---
title: "Criticism of nonstandard analysis"
chunk: 4/4
source: "https://en.wikipedia.org/wiki/Criticism_of_nonstandard_analysis"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T04:17:38.400334+00:00"
instance: "kb-cron"
---

== References ==
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Artigue, Michèle (1994), Analysis, Advanced Mathematical Thinking (ed. David O. Tall), Springer-Verlag, p. 172, ISBN 0-7923-2812-4
Bishop, Errett (1975), "The crisis in contemporary mathematics", Historia Math., 2 (4): 507–517, doi:10.1016/0315-0860(75)90113-5
Bishop, Errett (1977), "Review: H. Jerome Keisler, Elementary calculus", Bull. Amer. Math. Soc., 83: 205–208, doi:10.1090/s0002-9904-1977-14264-x
Bishop, E. (1983). "Schizophrenia in contemporary mathematics".  Written at San Diego, Calif.. Errett Bishop: reflections on him and his research. Contemp. Math. Vol. 39. Providence, RI: Amer. Math. Soc. (published 1985). pp. 1–32.
Bos, Henk J. M. (1974), "Differentials, higher-order differentials and the derivative in the Leibnizian calculus", Archive for History of Exact Sciences, 14: 1–90, doi:10.1007/BF00327456, S2CID 120779114
Chihara, C. (2007). "The Burgess–Rosen critique of nominalistic reconstructions". Philos. Math. 15 (1): 54–78. doi:10.1093/philmat/nkl023.
Connes, A. (1997). "Brisure de symétrie spontanée et géométrie du point de vue spectral" (PDF). Journal of Geometry and Physics. 23 (3–4): 206–234. Bibcode:1997JGP....23..206C. doi:10.1016/s0393-0440(97)80001-0.
Connes, A. (1995). "Noncommutative geometry and reality" (PDF). J. Math. Phys. 36 (11): 6194–6231. Bibcode:1995JMP....36.6194C. doi:10.1063/1.531241.
Dauben, J. (1988). "Abraham Robinson and Nonstandard Analysis: History, Philosophy, and Foundations of Mathematics" (PDF). In Aspray, William; Kitcher, Philip (eds.). History and philosophy of modern mathematics. Minnesota Stud. Philos. Sci. Vol. XI. Minneapolis, MN: Univ. Minnesota Press. pp. 177–200.
Dauben, J. (1992).  Written at Essen. "Arguments, logic and proof: mathematics, logic and the infinite. History of mathematics and education: ideas and experiences". Stud. Wiss. Soz. Bildungsgesch. Math. 11. Göttingen.: Vandenhoeck & Ruprecht (published 1996): 113–148.
Davis, Martin (1977), "Review: J. Donald Monk, Mathematical logic", Bull. Amer. Math. Soc., 83: 1007–1011, doi:10.1090/S0002-9904-1977-14357-7
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Feferman, Solomon (2000), "Relationships between constructive, predicative and classical systems of analysis", Synthese Library, 125 (292), Kluwer Academic Publishers Group: 317–332, doi:10.1023/A:1005223128130, S2CID 46283088; online PDF.
Gordon, E.I.; Kusraev, A.G. (2002). Kutateladze S.S. Infinitesimal Analysis. Dordrecht: Kluwer Academic Publishers. ISBN 978-1-4020-0738-5..
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Kanovei, Vladimir; Katz, Mikhail G.; Mormann, Thomas (2012), "Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics", Foundations of Science, 18 (2): 259–296, arXiv:1211.0244, Bibcode:2012arXiv1211.0244K, doi:10.1007/s10699-012-9316-5, S2CID 7631073
Kanovei, Vladimir; Shelah, Saharon (2004). "A definable nonstandard model of the reals". Journal of Symbolic Logic. 69 (1): 159–164. arXiv:math/0311165. doi:10.2178/jsl/1080938834. S2CID 15104702.
Katz, Karin; Katz, Mikhail (2010). "When is .999... less than 1?". The Montana Mathematics Enthusiast. 7 (1): 3–30. arXiv:1007.3018. doi:10.54870/1551-3440.1381. S2CID 11544878. Archived from the original on 2011-07-20.
Katz, Karin Usadi; Katz, Mikhail G. (2011), "Meaning in Classical Mathematics: Is it at Odds with Intuitionism?", Intellectica, 56 (2): 223–302, arXiv:1110.5456, Bibcode:2011arXiv1110.5456U
Katz, Mikhail G.; Leichtnam, Eric (2013), "Commuting and noncommuting infinitesimals", American Mathematical Monthly, 120 (7): 631–641, arXiv:1304.0583, Bibcode:2013arXiv1304.0583K, doi:10.4169/amer.math.monthly.120.07.631, S2CID 35391617
Keisler, H. Jerome (1977). "Letter to the editor". Notices Amer. Math. Soc. 24: 269.
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Sullivan, Kathleen (1976), "The Teaching of Elementary Calculus Using the Nonstandard Analysis Approach", The American Mathematical Monthly, 83 (5): 370–375, doi:10.2307/2318657, JSTOR 2318657
Tall, David (1980), Intuitive infinitesimals in the calculus (poster) (PDF), Fourth International Congress on Mathematics Education, Berkeley
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== External links ==
Online version of Elementary Calculus: An Infinitesimal Approach
S. Kutateladze "Teaching Calculus"