This book brings together young researchers from a variety of fields within mathematics
philosophy and logic. It discusses questions that arise in their work as well as themes and
reactions that appear to be similar in different contexts. The book shows that a fairly
intensive activity in the philosophy of mathematics is underway due on the one hand to the
disillusionment with respect to traditional answers on the other to exciting new features of
present day mathematics. The book explains how the problem of applicability once again plays a
central role in the development of mathematics. It examines how new languages different from
the logical ones (mostly figural) are recognized as valid and experimented with and how
unifying concepts (structure category set) are in competition for those who look at this form
of unification. It further shows that traditional philosophies such as constructivism while
still lively are no longer only philosophies but guidelines for research. Finally the book
demonstrates that the search for and validation of new axioms is analyzed with a blend of
mathematical historical philosophical psychological considerations.
