Graded modality

Obligation, goodness, certainty, likelihood, knowledge, belief, and ability are examples of modal concepts – concepts whose conditions for application depend not only on how the real world is, but also on various non-actual ways that the world could be. Ought, good, certain, likely, know, believe, and be able are examples of modal words whose meaning is closely related to the modal concepts just mentioned. Is there graded structure underlying (at least some) modal concepts – are they all-or-nothing, or can they come in degrees? To the extent that there is, how should semanticists model the meanings of modal expressions whose meanings make reference to graded concepts? Modals are usually thought of as (non-graded) quantificational expressions, but there is also a tradition of treating some modal concepts – such as goodness, likelihood, and obligation – on the analogy of graded concepts like height, weight, and temperature. Recently there has been increased attention to scalar aspects of the meanings of modal expressions, but there are still many interesting open questions about how far modal gradation extends, and how it relates to grammatical gradability of the type studied in the extensive literature on degree expressions.