The apparentist rightly emphasizes the fact that Socrates grounds the conditionalization
in the agent's own attitudes.
As for the diachronic constraint, it involves a probabilistic rule of inference given by a principle of conditionalization
By contrast, a global form of conditionalization
would allow the naturalist to conditionalize upon all their knowledge (and perhaps, it is implied, this might render the probability in question rather high).
The subjective counterpart, known as subjective probability theory, defines probability as the degree of belief in a given proposition and incorporates debates about Bayesian conditionalization
, (31) (subjective) expected utility theory, (32) and psychometrics.
12) I assume here that belief revision in the face of such evidence goes by conditionalization
, Jeffrey conditionalization
, or some other rule that keeps probability assignments of 0 and 1 fixed.
Before going into more details, recall that in rule theory (Braine & O'Brien, 1998; Rips, 1994), the conditional is involved in two basic inference schemas: (1) elimination, by way of MP; (2) introduction, by way of conditionalization
(or 'conditional proof'), that is, if C is derivable from a set of premises under the supposition that A, if A then C is a valid proposition.
involves the standard steps of marginalization (the summations shown above) to deal with unspecified values of various symptoms, and conditionalization
(the division) to compute the conditional probability; see Feller .
Dey and Sarkar  propose some operations such as conditionalization
and Nth-moment that have no analogs in our article and deserve further study.
Moshe Shaked and I have proved that when a credal agent's subjective likelihoods match the objective ones, and he uses Bayesian conditionalization
from observed evidence, then there is always an objectively expected positive change (increase) in truth-possession.
According to classical logics the conditionalization
, q given d is equivalent to the material implication d [contains] q.
But if conditionalization
on evidence of non-zero probability will give h a probability less than 1, then the present probability of h is less than 1, so h is not part of my present evidence.
Equation (1) suggests that the hypothesis to which the evidence pertains is revised via Bayesian conditionalization
and equation (2) suggests that there is a proportional revision of probabilities for the remaining hypotheses (Robinson and Hastie 1985).