Exactly a little vague

Vagueness is a concept that is a lot of fun. At the moment, I'm very fascinated with the Sorites Paradox as relating to a heap. If unfamiliar, I recommend clicking the link for more info, but I will illustrate the the basic premise of this riddle with the use of an alter ego: Lysta.

Althea: Welcome to the blog Lysta, glad to have you here.
Lysta: It's a pleasure to be here.
Althea: The concept that we're working with here is that you start with many, many grains of sand (e.g. 10,000) which collectively make up a heap. Now, if you take away a grain of sand, is it still heap?
Lysta: Yes, dummy.
Althea: OK, but if you take away another grain of sand, is it still a heap?
Lysta: You bet.
Althea: And again, if you take away another grain of sand, is it still a heap?
Lysta: F**cking hell...is this what I came here for? Yes!! It's still a heap!
Althea: So, if the quality of being a heap is not changed by taking away one grain of sand at a time, and because of the vagueness of the term heap, we cannot conclusively define at what point it ceases to be a heap, logically, you could say no matter how many grains you removed in this manner, you would still have a heap. In fact, you can remove all the grains of sand what and was left (nothing) would still constitute a heap.

(silence)

Lysta: But wait a minute. That's really stupid. You're using stupid logic.
Althea: No, it's just a erroneous conclusion. No matter how loosely we define our concept of a heap, you need to have some of something in order for it to qualify as a heap. So if you have nothing left, then we observe that it does not meet that condition and therefore, there can be no heap. That's why they call it a paradox.
Lysta: I still say that you're using stupid logic. I can smoke a cigarette and not get sick. I can smoke two, and three and four cigarettes and not get sick. But there is some quantity of cigarettes that I can smoke which will make me a cancer-riddled specimen of disease. Just because I don't know what that quantity is doesn't mean that it doesn't exist. And just because one cigarette won't do it, doesn't mean that several cumulative instances of one cigarette won't cumulatively get me in a position where I need to have my voicebox removed.
Lysta: Man, I feel like a cigarette.
Althea: Focus Lysta. Now, several people have used a spectrum approach to truth and falsehoods in trying to solve this problem, ie have 'true' on one end, 'false' and various conditions acting as mediums between truth and false that allow them to explain this paradox in a way that isn't contradictory.
Lysta: That's about the dumbest thing I've ever heard.
Althea: Agreed - it's just lazy non-thinking. Either something is true, or it's false. If there is enough complexity in an idea or statement that some parts of it are true, and some are false, then the statement can be clarified or otherwise broken down further into statements that either true or false. Whilst we may not know which is the case for each statement, it is not the case that statements lurk somewhere in some nether region between truth and falsehood.
Lysta: And people who make statements that are either both or neither a falsehood and a truth along the lines of "This statement is a lie" are bloody tools.
Althea: You said it.


Althea: So, getting back to the matter at hand, without some wishy-washy middle ground between true and false, how can we possibly define the point at which a heap of something ceases to be a heap? Or do we just accept the idea vague concepts such as this negate refinement and there will always be a paradox?
Lysta: There ain't no bloody paradox. My point is: it's all about the ranges. It's quite simple really, and it can be done mathematically defining variables. Only, because it's a vague, impression-based concept, you can't do it objectively. You take a sample of the population and put them in a room with the heap of sand, quiz them on whether at what point they would each consider grains to no longer be a heap and use that data to define your ranges. Here, I'll draw it up for you on the blackboard.....


Y = the number of grains in starting heap (everyone in the sample agrees that this is a heap)
X = the highest number of grains that everyone in the sample agrees constitutes a heap
X - 1 = the highest number of grains where there is dissension as to whether the grains constitute a heap or not
V = the highest number of grains where everyone in the sample population agrees that the collection of grains, for whatever reason, no longer constitutes a heap.
0 = zero grains (bloody well not a heap)

Random variable in series (X+1,Y) = An indisputable heap of sand. Marked by the condition that you can remove a grain of sand and what is left over still has quality of being a heap.
Random variable in series (V+1, X) = A quantity of sand that has some probability of qualifying as a heap, a probability that is dependent on various conditions, not least of which who the observer is. Marked by the condition that each grain of sand that is removed within this range (ie the closer you get to the V+1 end of the range) increases the probability that what is left over will not qualify as a heap of sand.
Random variable in series (0, V) = Not a heap of sand. You can take away a grain of sand if you like, but the not-heapness quality of this number of grains of sand will not have changed.

Paradox my ass.


Lysta: Any questions?
Althea: Just one or two. Do you believe that it's actually possible to conduct an experiment or a series of experiments that would conclusively define these ranges that you have referred to?
Lysta: No. I sure as hell wouldn't volunteer for removing 10,000 grains of sand one at a time anyway.
Althea: If you can't conclusively define these ranges, not just for this example, but for every example involving the concept of a heap, then the paradox isn't removed. We both agree that there's a point at which the things cease to be a heap, but we don't know what it is, and, near as can be determined, removing one of those things doesn't change the quality of whether it's a heap or not.
Lysta: Well, fine, if you want to be difficult about it.
Althea: Nyer, nyer, I'm right.
Lysta: There is one other option for determining whether a group of things constitute a heap or not.
Althea: What's than then?
Lysta: You could hire a property valuer. They're well-practiced at confidently making hard value determinations on that which they have very little real understanding. Pay them $5,000 to look at some grains of sand and specify that the valuation report must include a statement regarding the usefulness of the grains as a heap.
Althea: Brilliant!

Please give Lysta a round of applause for her outstanding contribution to this post!