The book is a research monograph on the notions of truth and
assertibility as they relate to the foundations of mathematics. It
is aimed at a general mathematical and philosophical audience. The
central novelty is an axiomatic treatment of the concept of
assertibility. This provides us with a device that can be used to
handle difficulties that have plagued philosophical logic for over
a century. Two examples relate to Frege's formulation of
second-order logic and Tarski's characterization of truth
predicates for formal languages. Both are widely recognized as
fundamental advances, but both are also seen as being seriously
flawed: Frege's system, as Russell showed, is inconsistent, and
Tarski's definition fails to capture the compositionality of truth.
A formal assertibility predicate can be used to repair both
problems. The repairs are technically interesting and conceptually
compelling. The approach in this book will be of interest not only
for the uses the author has put it to, but also as a flexible tool
that may have many more applications in logic and the foundations
of mathematics.
General
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