Unknowable?

Edit: As I read over this post, I realized it suffers from a problem of mixed audiences: On the one hand, I tried to address this to a relatively general audience, but on the other I tried to address it to those who have done a similar level of epistemological study as I have. The result is that things are awkwardly overexplained for the second audience and barely understandable to the first. I will try to address all future "thinking on paper" posts mainly to those on a similar level of study in the relevant field as myself, and preface each such post with a note to that effect.

As I was thinking of a response to Paul Hsieh's recent post over at Noodlefood asking whether it was ever possible to know if a seemingly-comatose person is (or is not) conscious, I started wondering about a more general question: What would it mean for something to be unknowable?

Since the question amounts to "what conditions make knowledge impossible?", I'll start by considering the question: "how do we gain knowledge?" While a full answer to that question would take books (like David Harriman's upcoming The Inductive Method in Physics), the essence of the answer is: we use the causal data available in perception to gain ever more abstract knowledge of the causal nature of reality. To concretize that a bit: a child pushing a ball learns that pushing balls make them roll, an older child pushing a ball first on a glass table then on a carpet learns that a ball rolls slower on the carpet than on the glass table, Galileo pushes drops balls down inclined planes and learns the acceleration due to gravity. The essence of experimentation is to control the causal behaviour of the entity under consideration in such a way as to manifest itself on the perceptual level. Benjamin Franklin's famous key experiment made the electrical nature of lightning to manifest itself in the form of (among other things) sparks jumping into a Leyden jar, X-ray film "translates" X-rays into visible dots on the film, etc.

While the above is merely a very broad and short overview of how knowledge is gained, I think it provides an answer to the question I care about in this post. For a fact to be unknowable, it would have to have no causal effects that can (directly or indirectly) be manifested on the perceptual level. This would require some sort of pocket of reality which is causally disconnected from the rest of reality, such that all causal influences only effect other entities in that pocket (otherwise, given enough time and effort, a causal connection could be teased out: a effects b effects c effects.... z, which turns brown instead of blue, etc.). But I think such a "pocket" is a metaphysical contradiction: it implies that something can be different from something else and yet be the same (one internal state of the "pocket" is different from another, and yet the causal result is exactly the same). This is a fallacy my friend Rory (a philosophy student) and I have been talking about about quite a bit recently, something I think of as "the fallacy of stolen identity". This fallacy involves treating "identity" as simply an attribute of an entity, which could be otherwise without changing the other attributes (I'm sure anyone who has taken a philosophy course has heard a hypothetical like "imagine someone exactly like you in behaviour, looks, etc. but who isn't you were to knock you out, walk into your workplace, do your job, and then leave," usually put forth in an attempt to discredit certainty). The thing is, if two things are the same, then they must be the same. If two things are different, then they must be different. It may not be obvious how they are the same or how they are different, but to claim that A has all the attributes of B but is somehow not B is to claim that A can be B and non-B at the same time.

Ok. This post isn't as clear as it could be, but the essence of my point is this: for something to be unknowable, it would have to have be causally isolated from the rest of reality, which would mean it has an identity disconnected from its action, which implies that that identity could be different without anything being different, which violates the law of identity.