Ad Infinitum ... the Ghost in Turing's Machine
Taking God out of Mathematics and Putting the Body Back in
Stanford University Press 1993

AD INFINITUM ... il fantasma nella macchina di Turing

 

" ... the basis for a much needed rhetoric of mathematics" Semiotica

"This polemical essay against acceptance of the potential infinite in arithmetic deserves careful investigation ... ." Mathematical Reviews

"... fashions a formidable critique of the idea of endlessness." Philosophia Mathematica

"... One of the most original and important recent contributions to the philosophy of mathematics ... reaching far beyond its implications for 'strict finitism'. " Philosophy of Mathematics Education Newsletter

"Philosophers ... have struggled with the infinite for millenia -- Rotman offers a new approach to these difficult questions and a solution with considerable sophistication and appeal." Choice

"... ce livre magnifique ..." La Recherche
... the dream of infinity, then, speaks to an old and familiar deity, floating free above the always unfinished business of human becoming. Do we want to go on dreaming it? If the analysis here of mathematics has any force, if the model it urges is coherent, if its formulation of number is intelligible, if it persuades that the dream of endless counting is a dream, then the question is rather: can we go on dreaming it -- in the same old way?