Mapping Traces

Representation from Categoricity to Definability

a Conference + Workshop in Bogotá

(versión en español) — Schedule

About the workshop

The meeting will be an interdisciplinary workshop around Representation as a bridge between the two notions of Categoricity and Definability, as understood from a triple perspective: Mathematics, Philosophy and Art – all of them purposely and carefully intertwined during the meeting. The invited participants are among the worldwide foremost specialists in their respective areas. The meeting will strive to create a dialogue between the following specialized subareas: mathematical logic, representation theory, phenomenology, philosophy of the mind, art creation, art history and art criticism.

This meeting is part of a series of conferences that started in Utrecht (Aesthetics and Mathematics, 2007), continued in New York (Simplicity – Ideals of Practice in Mathematics and the Arts, 2013) and will continue in May 2015 in Helsinki exploring linguistic issues (Getting There and Falling Short). These events have attracted a growing number of participants, mixing prominent mathematicians, philosophers, art theorists, artists, and architects in interaction and discussion around specific issues, thereby awakening new perspectives among researchers and students.

Our Bogotá meeting will be an exploration centered on specific responses to questions arising around mapping traces in both Mathematics and Art, and their philosophical implications. It will also explore conditions of possibility for representation of complex objects through better-established, better-grounded and more accessible constructs. It will inquire how these representations are established and grounded (are some modes better than others?), and which are more accessible. Furthermore, the meeting will explore limitations: linguistic, logical, geometric in Mathematics, as well as linguistic or aesthetic in Art.

The people invited in this occasion are a blend of Mathematicians, Artists, Art Historians and Philosophers – the explicit intention is to attempt provocative questions around the issues, originating from the work of each specialist.

The meeting will focus on the following specific issues, linking the three main subjects:

Avatars of Definability

Definability, the possibility of capturing linguistically and/or aesthetically something (a phenomenon, an item of the world, a problem in art, a mathematical construct) has been central as a concept both in logic as in art, since its beginnings; this is evidenced when we focus on questions such as: what can be captured from a given system of signs? What cannot be captured? Can we detect traces of definability (of something captured precisely) when our toolset seems to be insufficient or has been (so to speak) “destroyed”?

In Mathematics, definability is a central tool of research in works relating second order logic, set theory and model theory and different attempts at creating new theories and languages; in Art, it encompasses mimetic representation and its rupture, self-reflection of the artwork, indexic languages, processes of the artwork that leave or evoke traces in spectators (traces of memory, of loss, of existence, etc.) giving rise to fascinating works that may be evoking, criptic or surprising.

Representation and its back-and-forths

Representation, involving a transit from the complex to the simple, is almost immediately central to artistic activity; many of the ruptures in contemporary art can be described in terms of fractures in the representation of worlds. Representation has also been at the center of the work of mathematicians for a long time: representing complex objects is achieved by mapping them into well-grounded, well-defined, seemingly simpler objects. The problem in both art and mathematics is then the “information return”: how much of the original complexity is preserved? Which aspects are preserved? How do representation and definability interact?

The ideal of categoricity

Categoricity is the property according to which the description determines the object, “without exceptions”, the ultimate “a priori”. Categoricity involves uniqueness, determinacy, completeness; therefore, measuring distance to being categorical may be interpreted as providing a degree of lack of determinacy, of distance to an ideal of perfection. In Mathematics, this property has been described recently by Boris Zilber as “the new geometry”, the “new analyticity”. Aside from the depth of technicalities of the work involved, this idea has philosophical repercussions, and is central to Art: degrees of categoricity have involved ruptures and questionings of representation processes; the event will be an opportunity to explore the relevance of the notion and its many possible variants.

Trans-disciplinary criticism

A new critical theory, artistic and literary, has emerged in recent years from a careful interaction between mathematics, philosophy (phenomenology and epistemology) and art. It has involved the work of specialists in those fields and provided a host of new conceptual tools and methods. The work of Franks, Zalamea, Zwicky (essays providing new tools for the study of metaphor, synthetic philosophy of mathematics, and specific, technical bridges between mathematics, philosophy and art) and the work of Kennedy (essays on definability, categoricity, formalism freeness, etc. – combined with new proposals of curatorial work) dramatically stand out in this panorama. These are fresh and innovating ideas, parallel to new forms of writing and expression (oral, visual), that challenge us all to build new forms of thinking and understand ourselves across disciplines.

Graphs / Traces

As an exercise in cross pollination between disciplines we encourage the participants to create their own graph of their presentation with the intention of linking the trace of their own conceptualizations and the work of various local artists whose oeuvre has connections with the subjects of the conference.


Organizers: María Clara Cortés, Andrés Villaveces.


Departamento de Matemáticas
Instituto de Investigaciones Estéticas