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...
moreMATHEMATICAL 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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