Furthermore, it applies not only to the standard probability calculus
, but also to nonstandard models....
One should note that fuzzy set theory is not a decision theory but rather a calculus and a modeling language (like probability calculus
) whereby imprecise phenomena in decision processes and humanistic systems are dealt with systematically.
The most difficult of such interludes in the book come in the philosophical and logical arguments for theism which precede the discussion of Christ's teaching, Passion, and Resurrection and also in an appendix concerned with probability calculus
and interspersed with mathematical formulae.
The union of de Broglie's wave mechanics and of Born's wavelike probability calculus
gives birth to a spacetime telegraph transmitting causation by means of information.
But this conflicts with the Bayesian principle that a rational agent's degrees of belief must conform to the probability calculus
. For where p entails q, the Bayesian principle requires the rational agent to assign q at least as high a degree of belief as p; and if rationality requires one to do something, it obviously permits one to do it too.
This limiting case of PoI does not act as a constraint on existing subjective probability assignments, but rather as a rational way of filling in the gaps that aren't filled by the probability calculus
But he correctly points out that even if the laws of logic were constitutive of what it is to believe, the rules of the probability calculus
are not, and therefore it is clearly possible to have beliefs which are irrational (to assign a greater probability to a conjunction than to one of its conjuncts, for example).
If Shapiro is right, these intellectuals may have embraced a basic premise of a twentieth-century theory of uncertainty, the standard probability calculus
Joyce attempts to "depragmatize" de Finetti's prevision argument for the claim that our credences ought to satisfy the axioms of the probability calculus
. This article adapts Joyce's argument to give nonpragmatic vindications of David Lewis's original Principal Principle as well as recent reformulations motivated by Ned Hall and Jenann Ismael.
Bayesianism--as a normative epistemological theory holds that rational belief comes in precisely measurable degrees, which satisfy the probability calculus
and are modified by conditionalizing on acquired evidence.
Remarkably, Laudan makes the further claim that this is a consequence of demanding that one's degrees of belief conform to the probability calculus
: 'the empirical support flows upwards from observation to Galileo's law and then to Newton's theory and from there downwards to Kepler's laws.