions of truth) have been available in the Protean realm of contemporary mathematics. Whilst sophisticated tools and constructs in category theory, sheaf logic (where the synthetic-analytic continuity reflects in sheaf-presheaf categories) and post-Grothendieckian mathematics are to some extent compatible with the aforementioned synthetic universal environment, their speculative valence is still concealed behind formalization and certain desiderata imposed by inter-relations between mathematical fields. As easy as it is to be repelled by the level of mathematical knowledge required to engage contemporary fields of mathematics, it is also easy to be lured and mislead by the exotic formalism of certain mathematical concepts and tools in these fields such as category theory. Resisting suturing philosophy to mathematics, Zalamea’s project highlights the speculative scope of contemporary mathematics not by glossing category theory with contemporary philosophy or finding philosophical equivalents of mathematical concepts in subtle ways but by conducting a creative surgery on contemporary mathematics itself: Rather than directly working with category theory, Zalamea immerses category theory and sheaf logic in the Peircean program of universal and creative mathematization by passing the arsenal of category theory through natural and diverse filters inherent to the Peircean universal and open continuum, intermediating intuitionistic logic and classical logic through sheaf logic,[2] loosening Kripke’s discrete modal logic through the modal geometry sketched in Peirce’s existential graphs, asymmetrization of category theory-set theory dialectics through Freyd’s generalizing allegories and Peirce’s universalizing mathematics of modal geometry, broadening various forms of global-local dialectics in terms of trans-modality of the continuum, compossibilization of different analytical poles in the plastic environment provided by the open continuum, reinscription of the universal continuity within and between incommensurable loci of analysis, …. Here there is no suturing, only recombination of mathematical grafts, transplantation of one field into another, partial gluing, systematic generalization, filtering, decanting, magnification, dilution, Peircean trisection and triplasty.

It is the synoptic, panoramic and systematic surveying of this synthetic landscape – or universal transit of the abyss — through various mathematical lenses that characterizes Zalamea’s project and endows an immensely rich dimension to his universalist thesis. It is not controversial then to distinguish Zalamea — whose body of works spans mathematics, philosophy and cultural criticism (art, architecture, literature, …) — as a post-Copernican heir to Llull, a new Peirce for contemporary logic and mathematics, and a transmodernist Lautman for philosophy in the 21st century.

[1] An alternate and absolutist version of this speculative passage is also presented by Gabriel Catren in his fascinating essay The Outland Empire: Prolegomena to Speculative Absolutism: ‘The speculative movement par excellence is in effect the subsumption of extrinsic transcendental critique within an immanent speculative self-reflection. The reflexive passage from a knowledge-in-itself (i.e. a theoretical procedure that does not reflect in its own transcendental conditions of possibility) to a knowledge-for-itself would thus constitute the immanent dialectic of speculative knowledge itself.’ This is something we will return to in future posts.

[2] Colombian mathematician Xavier Caicedo has also admirably worked on this front: see L??gica de los haces de estructuras.