Statistics: The science of
drawing conclusions about a population
on the basis of data that normally come from a
sample from the population. Statistics is presently
basically a mathematical discipline (if properly used, as social scientists
may often not do, even if they apply statistical methods), though it is
interesting to reflect that originally 'statistics' derives from
the Italian, and describes the collection of numbers  relating to:
inhabitants, imports, exports, incomes, taxable commodities  that are
useful for the state and for government, which is a practice that
originated in the Italian cities of the Renaissance.
Some knowledge and understanding of statistics and its foundations is
mandatory both for scientists and
philosophers, and for whomever else is
aware how often one generalizes
from data or makes guesses about the future based on information in the
past.
The interested reader should be warned that a thorough understanding
of statistics requires a thorough understanding of
mathematics, including the
mathematics of probability. Also,
there are many subtle and at best partially resolved issues in both
probability and statistics  though skeptics about probability and
statistics should realize that gambling houses and insurance firms base
firm profits on these fundamentally mathematical disciplines, so it does
work in practice, mostly and usually.
Useful elementary introductions are Crowe
et al., Edwards, Hodges and Lehman or Moroney.
Kendall & Stuart is a thorough 3volume set of advanced
statistics that includes and explains a lot of the mathematics of
statistics. Hacking, Kyburg
and Pollock treat some of the problems of statistical inference.
Hirsch Ed. gives a useful and clear summary of the principles of
statistics and probability (and of much of mathematics). Hoel is
a good introduction to the mathematics of statistics. Halmos
provides the mathematical basis for much of both statistics and
probability. Stegmüller provides clear expositions of the
foundations of statistics and probability and of many of its problems,
issues and (attempts of) solutions and recent extensions. Burks
is a good introduction to the mathematics and philosophy of probability,
causality and chance. Freudenthal is a good, clear, concise and
elegant explanation of the foundations of probability and statistics.
