Word learning under infinite uncertainty

TL;DR

This paper formalizes how language learners can successfully acquire word meanings despite infinite ambiguity, showing that even weak plausibility rankings enable learning under uncertain conditions.

Contribution

It provides a mathematical model demonstrating that weak plausibility constraints suffice for word learning amid infinite referential uncertainty.

Findings

Learning is possible with plausibility ranking of meanings.

Weak constraints on meaning inference are sufficient.

The model formalizes infinite referential uncertainty in language learning.

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.