This historical study of the infinite covers all its aspects from the mathematical to the mystical. Anyone who has ever pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of the subject. Beginning with an entertaining 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.
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Medieval and Renaissance Thought
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actual infinite Anaximander apeiron argued argument Aristotelian Aristotle Aristotle 1984 axiomatic base axioms believed Bolzano Brouwer Burali-Forti paradox calculus Cantor Chapter concept constructed continuum hypothesis countable denied Descartes Dummett empiricists endless example existence experience fact finite follows Frege fundamental given Godel's theorem grasp Greek Hegel Hilbert human finitude idea incoherent infinite by addition infinite by division infinite sets infinite whole infinitely big infinitely divisible infinitely small infinitesimal infinitude infinity intuitionists intuitive Kant Kant's kind later Leibniz Lowenheim-Skolem theorem mathematician matical matter 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 Russell's paradox saying/showing distinction seemed self-consciousness sense Set construction set theory set-theoretical shown space Suppose talk temporal things thought Tractatus true truly infinite truth understanding unity well-ordering Wittgenstein