This historical study of the infinite covers all its aspects from the mathematical to the mystical, from the limitlessness of space and time, and the endlessness of numbers, to the perfection of God. Beginning with an account of the main paradoxes of the infinite, including those of Zeno, A.W. Moore traces the history of the topic from Aristotle to Kant, Hegel, Cantor, and Wittgenstein. Recent technical work is examined in the light of Cantor's remarkable discovery that infinity comes in degrees: some infinite sets are much bigger than others. Moore also gives a crisp sketch of Godel's celebrated proof, his clear presentation enabling the non-mathematical reader to grasp deep mathematical issues.
What people are saying - Write a review
LibraryThing ReviewUser Review - fpagan - LibraryThing
Covers much the same ground as Clegg's _Infinity_, but more in the style of a professional philosopher. Very good on Cantor's transfinite ordinals and cardinals. Read full review
Other editions - View all
actual infinite Anaximander apeiron argued argument Aristotelian Aristotle Aristotle 1984 Aristotle’s arithmetical axioms believed Bolzano Brouwer Burali-Forti paradox calculus Cantor cardinal Chapter concept constructed continuum hypothesis countable deny Dummett empiricists endless example fact finite follows fundamental given Gödel’s theorem grasp Greek Hegel hierarchy Hilbert human finitude idea important incoherent infinite by addition infinite by division infinite exists infinite sets infinite whole infinitely big infinitely divisible infinitely small infinitesimal infinitude infinity intuitionists intuitive Kant Kant’s kind later Leibniz limited Löwenheim-Skolem theorem mathematicians meaning metaphysically infinite natural numbers Nicholas of Cusa object ordinals pair paradoxes Parmenides particular philosophical Plato Plotinus possible potential infinite precisely principle problem proof Pythagoreans question rational real numbers reality reason recognize saying/showing distinction seemed self-consciousness sense Set construction set of natural set theory set-theoretical shown space Suppose talk temporal things thought Tractatus true truly infinite truth understanding unity well-ordering Wittgenstein