Probabilities are numbers that support defeasibility in reasoning.
To appreciate the significance of these numbers, it is useful to
try eliminating them. Two basic ways of employing probabilities
in defeasible reasoning are analyzed: one in which the information
probabilities provide can be captured by a filter, and another in
which the intersection/conjunction property of filters is weakened.
Elementary facts from logic (with generalized quantifiers) and
linear algebra are used in the analysis, with an eye to applications
in natural language interpretation.