One must always be careful not to be impressed by commonsense, especially if a particular piece of commonsense is expressed in fuzzy language. Let me offer you an example:
" After working on it for a year or two, I came away convinced that his fundamental equation is a theorem of Probability Theory which places necessary constraints on certain patterns in an arbitrary set of numbers. This has direct implications for anything that can be represented by a set of numbers. "
Paul is arguing that Dick's "theorem" has implications. That is simply because Paul doesn't understand it, his two years of study notwithstanding. I will remove the mysticism from Dick's argument and you'll see what it really means:
Sets of numbers don't have patterns, all they have is, well, numbers. Patterns are a creation of our minds, a product of our imagination. Sometimes those patterns are easy to imagine. For instance, the set [1, 2, 3, 4, ...] immediately suggests the pattern "previous plus one". But what about sets such as [32, 77, 4, 109, ...]? Can you imagine a pattern for a set like that?
Dick's argument, and he's absolutely right, is yes, it's always possible to imagine a pattern if you are free to postulate the "existence" of other numbers whose values cannot be known by direct observation. The "unknownable" data. For instance, you can argue that the missing '5' in the set [1, 2, 3, 4, 6, 7, 8, ...] is out there somewhere in a place where you can't see it. Can anybody prove you wrong? Absolutely not.
You'd think this is sensible enough, although perhaps a little trivial. But the problem with Dick's (and Paul's) argument is not that it lacks logic, the problem is that it lacks meaning. So what if you can artificially "fill the gaps" in a set of numbers? What does that have to do with anything? Try to get them to answer that question, and you'll see that they will either shift the discussion from logic to metaphysics, or simply argue that the whole issue is over your head.
But, don't take my word for it, try it yourself.