Thinking in terms of probabilities can give us a valuable lens on uses of vague language. In particular, it holds out the promise of bringing formally-tractable theories closer to empirical observations about how speakers actually use vague language. However, most existing applications of probability to vague language assume a classical approach to probability. This may be fine as a first approximation, but does not deal well with certain observed phenomena that have been used to motivate formal treatments of vague language based on nonclassical logics. Here I have in mind some phenomena around what have been called "borderline contradictions". In particular, speakers seem relatively happy to agree, of a borderline case of "tall" (for example), that they are both tall and not tall; but speakers are also resistant, in such cases, to agree that such a person is tall, or that they are not tall. These phenomena have been used to motivate three-valued non-probabilistic theories of vague language.
In this talk, try to bring these approaches together, in a way that hopefully achieves some of the virtues of both probabilistic and nonclassical approaches. I give an outline of some of the reasons probabilistic approaches to vague language seem promising and enlightening. Then I turn to borderline contradictions, arguing that classical probabilities are not well-suited for understanding this phenomenon. Finally, I make steps towards a theory of nonclassical probabilities that (I hope) can achieve the goods of existing probabilistic theories of vagueness, while fitting with a plausible approach to borderline contradictions.
A speaker often uses a word to communicate what linguists call an “ad hoc concept” – an occasion-specific meaning – that is different from the word’s stable encoded meaning, and the hearer can usually construct the intended ad hoc concept through pragmatic inference. Appreciating this linguistic insight can shed significant light on a wide range of issues in both philosophical and public discourse. In this talk, I explore how the notion of ad hoc concepts can provide a framework for theorising the cognitive-linguistic mechanisms underpinning characteristic instances of verbal disputes. Crucially, I distinguish between two kinds of communicative failures that frequently occur in verbal disputes – “failures to recognise” and “failures to adopt”. I will analyse cognitive-linguistic factors driving these failures and draw implications with respect to verbal disputes in both public discourse and philosophy.
