Brief introduction to a long-standing problem: instant and phases in speech and thought

Abstract

The present paper advances, in an extremely sketchy manner, the argumentative core of several forthcoming articles. The author claims that the Cartesian problem of the instant comes up with renewed force in contemporary linguistics ⎯ in different directions represented by Gustave Guillaume, Agustin García Calvo, or Noam Chomsky ⎯,
a discipline which faces (being for the most
part unaware of it) a seemingly unsolvable
contradiction or paradox. The overcoming of
these difficulties started in another area of
similar constructive importance (the focus here
being no longer the architecture of sound with
meaning, but the geometric constitution of
what appears to be real), namely, mathematics.
A solution is put forward which hinges on the
study of homotopy, as suggested by the so
called theory of operads, initiated by Peter
May, and, based on it, on what has come to be
known as higher topos theory and associated
with the name of Jacob Lurie