Review Article
Volume 13 Issue 6 - 2021
Exploring the Historical Debates on Irrational Numbers Using Neutrosophic Logic as a Balance between Intuition and Rational
Victor Christianto1* and Florentin Smarandache2
1Malang Institute of Agriculture, Indonesia
2Department of Mathematics and Sciences, University of New Mexico, Gallup, NM, USA
*Corresponding Author: Victor Christianto, Department of Forestry, Malang Institute of Agriculture, Indonesia.
Received: March 27, 2021; Published: May 25, 2021


A short book by Dennis P. Allen, Jr, a senior mathematician, inspires this article, and henceforth it is dedicated to him. A good movie about S. Ramanujan, The Man who knew Infinity, also triggers this work. As a note, this is not a conventional math paper. Instead, its purpose is to dig deeper into how a mathematician or a scientist should deal with intuition and balance it with a logical thinking process. Literature exploration on important inventions in mathematics becomes the method of this study combined with analysis of Iain McGilchrist’s theory and Wittgenstein’s Philosophy of Language added with the Cognitive Language Theory. The findings show the absolutistic view of rationality or rational number will not suffice to give a holistic insight into reality. Such finding serves as a reminder concerning whom should be the Master and who should be the emissary in the path toward knowledge. Based on Neutrosophic Logic, the “intuilytics” which combines both parts of brain hemispheres might become the best contribute a holistic approach, something that hints that further exploration on the capacity of human brain or the essence of human beings is needed.

Keywords: Irrational Numbers; Intuition; Mathematics; Right-Left Brain; Logico Philosophico; Cognitive Linguistics Analysis; Neutrosophic Logic; Philosophical-Theological View of Human Beings, Intuilytic


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  2. Robert Kanigel. “The Man Who Knew Infinity”. Charles Scribners (1991).
  3. Iain Mc Gilchrist. “The Master and his emissary: The divided brain and the making of the Western World”. Yale University Press (2009).
  4. Mario Beauregard and Denyse O'Leary. “The spiritual brain”. Jakarta: Penerbit Obor (2009).
  5. R Burn. “The irrational Numbers in English Language Textbooks, 1890-I915: Constructions and Postulates for the Completeness of the Real Numbers”. Historia Mathematica 19 (1992): 158-176.
  6. Ivan Niven. “Irrational Numbers”. The Mathematical Association of America (1956).
  7. Julian Havil. “The Irrationals”. Princeton: Princeton University Press (2012).
  8. V Christianto., et al. “How to balance the intuitive and analytical function of the human brain”. EC Neurology7 (2019): 495-499.
  9. Geeraerts Dirk. “Cognitive Linguistics: Basic Readings” (2008).
  10. Ladov Vsevolod. "Wittgenstein's Tractatus Logico-Philosophicus and a Hierarchica] Approach to Solving Logical Paradoxes”. Filosofija Sociologija1 (2019).
  11. Lakoff G and M Johnson. "Conceptual Metaphor in Everyday Language”. In Shaping Entrepreneurship Research (Eds, Saras D. Sarasvathy, Nicholas Dew, Sankaran Venkatarama), (2020): 475-404.
  12. Liz Gutiérrez Antonio Manuel. “ZALABARDO, José Luis (2015): Representation and Reality in Wittgenstein’s Tractatus. Oxford: Oxford University Press”. Daímon 75 (2018).
  13. Miller David. "The Uniqueness of Atomic Facts in Wittgenstein's Tractatus”. Theoria3 (1977): 174-185.
  14. Iain Mc Gilchrist. The Divided Brain and the Search for Meaning. New Haven: Yale University Press (2011).
Citation: Victor Christianto and Florentin Smarandache. “Exploring the Historical Debates on Irrational Numbers Using Neutrosophic Logic as a Balance between Intuition and Rational”. EC Neurology 13.6 (2021): 28-36.

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