The structure of epistemic probabilities

Abstract

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object's weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities are not determined in this way-these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the "problem of the priors."

Scientific Theories as Bayesian Nets: Structure and Evidence Sensitivity

“…Lessons from causal models can also be generalized (Schaffer 2016;Climenhaga 2019). The propositions within a scientific theory need not be descriptions of events, and the relations between them need not be those of causal inference.…”

“…The first of these is restricted to strictly linear hierarchical models of levels of abstraction with a focus on Bayesian issues of simplicity. Climenhaga represents explanatory relations between propositions as Bayesian nets in ways that complement our work here, informally in Climenhaga (forthcoming) and more formally, but with a focus on the specific question of which probabilities determine the values of other probabilities, in Climenhaga (2019). A more complete quantitative model of scientific theories, tracing the dynamics of evidence, implication, and confirmation percolating through branching networks of propositions, has not yet been fully drawn.…”

Houston, Do We Have a Problem?

“…Since the correct theory of cosmic origins causally influences the subsequent distribution of evil throughout the universe, even if we have no positive evidence for theism, the likely distribution of evil still must be evaluated with respect to the intrinsic probability of different versions of theism, naturalism, and any other rival theories of cosmic origins. See Climenhaga (2019) on the dependence relations that hold among different probabilities. In accordance with the theorem of total probability, the likely distribution of evil in the universe is a weighted average of the likely distribution of evil conditional on each of these theories, weighted by their intrinsic probabilities.…”

The intrinsic probability of theism

“…Since positing no entities yields no explanatory power, and so any genuine rival theory posits at least one entity, there is little comparative cost here.21 It is on these grounds thatSwinburne (2004) argues that the Trinity is nevertheless a simple entity, since, on his view, the latter two persons derive from the first. Also seeClimenhaga (2018) for a reason based on the structure of induction to think that more fundamental states should be considered when applying these criteria.22 SeeDawes (2009) and Oppy (2013) for a defense of this position.23 Lataster and Philipse (2017) offer a similar argument against monotheism based on the comparatively large number of possible polytheistic hypotheses. Saward's (2017) response is decisive, though the considerations ofMiller (2016) and…”

“…It is on these grounds that Swinburne () argues that the Trinity is nevertheless a simple entity, since, on his view, the latter two persons derive from the first. Also see Climenhaga () for a reason based on the structure of induction to think that more fundamental states should be considered when applying these criteria.…”