The purpose of this book is to introduce the technical tools
and concepts that are indispensable for advanced work in philosophy
and to do so in a way that conveys the important concepts
and techniques without becoming embroiled in unnecessary
technical details. The most valuable technical tools are those
provided by set theory and the predicate calculus. Knowledge of
the predicate calculus is indispensable if for no other reason than
that it is used so widely in the formulation of philosophical
theories. This is partly because it has become conventional to
formulate theories in that way, but it is also because the predicate
calculus provides a medium for such formulations that is both
concise and unambiguous. Furthermore, a knowledge of the
predicate calculus is required for an understanding of Godel's
theorem. Godel's theorem is one of the intellectually most
important achievements of this century. Godel's theorem and
related theorems concerning the predicate calculus appear to have
amazing implications for epistemology and the philosophy of
mathematics. No student of philosophy can be regarded as
properly educated without some grasp of these theorems.