[FOM] Free review/article on type theory by Corcoran
John Corcoran
corcoran at buffalo.edu
Sun Mar 6 17:47:26 EST 2016
The following review/article about type theory is now available cost-free.
https://www.academia.edu/s/80e9d9d6a4?source=link
MATHEMATICAL REVIEWS 3337386: a review of Hodes, Harold T., Why ramify?,
Notre Dame J. Form. Log. 56 (2015), no. 2, 379—415.
“Why ramify?”—hereafter WR—revisits investigations in logic and foundations
of mathematics spanning three centuries. WR is a massive effort: 36 pages
long, 57 references, 77 footnotes. WR is replete with delicate philosophical
argumentations buttressed with interesting quotations, intricate
mathematics, and contemporary mathematical logic; its stated purpose: “to
better understand Russell’s philosophy and his century-old project in the
foundations of logic and mathematics”.
WR’s subject is type theory or the theory of types, hereafter
TT, initially conceived by Bertrand Russell before 1903 and intended to deal
with paradoxes prominent in the 1800s . After some reworking, TT formed the
basis of the monumental Principia Mathematica by A. N. Whitehead and B.
Russell, which, they asserted, reduced mathematics to logic. Although few
accept that assertion today, TT is still of intense interest, mainly to
historians of mathematics, of logic, and of philosophy. Understanding early
TT is a prerequisite for appreciation of the achievements of modern logic.
Acknowledgements: David Braun, William Demopoulos, Thomas Drucker, Warren
Goldfarb, Idris Samawi Hamid, Allen Hazen, Harold Theodore Hodes, David
Marans, Hassan Masoud, Christopher Menzel, Joaquin Miller, Frango Nabrasa,
Sriram Nambiar, Stephen Read, José Miguel Sagüillo, Michael Scanlan, Kevin
Tracy, Jeffrey Welaish, George Williams, and others.
Special thanks to Warren Goldfarb, Idris Samawi Hamid, Allen Hazen, Harold
Theodore Hodes, Christopher Menzel, Joaquin Miller, and Kevin Tracy for
instructing me in the nuances of this important but Byzantine field.
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