 As with three-valued approaches, a number of problems beset infinite-valued approaches to vagueness. Firstly, where the infinitude of semantic values are taken to model degrees of truth, the very idea of a degree of truth needs explanation. Secondly, if numerical truth-values are used some justification seems required for the particular truth-value assignments. Thirdly, the full implications of abandoning the well-understood classical theory in favour of degree theory need spelling out before a proper evaluation of its worth can be made. (On these points see Sainsbury 1995: ch.2; Keefe 2000: ch.4. For an extended defense see Smith 2008: ch.5.) Furthermore, it is far from clear whether such an approach successfully avoids problems of higher order vagueness. And the assumption of a totally ordered truth-set is overly simple. Not all natural language sentences are comparable as regards their truth. Due to the multi-dimensional nature of a concept such as redness, we may be unable to say of two reddish patches differing in hue or brightness or colour-saturation, whether one is redder than the other. (On the latter points see Williamson 1994a: ch.4; Keefe 2000: ch.4. Smith [2008: ch.6] argues that the so-called problem of higher order vagueness is in fact a distinct phenomenon and proposes a distinct response.)