Foundations of Mathematics I

Hilbert and Bernays' 'Grundlagen der Mathematik'
appeared in two volumes in 1934 and 1939, a
second edition in 1968 and 1970. It offers a
foundation for proof theory and is a major source on
David Hilbert's formalist programme, Paul Bernays'
philosophy, the epsilon operator, and much more.
It has been a profound infl uence on mathematics,
logic, and philosophy, and it covers formal ground
and philosophical perspectives beyond the scope of
Whitehead and Russell's 'Principia Mathematica' and
Frege's 'Grundlagen der Arithmetik'.

This book is not only essential to any scholar of the
history and philosophy of modern mathematics, but it
also contains formal research - on the epsilon and iota
operators - of contemporary relevance to logicians,
mathematicians and computer science. For us, it is
one of the most fascinating books ever written.

This a bilingual German-English, commented edition
of the 'Grundlagen'. It is the fi rst English publication
of these texts and shows the facsimile of the German
original text on the left-hand side of a double page,
and its English translation on the right-hand side.
In addition to extensive comments on the history
and the interpretation of the text's mathematical
and philosophical content, there are also careful
annotations regarding the differences between the
two German editions (1934/39,1968/1970) of this
two volume monograph.