A little late, but I hope this kind of resembles something of a comment paper. I am still trying to wrap my head around some of the material, so if anyone is reading this, please don't mock me.
My comment paper is in regards to the Sorites paradox (i.e. what the heck is a heap?) and one of the proposed solutions mentioned in "The Era of Specialization."
1) A single grain of sand by itself is not a heap of sand
2) If one has something that is not a heap of sand, and one adds a single grain of sand to it, it is still not a heap of sand
Since the term "heap" is a vague predicate, it would seem that there is no exact dividing line between heaps of sand and non-heaps of sand. However, this taken with #2 seems to suggest that no matter how many grains of sand one adds, it will never sufficiently constitute a heap, which seems odd to say.
Several positions on the Sorites paradox are mentioned, but I have chosen the view that makes the least sense to me, namely, the degree-of-truth-and-application views. This view is that "the application of a vague predicate is not an all or nothing affair, but comes in degrees, as does the truth claims made using such a predicate..."
So essentially, as I understand it: "On a scale of one to ten, the truth value of saying "yes" to the phrase 'this pile is a heap of sand,' is 3."
It seems odd to say, that something is “sort of” a heap of sand, and moreover this just splits the problem down further. For, if a predicate comes in degrees, then it would seem difficult to discern between the varying degrees. Where does one draw the line to which something is a heap to a lesser degree, until the point in which it no longer becomes a heap? If something is definitely not a heap at one grain of sand, and still definitely not a heap at two grains of sand but a heap to a greater degree than just one grain, where is the exact point in which there is a distinct “heap” of sand present, equal to the degree of certainty that we can clearly state as being the case when we assert that one grain of sand is definitely not a heap of sand?
(Also, the statement “two grains of sand is not a heap, but is more a heap than one grain of sand” doesn’t seem to make sense in itself, because two grains of sand is clearly no more of a heap than one grain. Though it is closer to having enough grains of sand to be a heap, it is still no closer to being a heap in and of itself than the one grain of sand.)