This ambitious work puts forward a new account of
mathematics-as-language that challenges the coherence of the
accepted idea of infinity and suggests a startlingly new conception
of counting. The author questions the familiar, classical,
interpretation of whole numbers held by mathematicians and
scientists, and replaces it with an original and radical
alternative-what the author calls non-Euclidean arithmetic. The
author's entry point is an attack on the notion of the mathematical
infinite in both its potential and actual forms, an attack
organized around his claim that any interpretation of "endless" or
"unlimited" iteration is ineradicably theological. Going further
than critique of the overt metaphysics enshrined in the prevailing
Platonist description of mathematics, he uncovers a covert theism,
an appeal to a disembodied ghost, deep inside the mathematical
community's understanding of counting.
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