  We present and examine a result related to uncertainty reasoning, namely that
a certain plausibility space of Cox's type can be uniquely embedded in a
minimal ordered field. This, although a purely mathematical result, can be
claimed to imply that every rational method to reason with uncertainty must be
based on sets of extended probability distributions, where extended probability
is standard probability extended with infinitesimals.
  This claim must be supported by some argumentation of non-mathematical type,
however, since pure mathematics does not tell us anything about the world. We
propose one such argumentation, and relate it to results from the literature of
uncertainty and statistics.
  In an added retrospective section we discuss some developments in the area
regarding countable additivity, partially ordered domains and robustness, and
philosophical stances on the Cox/Jaynes approach since 2003. We also show that
the most general partially ordered plausibility calculus embeddable in a ring
can be represented as a set of extended probability distributions or, in
algebraic terms, is a subdirect sum of ordered fields. In other words, the
robust Bayesian approach is universal. This result is exemplified by relating
Dempster-Shafer's evidence theory to robust Bayesian analysis.
