### Steklov Institute of Mathematics at St.Petersburg

# PREPRINT 05/2003

O. Prosorov

## Formal hermeneutics and Frege Duality

This preprint was accepted March 12, 2003

Contact: `O.B. Prosorov`

__ABSTRACT__ : In this article
we continue to develop the formal hermeneutics intended to be a kind of discourse
interpretation theory. Our approach will provide the common categorical framework
for generalized Frege's compositionality and contextuality principles.
Thus for any given admissible text *X*, we introduce the Schleiermacher category
**Schl**(*X*) of sheaves of fragmentary meanings in termes of which the
general compositionnality principle is formulated. We also introduce another category
**Context**(*X*) of étale bundles of contextual meanings in termes of which
the general contextuality principle is formulated.
We have considered these categories in our previous works [1], [2],
[3].
This categorical point of view leads to the important Frege Duality obtained by the same
procedure as many of well-known important classic dualities and defined as an equivalence
of categories

**Schl**(*X*) | $$_{Λ} |
–––––––––> |
<––––––––– |
$\Gamma $ |
| **Context**(*X*) |

established by the well-known section-functor $\Gamma $ and germ-functor
$\Lambda $. Moreover, this equivalence gives rise to some kind of functional
representation for any fragmentary meaning which allows to establish some kind of inductive
theory of meaning describing the creative process of text understanding. This inductive theory
of meaning based on Frege Duality, and also the different categories and functors related to
discourse interpretation are the principal objects of study in the formal hermeneutics
as we understand it.

__Classification MS2000__ : 03B65, 68Q55, 68T50, 91F20

__Key words__ : formal hermeneutics, hermeneutic circle, admissible text,
fragmentary meaning, contextual meaning,
Frege's principle of compositionality of meaning,
Frege's principle of contextuality,
Frege Duality, category, functor,
phonocentric topology, logocentric topology, sheaf,
bundle, étale bundle, textual space, formal discourse scheme.
[Full text: (.ps.gz)]

Back to all preprints

Back to the Petersburg Department of
Steklov Institute of Mathematics