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  1. Non-Standard Analysis.A. Robinson - 1961 - North-Holland Publishing Co..
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  • Picturing the Infinite.Jeremy Gwiazda - manuscript
    The purpose of this note is to contrast a Cantorian outlook with a non-Cantorian one and to present a picture that provides support for the latter. In particular, I suggest that: i) infinite hyperreal numbers are the (actual, determined) infinite numbers, ii) ω is merely potentially infinite, and iii) infinitesimals should not be used in the di Finetti lottery. Though most Cantorians will likely maintain a Cantorian outlook, the picture is meant to motivate the obvious nature of the non-Cantorian outlook.
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  • Leibniz on Mathematics and the Actually Infinite Division of Matter.Samuel Levey - 1998 - Philosophical Review 107 (1):49-96.
    Mathematician and philosopher Hermann Weyl had our subject dead to rights.
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  • The Foundations of Mathematics in the Theory of Sets.J. P. Mayberry - 2000 - Cambridge University Press.
    This book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
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  • Paradoxes of the Infinite.Bernard Bolzano - 1950 - London: Routledge and Kegan Paul.
    Paradoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19 th century: Dr Bernard Bolzano’s Paradoxien . This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.
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  • Infinite Numbers Are Large Finite Numbers.Jeremy Gwiazda - unknown
    In this paper, I suggest that infinite numbers are large finite numbers, and that infinite numbers, properly understood, are 1) of the structure omega + (omega* + omega)Ө + omega*, and 2) the part is smaller than the whole. I present an explanation of these claims in terms of epistemic limitations. I then consider the importance, part of which is demonstrating the contradiction that lies at the heart of Cantorian set theory: the natural numbers are too large to be counted (...)
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  • Infinite Pains: The Trouble with Supertasks.John Earman & John Norton - 1996 - In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell. pp. 11--271.
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