Nick Smith

Different formal tools are useful for different purposes. For example, when it comes to modelling degrees of belief, probability theory is a better tool than classical logic; when it comes to modelling the truth of mathematical claims, classical logic is a better tool than probability theory. In this paper I focus on a widely used formal tool and argue that it does not provide a good model of a phenomenon of which many think it does provide a good model: I shall argue that while supervaluationism may provide a model of probability of truth, or of assertability, it cannot provide a good model of truth -- supertruth cannot be truth. The core of the argument is that an adequate model of truth must render certain connectives truth-functional (at least in certain circumstances) -- and supervaluationism does not do so (in those circumstances).

A common objection to theories of vagueness based on fuzzy logics centres on the idea that assigning a single numerical degree of truth -- a real number between 0 and 1 -- to each vague statement is excessively precise. A common objection to Bayesian epistemology centres on the idea that assigning a single numerical degree of belief -- a real number between 0 and 1 -- to each proposition is excessively precise. In this paper I explore possible parallels between these objections. In particular I argue that the only good objection along these lines to fuzzy theories of vagueness does not translate into a good objection to Bayesian epistemology. An important part of my argument consists in drawing a distinction between two different notions of degree of belief, which I call dispositional degree of belief and epistemic degree of belief.

In his writings Jim Marshall has helpfully emphasized such Wittgensteinian themes as the multiplicity of language games, the deconstruction of ‘certainty,’ and the contexts of power that underlie discursive systems. Here we focus on another important legacy of Wittgenstein's thinking: his insistence that human activity is rule‐governed. This idea foregrounds looking carefully at the world of education and learning, as against the empirical search for new psychological or other facts. It reminds us that we need to consider, in Peter Winch's words, ‘what it makes sense to say’ about certain educational phenomena, and how these meanings stand against understanding a wider form of life. This insight has important implications for doing educational research, and we examine some of these.