Steklov Institute of Mathematics at St.Petersburg

PREPRINT 05/2003

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.

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