In May of 1973 we organized an international research colloquium on
foundations of probability, statistics, and statistical theories of
science at the University of Western Ontario. During the past four
decades there have been striking formal advances in our
understanding of logic, semantics and algebraic structure in
probabilistic and statistical theories. These advances, which
include the development of the relations between semantics and
metamathematics, between logics and algebras and the
algebraic-geometrical foundations of statistical theories
(especially in the sciences), have led to striking new insights
into the formal and conceptual structure of probability and
statistical theory and their scientific applications in the form of
scientific theory. The foundations of statistics are in a state of
profound conflict. Fisher's objections to some aspects of
Neyman-Pearson statistics have long been well known. More recently
the emergence of Bayesian statistics as a radical alternative to
standard views has made the conflict especially acute. In recent
years the response of many practising statisticians to the conflict
has been an eclectic approach to statistical inference. Many good
statisticians have developed a kind of wisdom which enables them to
know which problems are most appropriately handled by each of the
methods available. The search for principles which would explain
why each of the methods works where it does and fails where it does
offers a fruitful approach to the controversy over foundations.
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