title: Word learning under infinite uncertainty.
abstract: Language learners must learn the meanings of many thousands of words, despite those words occurring in complex environments in which infinitely many meanings might be inferred by the learner as a word's true meaning. This problem of infinite referential uncertainty is often attributed to Willard Van Orman Quine. We provide a mathematical formalisation of an ideal cross-situational learner attempting to learn under infinite referential uncertainty, and identify conditions under which word learning is possible. As Quine's intuitions suggest, learning under infinite uncertainty is in fact possible, provided that learners have some means of ranking candidate word meanings in terms of their plausibility; furthermore, our analysis shows that this ranking could in fact be exceedingly weak, implying that constraints which allow learners to infer the plausibility of candidate word meanings could themselves be weak. This approach lifts the burden of explanation from 'smart' word learning constraints in learners, and suggests a programme of research into weak, unreliable, probabilistic constraints on the inference of word meaning in real word learners.
authors.affiliation: SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, UK. Electronic address: r.a.blythe@ed.ac.uk.
authors.forename: Richard A
authors.initials: RA
authors.lastname: Blythe
authors.affiliation: Literature and Languages, School of Arts and Humanities, University of Stirling, Stirling FK9 4LA, UK.
authors.forename: Andrew D M
authors.initials: ADM
authors.lastname: Smith
authors.affiliation: School of Philosophy, Psychology and Language Sciences, University of Edinburgh, Edinburgh EH8 9AD, UK.
authors.forename: Kenny
authors.initials: K
authors.lastname: Smith
mesh_terms: D002648:Child; D006801:Humans; D008962:Models, Theoretical; D011340:Problem Solving / Q000502:physiology*; D035501:Uncertainty; D014706:Verbal Learning / Q000502:physiology*
keywords: Cross-situational learning; Quine’s Problem; Word learning