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Philosophy of Mathematics (Paperback)
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Philosophy of Mathematics (Paperback)
Series: De Gruyter STEM
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The present book is an introduction to the philosophy of
mathematics. It asks philosophical questions concerning fundamental
concepts, constructions and methods - this is done from the
standpoint of mathematical research and teaching. It looks for
answers both in mathematics and in the philosophy of mathematics
from their beginnings till today. The reference point of the
considerations is the introducing of the reals in the 19th century
that marked an epochal turn in the foundations of mathematics. In
the book problems connected with the concept of a number, with the
infinity, the continuum and the infinitely small, with the
applicability of mathematics as well as with sets, logic,
provability and truth and with the axiomatic approach to
mathematics are considered. In Chapter 6 the meaning of
infinitesimals to mathematics and to the elements of analysis is
presented. The authors of the present book are mathematicians.
Their aim is to introduce mathematicians and teachers of
mathematics as well as students into the philosophy of mathematics.
The book is suitable also for professional philosophers as well as
for students of philosophy, just because it approaches philosophy
from the side of mathematics. The knowledge of mathematics needed
to understand the text is elementary. Reports on historical
conceptions. Thinking about today's mathematical doing and
thinking. Recent developments. Based on the third, revised German
edition. For mathematicians - students, teachers, researchers and
lecturers - and readersinterested in mathematics and philosophy.
Contents On the way to the reals On the history of the philosophy
of mathematics On fundamental questions of the philosophy of
mathematics Sets and set theories Axiomatic approach and logic
Thinking and calculating infinitesimally - First nonstandard steps
Retrospection
General
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