Inconstancy and Inconsistency

In everyday language, we can call someone ‘consistent’ to say that they’re reliable, that they don’t change over time. Someone who’s consistently on time is always on time. Similarly, we can call someone ‘inconsistent’ to say the opposite: that they’re changeable, mercurial. A student who receives inconsistent grades on her tests throughout a semester has performed better on some than on others. With our philosophy hats on, though, we mean something quite different by ‘consistent’ and ‘inconsistent’. Something consistent is simply something that’s not contradictory. There’s nothing contradictory about being on time, so anyone who’s on time at all is consistently on time, in this sense of ‘consistent’. And only a student with an unusual teacher can receive inconsistent grades on her tests throughout a semester, in this sense of ‘inconsistent’. In this paper, I’ll use ‘consistent’ and ‘inconsistent’ in their usual philosophical sense: to mark the second distinction. By contrast, I’ll use ‘constant’ and ‘inconstant’ to mark the first distinction. And although we can, should, and do sharply distinguish the two distinctions, they are related. In particular, they have both been used to account for some otherwise puzzling phenomena surrounding vague language. According to some theorists, vague language is inconstant. According to others, it is inconsistent. I do not propose here to settle these differences; only to get a bit clearer about what the differences amount to, and to show what it would take to settle them. In §1 I’ll give a brief overview of theories of vagueness that crucially invoke inconstancy, and theories that crucially invoke inconsistency. (I’ll also briefly mention inconsistency’s twin, incompleteness.) In §2, I present a formal framework (along the lines of that in [9]) for inconstancy and inconsistency. This will clarify just how the target theories of vagueness differ. §3 summarizes one strain of experimental research on speakers’ use of vague predicates: research into claims like ‘Man x is both tall and not tall’, when man x is a borderline case of ‘tall’. Such phenomena invite explanation in terms of inconstancy or inconsistency, and I’ll explore explanations of both sorts. These explanations will lead me to revisit the formal framework in §4, and prove that, in a certain sense to be clarified there, inconstancy and inconsistency are deeply related; each can do everything the other can do. Finally, §5 offers some lessons to be drawn from the preceding discussion, and points out ways around the equivalence result proved in §4. The overall lesson is this: only with a theory of context in hand can we distinguish inconstancy from inconsistency.