The Role of Induction for Human Reasoning and Science

Michael Gr. Voskoglou^1, , Joachim Feuerstein² and Evangelos Athanassopoulos³

¹Mathematical Sciences, University of Peloponnese, Patras, Greece

²Independent Researcher, Saarbrucken, Germany

³Independent Researcher, Gastouni, Greece

Cite this paper:
Michael Gr. Voskoglou, Joachim Feuerstein and Evangelos Athanassopoulos. The Role of Induction for Human Reasoning and Science. American Journal of Educational Research. 2023; 11(5):321-326. doi: 10.12691/education-11-5-10

Abstract

The present paper investigates the valuable role of induction for human reasoning and in particular for the scientific method of thinking, which is analyzed in detail. It is made clear that the possible error of induction is transferred to the inference of deduction, which, therefore, is not an infallible method, although it is always a valid method. Aristotle’s bivalent logic disputes the effectiveness of inductive reasoning, which, however, finds its real value within a multi-valued logic, completing and extending the traditional logic. The unreasonable effectiveness of mathematics for the natural sciences, known as the Winger’s enigma, is also studied and the paper closes with some remarks on the concept of randomness.

Keywords:
human reasoning induction deduction absolute words scientific method bivalent logic multi-valued logics Winger’s enigma randomness free will

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References:

[1]	Barnes J. (Ed.), The Complete Works of Aristotle, The Revised Oxford Translation (2 Vols.), Bollingen Series, Princeton University, Princeton, 1984.
[2]	Vanderah, T.W. & Gould, D.J., Nolte’s the Human Brain, An Introduction to its Functional Anatomy, 8th Edition, Elsevier Health Bridge, London – Amsterdam, 2020.
[3]	Tarski, J., Introduction to Logic and to the Methodology of Deductive Sciences, 4th Edition, Oxford University Press, NY, 1994.
[4]	Pizzey, G., A Field Guide to the Birds of Australia, Collins, Sydney, 1984, p.66.
[5]	Ayer, A.J., Language, Truth and Logic, 3d Edition, Dover Books on Western Philosophy, NY, 1952.
[6]	Voskoglou, M.Gr., Methods for Assessing Human-Machine Performance under Fuzzy Conditions, Mathematics, 7, 2019, 230, Section 2.
[7]	Zadeh, LA. Fuzzy Sets, Information and Control, 8, 1965, 338-353.
[8]	Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern., 3, 1973, 28-44.
[9]	Zadeh, L.A. Fuzzy Sets as a basis for a theory of possibility, Fuzzy Sets Syst., 1, 1978, 3-28.
[10]	Dubois, D.; Prade, H. Possibility theory, probability theory and multiple-valued logics: A clarification, Ann. Math. Artif. Intell., 32, 2001, 35-66.
[11]	Klir, G. J. & Folger, T. A., Fuzzy Sets, Uncertainty and Information, Prentice-Hall, London, 1988.
[12]	Jaynes, E.T., Probability Theory: The Logic of Science, Cambridge University Press, UK, 8th Printing, 2011 (first published, 2003).
[13]	Kosko, B., Fuzziness Vs Probability, Int. J. of General Systems, 17(2-3), 1990, 211-240.
[14]	Voskoglou, M.Gr., Fuzzy Systems, Extensions and Relative Theories, WSEAS Transactions on Advances in Engineering Education, 16, 2019, 63-69.
[15]	Athanassopulos, E. & Voskoglou, M.Gr., A Philosophical Treatise on the Connection of Scientific Reasoning with Fuzzy Logic, Mathematics, 8, 2020, 875.
[16]	Ladyman, J., Understanding the Philosophy of Science, Routledge, Oxon, UK, 2002.
[17]	Gingerich, O., The Eye of the Heaven – Ptolemy, Copernicus, Kepler, American Institute of Physics, NY, 1993.
[18]	Singh, S., Bing Bang - The Origin of the Universe, Harper Perennian Publishers, NY, 2005.
[19]	Thrope, W.H., The origins and rise of ethology: The science of the natural behavior of animals, Praeger, London-NY, 1979.
[20]	Popper, K. R., The Logic of Scientific Discovery, Routlege, Oxon, UK, 2002 (Edition in German, 1934, translated in English, 1959).
[21]	Livio, M., Is God a Mathematician? Simon & Schuster, London, 2009.
[22]	Winger, E.P., The unreasonable effectiveness of mathematics in the natural sciences, Communications in Pure and Applied Mathematics, 13, 1960, 1-14.
[23]	Voskoglou, M.Gr., Simple Skew Polynomial Rings, Publ. Inst. Math. (Beograd), 37(51), 1985, 37-41.
[24]	Voskoglou, M.Gr., Derivations and iterated skew polynomial rings, arXiv preprint, arXiv:1210.1476, 2012
[25]	Majid, S., What is a Quantum Group? , Notices of the American Math. Soc., 2006, 53, 30-31.
[26]	Lopez-Permouth, S., Matrix Representations of Skew Polynomial Rings with Semisimple Coefficient Rings, Contemporary Mathematics, 2009, 480, 289-295.