When you ask ‘how?’, I assume you are asking in what way are you begging the question. It is this: in the post I was replying to, where you wrote &quot;the same [as] in the essay”, you used the author’s conclusion, that there is a sharp boundary, in your argument that the author’s argument is correct.<p>Part of the difficulty here is that you are making a somewhat different argument than the author’s , but I don’t think you realize it. Your argument differs crucially when you write (and I quote) &quot;go down the list and ask which is the first not to be unambiguously a pumpkin”. The author is very careful not to say this, no doubt because he realizes that would be begging the question. Also, someone like me could come along and say “if you can do that, then you can answer the question, “what is the least number of grains of sand in a heap of sand”, and go down in the history of philosophy as the person who solved the sorities paradox.”<p>As I don’t think you intended to make this argument, let’s get back to the author’s. If you go back to my first post in this thread, you will see that I raised several objections to the author’s argument, which haven&#x27;t been refuted in this thread.<p>Here’s another one, specifically addressing the way the author avoids requiring that you actually find the boundary. He says that if you look at one end of the list, you see true, and at the other you see false, so you can deduce that there is at least one boundary where it is true on one side and false on the other (the argument actually assumes that there is only one such switch, but we can put that issue aside, as it will turn out to be moot.) As far as the model goes, this is correct, but the model does not fit the problem. The model is a Boolean one, and as such, excludes vagueness by construction, but pumpkin-ness is not a well-formed Boolean predicate.<p>This reminds me of a passage early in ‘Godel, Escher, Bach’, where Hofstadter points out that Euclid and his successors tacitly assumed that his formal system of geometry was the one and only possible model of space, but Einstein said ’not exactly.’ It took me a while to see what Hofstadter was saying here.<p>It also reminds me of Zeno’s Achilles vs. Hare paradox. Zeno presents a model for the race, but that model avoids, by construction, actually considering the time when Achilles catches up to and passes the hare. Zeno’s analysis of his model is correct, as far as it goes, but it does not go far enough -  it is not a valid model for the problem.<p>I am intrigued by the way some people will accept the most unlikely proposition, if they think it is a logical deduction. Did Zeno really believe that motion was an illusion? Do you really believe that you can see a qualitative difference between a given pumpkin and that pumpkin with a single molecule removed?