A Computational Learning Semantics for Inductive Empirical Knowledge
A COMPUTATIONAL LEARNING SEMANTICS FOR INDUCTIVE EMPIRICAL KNOWLEDGE KEVIN T. KELLY Abstract. This paper presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent's belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within the semantics, such as inductive skepticism, the logic of discov- ery, Duhem's problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch's paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know in- ductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge|as opposed to mere, true belief|through a community of gullible pupils. Keywords: learning, inductive skepticism, deductive closure, knowability, epistemic logic, serendipity, inference, truth conduciveness, bounded rationality, common knowl- edge. 1. Introduction Science formulates general theories. Can such theories count as knowledge, or are they doomed to the status of mere theories, as the anti-scientific fringe perennially urges? The ancient argument for inductive skepticism urges the latter view: no finite sequence of observations can rule out the possibility of future surprises, so universal laws and theories are unknowable. A familiar strategy for responding to skeptical arguments is to rule out skeptical possi- bilities as \irrelevant" (Dretske 1981).
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