86 research outputs found
Nestes Modes, ’Qua’ and the Incarnation
A nested mode ontology allows one to make sense of apparently contradictory Christological claims such as that Christ knows everything and there are some things Christ does not know
On the Law of Large Numbers for Nonmeasurable Identically Distributed Random Variables
Let be a countable infinite product of copies of the
same probability space , and let be the sequence of the
coordinate projection functions from to . Let be a
possibly nonmeasurable function from to , and let . Then we can think of as a sequence of independent
but possibly nonmeasurable random variables on . Let . By the ordinary Strong Law of Large Numbers, we almost surely
have , where
and are the lower and upper expectations. We ask if anything more precise
can be said about the limit points of in the non-trivial case where
, and obtain several negative answers. For instance, the
set of points of where converges is maximally nonmeasurable:
it has inner measure zero and outer measure one
Being Sure and Being Confident That You Won’t Lose Confidence
There is an important sense in which one can be sure without being certain, i.e., without assigning unit probability. I will offer an explication of this sense of sureness, connecting it with the level of credence that a rational agent would need to have to be confident that she won’t ever lose her confidence. A simple formal result then gives us an explicit formula connecting the threshold α for credence needed for confidence with the threshold needed for being sure: one needs 1−(1−α) to be sure. I then suggest that stepping between α and 1−(1−α) gives a procedure that generates an interesting hierarchy of credential thresholds
- …