Ontological-epistemological formalizations

It seems that the voluminous discussion going under names such as positivism vs. interpretivism, modernism vs. post-modernism, foundatonalism vs. non-foundationalism, and behaviorism, realism and pluralism could benefit from a formalization of the ontological and epistemological models implied by the various positions staked in the discussion. It may be predictably claimed by some of the discussants that the attempt at formalization stakes a position in the contested landscape rather than maps it. I tend to disagree, but do not address this issue. Below is a generic ontological-epistemological formalization framework which allows the description of a wide variety of ontological-epistemological models by setting different values for its parameters. A few specializations, corresponding to radically different situations on the positivist-interpretivist spectrum, are presented.

Setup

Let the “objective, impersonal” universe (that is, all that is observable other than other observers) be a time series of points in an observation space R – r(t) ∈ R^T.

In addition the world contains a set of observers I, each with an internal state that develops over time s_i(t) ∈ S, i ∈ I, t ∈ T. The observations made by each observer at time t depend upon the state of the objective world at this time and upon the state of the observer at the time: f_i(t) = f(r(t), s_i(t)).

The observers can communicate between themselves. These communications are messages of finite length over a certain finite alphabet A, so the communications of observer i at time t is b_i(t) ∈ A*. The communication of each observer at each time depend on their state at the time: b_i(t) = b(s_i(t)).

Finally, each observer’s internal state, s_i can develop based on the observer’s observations and on the history of communications by other observers (and himself): ∆s_i(t) = s'(s_i(t), f_i(t), B_j(t), j ∈ I), where B_j(t) is the concatenation of all the messages of observer j up to time t: b_j(t’), t’ ≤ t.