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After a brief account of the problem of higher‐order vagueness, and its seeming intractability, I explore what comes of the issue on a linguistic, contextualist account of vagueness. On the view in question, predicates like‘borderline red’and‘determinately red’are, or at least can be, vague, but they are different in kind from‘red’. In particular,‘borderline red’and‘determinately red’are not colours. These predicates have linguistic components, and invoke notions like‘competent user of the language’. On my view, so‐called‘higher‐order vagueness’is actually ordinary, first‐order vagueness in different predicates. I explore the possibility that, nevertheless, a pernicious regress ensues.

Conceptual engineers often invoke a distinction between happy-face and unhappy-face solutions to alethic paradoxes. Happy-face solutions are thoroughly specific: they isolate a single, basic principle (“the culprit”). Unhappy-face solutions, meanwhile, are thoroughly non-specific: they merely establish the collective guilt of a group of principles which together produce the paradox. According to this taxonomy, conceptual engineering can only take place via unhappy-face solutions. In this chapter, I: (1) give an expanded taxonomy which allows for both Happy-Face and two forms of Unhappy-Face Conceptual Engineering and show that (2) happy-face treatments represent a limit case. (3) Unhappy-face treatments also represent a kind of limit case. (4) Between these limit cases are treatments which are neither maximally specific nor maximally unspecific but nonetheless specific enough to treat a paradox. (5) Such treatments become thoroughly neutralist when they reject some principle at work in a paradox from a theory-neutral perspective. The upshot is Neutralism—the view that philosophical progress can take place when (and sometimes only when) a thoroughly neutral, non-specific theory is adopted.