Steklov Institute of Mathematics at St.Petersburg


O. Prosorov

Herméneutique formelle et principe de Frege généralisé

This preprint was accepted January 31, 2002
Contact: O.B. Prosorov

Formal hermeneutics and Frege's principle generalized. -  Various discourse 
interpretation procedures reveal the existence of mathematical structures which 
can be formulated within the framework of sheaf theory. The object of this paper
is to establich the theory of discourse interpretation which we name as formal
hermeneutics. For an admissible text X corresponds very naturally one category 
of particulars sheaves Schl(X) named in the honour of Schleiermacher.
We propose the generalisation of Frege's principle of compositionality of meaning
which extends it's domain from the level of individual sentence to those of discourse 
interpretation and provides so a basis for this correspondance. The formal hermeneutics 
describes semantics of a natural language in the category of textual spaces. 
Every particular genre of texts and discours defines there the full subcategory of 
formal discourse schemes. These categories and the different 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, hermeneutical circle, Frege's principle
of compositionality of meaning, topology phonocentric, topology logocentric,
étale bundle, sheaf, category, functor, topology of Grothendieck, site, topos,
textual space, formal discourse scheme.  
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