The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel
I. Grattan-Guinness
Princeton University Press
While many books have been written about Bertrand Russell’s philosophy 
and some on his logic, I. Grattan-Guinness has written the first 
comprehensive history of the mathematical background, content, and 
impact of the mathematical logic and philosophy of mathematics that 
Russell developed with <span>A. N.</span> Whitehead in their <i>Principia mathematica (1910-1913)</i>?<br><br>
 This definitive history of a critical period in mathematics includes 
detailed accounts of the two principal influences upon Russell around 
1900: the set theory of Cantor and the mathematical logic of Peano and 
his followers. Substantial surveys are provided of many related topics 
and figures of the late nineteenth century: the foundations of 
mathematical analysis under Weierstrass; the creation of algebraic logic
 by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of
 Dedekind and Frege; the phenomenology of Husserl; and the proof theory 
of Hilbert. The many-sided story of the reception is recorded up to 
1940, including the rise of logic in Poland and the impact on Vienna 
Circle philosophers Carnap and Gödel. A strong American theme runs 
though the story, beginning with the mathematician <span>E. H.</span>
 Moore and the philosopher Josiah Royce, and stretching through the 
emergence of Church and Quine, and the 1930s immigration of Carnap and 
GödeI.<br><br> Grattan-Guinness draws on around fifty manuscript 
collections, including the Russell Archives, as well as many original 
reviews. The bibliography comprises around 1,900 items, bringing to 
light a wealth of primary materials.<br><br> Written for 
mathematicians, logicians, historians, and philosophers — especially 
those interested in the historical interaction between these 
disciplines — this authoritative account tells an important story from 
its most neglected point of view. Whitehead and Russell hoped to show 
that (much of) mathematics was expressible within their logic; they 
failed in various ways, but no definitive alternative position emerged 
then or&nbsp;since.</br></br></br></br></br></br>