Addendum on the Retrodiction Wall

26 October 2013

Saturday


past and future

In my last post, The Retrodiction Wall, I introduced several ideas that I think were novel, among them:

A retrodiction wall, complementary to the prediction wall, but in the past rather than the present

A period of effective history lying between the retrodiction wall in the past and the prediction wall in the future; beyond the retrodiction and prediction walls lies inaccessible history that is not a part of effective history

A distinction between diachronic and synchronic prediction walls, that is to say, a distinction between the prediction of succession and the prediction of interaction

A distinction between diachronic and synchronic retrodiction walls, that is to say, a distinction between the retrodiction of succession and the retrodiction of interaction

I also implicitly formulated a principle, though I didn’t give it any name, parallel to Einstein’s principle (also without a name) that mathematical certainty and applicability stand in inverse proportion to each other: historical predictability and historical relevance stand in inverse proportion to each other. When I can think of a good name for this I’ll return to this idea. For the moment, I want to focus on the prediction wall and the retrodiction wall as the boundaries of effective history.

The retrodiction wall in the past and the prediction wall in the future mask inaccessible portions of history from us.

The retrodiction wall in the past and the prediction wall in the future mask inaccessible portions of history from us.

In The Retrodiction Wall I made the assertion that, “Effective history is not fixed for all time, but expands and contracts as a function of our knowledge.” An increase in knowledge allows us to push the boundaries the prediction and retrodiction walls outward, as a diminution of knowledge means the contraction of prediction and retrodiction boundaries of effective history.

certainty risk uncertainty

We can go farther than this is we interpolate a more subtle and sophisticated conception of knowledge and prediction, and we can find this more subtle and sophisticated understand in the work of Frank Knight, which I previously cited in Existential Risk and Existential Uncertainty. Knight made a tripartite distinction between prediction (or certainty), risk, and uncertainty. Here is the passage from Knight that I quoted in Addendum on Existential Risk and Existential Uncertainty:

1. A priori probability. Absolutely homogeneous classification of instances completely identical except for really indeterminate factors. This judgment of probability is on the same logical plane as the propositions of mathematics (which also may be viewed, and are viewed by the writer, as “ultimately” inductions from experience).

2. Statistical probability. Empirical evaluation of the frequency of association between predicates, not analyzable into varying combinations of equally probable alternatives. It must be emphasized that any high degree of confidence that the proportions found in the past will hold in the future is still based on an a priori judgment of indeterminateness. Two complications are to be kept separate: first, the impossibility of eliminating all factors not really indeterminate; and, second, the impossibility of enumerating the equally probable alternatives involved and determining their mode of combination so as to evaluate the probability by a priori calculation. The main distinguishing characteristic of this type is that it rests on an empirical classification of instances.

3. Estimates. The distinction here is that there is no valid basis of any kind for classifying instances. This form of probability is involved in the greatest logical difficulties of all, and no very satisfactory discussion of it can be given, but its distinction from the other types must be emphasized and some of its complicated relations indicated.

Frank Knight, Risk, Uncertainty, and Profit, Chap. VII

This passage from Knight’s book (as the entire book) is concerned with applications to economics, but the kernel of Knight’s idea can be generalized beyond economics to generally represent different stages in the acquisition of knowledge: Knight’s a priori probability corresponds to certainty, or that which is so exhaustively known that it can be predicted with precision; Knight’s statistical probably corresponds with risk, or partial and incomplete knowledge, or that region of human knowledge where the known and unknown overlap; Knight’s estimates correspond to unknowns or uncertainty.

Frank Knight's tripartite distinction among certainty, risk, and uncertainty can be employed in a decomposition of the epistemic continuum into the knowable, the partially knowable, and the unknowable.

Frank Knight’s tripartite distinction among certainty, risk, and uncertainty can be employed in a decomposition of the epistemic continuum into the knowable, the partially knowable, and the unknowable.

Knight formulates his tripartite distinction between certainty, risk, and uncertainty exclusively in the context of prediction, and just as Knight’s results can be generalized beyond economics, so too Knight’s distinction can be generalized beyond prediction to also embrace retrodiction. In The Retrodiction Wall I generalized John Smart‘s exposition of a prediction wall in the future to include a retrodiction wall in the past, both of which together define the boundaries of effective history. These two generalizations can be brought together.

Effective history lies between the brick walls of prediction and retrodiction.

Effective history lies between the brick walls of prediction and retrodiction.

A prediction wall in the future or a retrodiction wall in the past are, as I noted, functions of knowledge. That means we can understand this “boundary” not merely as a threshold that is crossed, but also as an epistemic continuum that stretches from the completely unknown (the inaccessible past or future that lies utterly beyond the retrodiction or prediction wall) through an epistemic region of prediction risk or retrodiction risk (where predictions or retrodictions can be made, but are subject to at least as many uncertainties as certainties), to the completely known, in so far as anything can be completely known to human beings, and therefore well understood by us and readily predictable.

If we open up the prediction wall or the retrodiction wall and allow them to be thick, we can interpolate Knight's tripartite epistemic continuum into both the boundary of future knowledge and the boundary of past knowledge.

If we open up the prediction wall or the retrodiction wall and allow them to be thick, we can interpolate Knight’s tripartite epistemic continuum into both the boundary of future knowledge and the boundary of past knowledge.

Introducing and integrating distinctions between prediction and retrodiction walls, and among prediction, risk and uncertainty gives a much more sophisticated and therefore epistemically satisfying structure to our knowledge and how it is contextualized in the human condition. The fact that we find ourselves, in medias res, living in a world that we must struggle to understand, and that this understanding is an acquisition of knowledge that takes place in time, which is asymmetrical as regards the past and future, are important features of how we engage with the world.

This process of making our model of knowledge more realistic by incorporating distinctions and refinements is not yet finished (nor is it ever likely to be). For example, the unnamed principle alluded to above — that of the inverse relation between historical predictability and relevance, suggests that the prediction and retrodiction walls can be penetrated unevenly, and that our knowledge of the past and future is not consistent across space and time, but varies considerably. An inquiry that could demonstrate this in any systematic and schematic way would be more complicated than the above, so I will leave this for another day.

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Grand Strategy Annex

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