How real is real (part 2)

My knowledge is incomplete.

The incompleteness of my knowledge extends to my knowledge of its incompleteness: I don’t know what I don’t know. 

Plato believed this meant it was impossible to find out anything new: one must first understand the question, explicit or implicit, to which an item of knowledge is the answer, before one can acquire and assimilate that knowledge, and this is a contradiction, since understanding the question relies on possessing that knowledge prior to acquiring it. It is as if knowledge is both treasure and treasure map, one that has been buried and records its own location. 

Various thinkers have moved beyond this position by interrogating what we mean by knowledge. All chart in one form or another those penumbra around cognition through which knowledge enters our awareness. These descriptions all have one thing in common: that waiting room of knowledge, that vestibule through which it enters, is a social space. Maybe you know what I don’t know I don’t know? That is to say, we cannot predict what we can learn from each other. We rely on each other to point out what we may have overlooked ourselves.

This means we must measure, derive, discuss, disagree and debate in a collaborative way to learn about the world. Science and progress are fundamentally social rather than solitary activities. The lone maverick does not really work in isolation. Her solitude is populated with predecessors, imagined interlocutors, occasional encounters and confrontations which occur in this social space where knowledge can be codified and formulated in some mutually agreed manner. 

In deconstructionist terms one might say everything is described in terms of relations rather than essential attributes. Acquiring knowledge is a process of drawing connections. We are not digging for treasure. We are making maps. 

But when we finally reach agreement, how can we be certain that everything we think we agree on about the world isn’t just a coincidence? How do I know (rather than just believe) that what you think I mean and what I actually mean (or, for that matter, what I think you mean and what you actually mean) aren't two entirely different things which we both just think are the same, while both the perceived and intended meanings remain coherent with observation? The fact that knowledge is necessarily a social artefact makes this question crucial to our epistemology. 

Even if it wasn't, the interlocution in which cross-purposes may arise and persist and acquire some indelible verisimilitude is our limited individual encounter with evidence, with the universe itself, with the incompleteness of our information and the uniqueness of our perspective on it, and so the dilemma still exists. The maps we draw need have no boundary, and the cross-purposes we mistake for reality can arise in that truncated dialogue in which we meet our infinite selves, unlimited by contingencies of identity, that haste in which we inadvertently fold away a continent. 

Certainly, circumstances can arise which make a cross-purpose obvious, that result in contradictions that reveal we had the wrong end of the stick. Our maps may extend until, like Cortez at Darien, we catch sight of the Pacific. But, although we can be certain of a misunderstanding once this becomes apparent, we cannot be certain we fully understand each other if it hasn't, not without an infinite amount of time to eliminate every possible cross-purpose, every possible situation where we mistake the Americas for the Indies. Agreement is a gross and fictitious thing and reality resides in the infinite variety and the eternal subtleties of our confusion. 

The observation that certainty only applies to the errors we detect is a commonplace of scientific reasoning: we do not confirm a proposition, we falsify its opposite. The scientific method is the most efficient way possible for generating circumstances that reveal our misunderstandings, and its power is derived precisely from the way the incompleteness of the task is formalised in its procedures and the provisionality of the conclusions they underwrite. Science is a contradiction factory. What a scientist calls "certainty" does not have the eternal significance of theology or popular parlance. It has a heavily qualified, tightly technical meaning of the sort journalists often rejoice in disregarding for the sake of a headline.  

But what I am saying here is more than just a trivial statement of the conjectural nature of our conclusions. I am not just observing that they are based on logically coherent appraisals of incomplete information evaluated from distinct points of view and so are limited, provisional, and highly qualified. I am speculating about a structure to coincidence that forms a substrate to knowledge, because in the final analysis these potential cross-purposes are the only kind of knowledge to which we have access. It must be useful to consider how misunderstandings arise, to discern the necessities of error, to see the structure of cross-purposes. I am inclined to speculate we end up with an algorithmic information theory basis to what we can say about the world, and structures that conform to the provisions I described in the first of this occasional series of articles ("How real is real (part 1)").

Returning to the original question: in order to overcome the paradox raised by Plato we must consider knowledge to be a social artefact, that is, our agreement, rather than what (we think) we can agree on (even what we think we are agreeing on is subject to agreement!) is the substance of our knowledge. All knowledge that is not a social artefact is a mysterious contract with infinity, a mystical experience that cannot be communicated.  

Put it another way: there can be no final theory until every other possible theory has been rejected. A falsehood may fail to stand in the full passage of time, but proving something is final, seeing it stand time's toughest test, can only be achieved once time has ended. Until then every object is an illusion and all truth is useless, indistinguishable from lies. We reside in error until the End of Days. And even then we have no way of knowing if what's left is correct. It might not be right. 

Proving a theory is final is equivalent to the algorithmic information theory concept of proving a finite random sequence is random, that no residual structure inheres that can be exploited algorithmically to express the sequence in a more compact manner. This is a mathematical impossibility akin to G?del's incompleteness theorems or the undecidability of the Halting Problem over Turing machines. 

Yet to make use of any theory, to confer any instrumentality on it, we must treat it as final, even though the likelihood it is final is vanishingly small. You have heard people say that they “agree to disagree”. We have to acknowledge that the rest of the time we don't agree, we merely “agree to agree,” in precisely the same sense that we "agree to disagree". There are only unknowns and everything else is a story we tell ourselves to help us get on with things until we inevitably cock things up.

The choice between whether the universe is meaningless or miraculous is then just point of view. We can take a statement about the universe and flip it between paradox and axiom with successive iterations of self-referentiality. What it all means is a matter of choice. Indeed, this choice is the only aspect of the universe in relation to which we are truly and completely free.