I have said this before to no avail, getting no attention from either side. What Percy is basically saying is that any useful definition of information requires you to provide a metric.
It MUST satisfy those exact properties or else you cannot use that definition to do useful things such as build an algorithm that tells you when one thing has "more" or "less" information than another thing. Or equivalently, to tell if information has "increased" or "decreased".
Without proving that your metric satisfies all 4 strong properties of a metric:
Yes you are right, I was a bit too harsh but only because I backed off of the definition I am trying to drive home which is a distance between two points. Really I was just plain using an incorrect analogy. I should have talked about a measuring tool by which the difference of information between two things is concerned.
My main point still stands though that I think this is a more effective line of argument against the whole "information" gambit. Show me exactly how you tell that one thing has more or less information than another thing, regardless of what "information" really is, and then we can BEGIN to have a discussion about if it is possible for it to increase or decrease.
If a nation expects to be ignorant and free, in a state of civilization, it expects what never was and never will be. --Thomas Jefferson