Identification through Inductive Verification

Abstract

In this paper we are concerned with some general properties of scientific hypotheses. We investigate the relationship between the situation when the task is to verify a given hypothesis, and when a scientist has to pick a correct hypothesis from an arbitrary class of alternatives. Both these procedures are based on induction. We understand hypotheses as generalized quantifiers of types $\left\langle 1\right\rangle$ or $\left\langle 1,1\right\rangle$. Some of their formal features, like monotonicity, appear to be of great relevance. We first focus on monotonicity, extendability and persistence of quantifiers. They are investigated in context of epistemological verifiability of scientific hypotheses. In the second part we show that some of these properties imply learnability. As a result two strong paradigms are joined: the paradigm of computational epistemology (see e.g.[6,5] ), which goes back to the notion of identification in the limit as formulated in [4], and the paradigm of investigating natural language determiners in terms of generalized quantifiers in finite models (see e.g.[1]).