Two theories are being presented and advanced. While the philosophical theory of Philosophical processualism is general and aims at supporting the application of mathematics to guide action with precision, the computational theory of Decision Entropy is specific and aims at establishing a set of objective rules for assigning Bayesian priors, that are non-informative regarding the decision at hand. Besides, the concept of probability is being analyzed from a process-centered perspective, and three types of probability are being introduces: propensity, possibility, and credibility. The highlighted distinction is hoped to settle a number of long-standing disputes regarding the interpretation of probabilities. Also, three properties of objectivity, transparency, and defensibility are offered to characterize inductive systems. To evaluate defensibility, a set of seven theoretical principles are being offered including the principle of “unbiased evaluation,” which can be interpreted as the informativeness of priors for the case of Bayesian inductions.
Philosophical processualism is an original philosophical perspective advanced as the foundation for an epistemic machinery called pragmatic mathematics; a system of linguistically manifested mental constructs aimed at guiding purposive actions with precision. Philosophical processualism relies upon a process-centered interpretation of causality, which sees an event as a constellation of changes made by a process in certain states of the world and/or the mind. By taking concept as the fundamental constituent of the purposive agents’ evaluation processes, the view presents its ontological account of concepts and elaborate on how concepts could look like, where they could be present, and how they could come to realization. Philosophical processualism opposes Platonism by asserting that every concept is the outcomes of cognitive processes unfolding in time and space and is not an abstract entity in the so-called third realm, to which mind can gain access through unknown metaphysical processes.
Probability concept is being analyzed from a process-centered perspective, and it is being divided into three types of propensity, possibility, and credibility. Propensity values are relative repetitions of processual outcomes, as they have come to realization. Possibility values for the outputs of a more-to-less process are the relative contributions of inputs; i.e. the relative number of inputs associated to every output. Credibilities are imaginary relative weights assigned to (the parameters of) the processes, who are hypothesized to deliver the intended outcomes. Credibilities are only means to the end of assessing propensities and/or possibilities, whose exact values are unknown. Bayesian priors are prime examples of credibilities. While the imaginary nature of credibilities allows subjects to assign credibilies of their own preference, their assignment might not be justifiable to others. Alternatively, it is possible to establish a set of theoretical assignment rules on purely logical grounds, and to justify the designations based on their effects, or lack thereof, on the assessed propensities and/or possibilities. Due to their rule abidance, theoretically constructed credibilities may be described as objective, even though imaginary and only existing in subjects’ minds. The class of credibilities called non-informative are the ones, whose assignment are aimed at not informing (certain aspects of) the assessed propensities and/or possibilities.
A set of properties including objectivity, transparency, and defensibility are defined to characterize an inductive assessment procedure. Objectivity is concluded to be the result of transparency and community acceptance. Although every communal rule is contractual by nature, its justification makes the procedures defensible, especially when a community is deciding whether to adopt it as the rule. A set of seven theoretical principles are proposed to evaluate the defensibility of an inductive system, namely (I) Evaluative Orientation, (II) Investigative Prioritization, (III) Explicative Sufficiency, (IV) Evaluative Inclusion, (V) Credibility Conception, (VI) Artifact-Reality Division, and (VII) Unbiased Evaluation.
Decision Entropy Theory (DET) offers an original method for assessing credible outcomes of uncertain processes by incorporating Bayesian probabilities. Since DET is aimed at guiding purposive action with precision and through the use of mathematical measures, it falls under the category of pragmatic mathematics. DET aims at representing uncertainty in an objective and defensible way. The motivation to develop the theory is to account for the possibility of events occurring that are beyond our range of experience. The theory characterizes uncertainty in the context of making a decision; the case of maximum uncertainty corresponds to the maximum entropy for the possible outcomes of the decision. Therefore, the starting point for assessing probabilities, i.e., the non-informative prior probabilities of possibilities before information is included, depends on the decision at hand. Decision Entropy Theory is developed from the following principles that describe the case of no information or maximum uncertainty in making a decision between various alternatives.
1. If no information is available about the probabilities of decision outcomes, then a selected alternative is equally probable to be or not to be the preferred alternative.
2. If no information is available about the probabilities of decision outcomes, then the possible differences in preference between a selected alternative and the preferred alternative are equally probable.
3. If no information is available about the probabilities of decision outcomes, then the possibilities of learning with new information about the selected alternative compared to the preferred alternative are equally probable.
To illustrate the theory, two examples from engineering are being worked out:
(a) selecting the appropriate design wave height for offshore structures, and
(b) assessing the value of test wells before committing to developing a hydrocarbon resource play.
The examples highlight the following points:
• The prior sample space depends on the decision, meaning that the importance of extreme uncertainty depends on its consequences to the decision and the availability of feasible decision alternatives to compensate for these consequences.
• The prior sample space emphasizes the possibilities that distinguish two alternatives from one another.
• The prior sample space can affect the final decision, even when substantive data are available to inform (update) this sample space.
• It is unreasonable to assume that the probability distribution for the frequencies can be established based entirely on experience because that precludes the possibility of events beyond our experience. Such events can be particularly important where experience tends to be limited.
• The value of information is enhanced when leaving open the possibilities for making excessive gains and losses.
• It is possible to rationally balance between relying entirely on historical data versus not relying on them at all. Within this balance, direct information can be combined with information from analogous cases of the past to inform the decision.Civil, Architectural, and Environmental Engineerin
