EAN: 9783319220864

STUDIES IN UNIVERSAL LOGIC TOWARDS AN ARITHME...

This book offers an original contribution to the foundations of logic and mathematics and
focuses on the internal logic of mathematical theories  from arithmetic or number theory to
algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of
classical arithmetic  here called Fermat-Kronecker arithmetic and combines Fermat's method of
infinite descent with Kronecker's general arithmetic of homogeneous polynomials. The book also
includes a treatment of theories in physics and mathematical physics to underscore the role of
arithmetic from a constructivist viewpoint. The scope of the work intertwines historical 
mathematical  logical and philosophical dimensions in a unified critical perspective  as such 
it will appeal to a broad readership from mathematicians to logicians  to philosophers
interested in foundational questions. Researchers and graduate students in the fields of
philosophy and mathematics will benefit from the author's critical approach to the foundations
of logic and mathematics.

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