"a necessary condition on a change looking continuous is that narrow enough regions/close enough points appear to be homogenous [the same color]"? (Graff 924)
This is rejected in favor of a more mathematical definition in terms of epsilons and deltas. Here is the criterion for continuous color-change:
"for change in color across a spectrum to look continuous, it is require only that given any positive amount of change in color, there is a narrow enough width such that in any region on the spectrum narrower than that width, the color looks to change less than that amount in that region. Crucially, it is not required that any region, however narrow, look either homogeneous in color, or the same as its immediate neighbors." (925)
Is this too demanding a notion of continuity for continuous change to be represented in our experience at all?
"It may seem that these conditions would be pretty difficult, if not impossible, to satisfy. If so, so much the better for my case, since it is my opponent's first premise that such conditions can be satisfied." (925)
The dialectic here is that the opponent argues from the continuity of the sorites series to the intransitivity of "looks the same as" via the "homogeneity thesis", which has just been rejected.
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