Topological Epistemology as Epistemology First

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Abstract. The aim of this paper is to sketch a topological epistemology that can be characterized as a knowledge first epistemology. For this purpose, the standard topological semantics for knowledge in terms of the interior kernel operator K of a topological space is extended to a topological semantics of belief operators B in a new way. It is shown that a topological structure has a kind of “derivation” (its “assembly” or “lattice of nuclei”) that defines a profusion of belief operators B. These operators are compatible with the knowledge operator K in the sense that the all the pairs (K, B) satisfy the rules and axioms of a (weak) Stalnaker logic of knowledge and belief. The family of belief operators B compatible with K is partially ordered such that different belief operators can be compared according to their strength or reliability. Thereby, for a given topological knowledge operator, a kind of intuitionist logic of belief operators B compatible with K is defined. In sum, the topological knowledge first epistemology presented in this paper amounts to a pluralist knowledge first epistemology that conceives the relation between knowledge and belief not as a 1-1-relation but as a pluralist 1-n-relation, i.e., one knowledge operator K gives rise to a numerous family of compatible belief operators B.
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First archival date: 2021-12-29
Latest version: 6 (2021-12-30)
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