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http://dx.doi.org/10.14477/jhm.2022.35.2.043
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On Induction and Mathematical Induction |

Koh, Youngmee (Dept. of Data Sci., Univ. of Suwon) |

Publication Information

Abstract

The 21st century world has experienced all-around changes from the 4th industrial revolution. In this developmental changes, artificial intelligence is at the heart, with data science adopting certain scientific methods and tools on data. It is necessary to investigate on the logic lying underneath the methods and tools. We look at the origins of logic, deduction and induction, and scientific methods, together with mathematical induction, probabilistic method and data science, and their meaning.

Keywords

Logic; Induction; Deduction; Mathematical induction; Probability;

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- Reference
- Cited By KSCI

1 | Wikipedia, Empiricism. https://en.wikipedia.org/wiki/Empiricism (17 December 2021) |

2 | Karl Popper, The Logic of Scientific Discovery, Taylor & Francis e-library, 2005. (Originally, Logik der Forschung, Verlag von Julius Springer, Vienna, Austria, 1935.) |

3 | Ree Sangwook, Koh Youngmee, MaPhiA: Mathematics, Philosophy, and Artificial Intelligence, Journal for History of Mathematics 32(5) (2019), 217-231. DOI |

4 | Joseph Agassi, Popper and His Popular Critics, Springer, 2014. |

5 | Field Cady, The Data Science Handbook, Wiley, 2017. |

6 | Martin Davis, Engines of Logic: Mathematicians and the Origin of the Computer, W. W. Norton & Company, 2001. |

7 | Ian Hacking, The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference, 2nd edition, Cambridge Univ. Press, 2006 (1975). |

8 | Kim Yongdai, Thinking Ways of Data Scientists, Gimmyoung sa, 2021 |

9 | Koh Youngmee, Ree Sangwook, On Mathematical Induction, Journal for History of Mathematics 34(6) (2021), 195-204. |

10 | Park Sung Hyun, Oh JinHo, Kwon Soon-Sun, Charms of Data Science: Data...Future Economical Power of AI Era, Free Academy, 2021. |

11 | Joel Spencer, The Strange Logic of Random Graphs, Springer Verlag, 2001. |

12 | Wikipedia, Scientific method. https://en.wikipedia.org/wiki/Scientific_method (14 January 2022) |

13 | Brian Skyrms, Carnapian Inductive Logic and Baysian Statistics, Statistics, Probability and Game Theory, IMS Lecture Notes-Monograph Series 30 (1996), 321-336. DOI |

14 | David Mumford, The Dawning of the Age of Stochasticity, Mathematics: Frontiers and Perspectives 2000, 197-228, AMS, 2000. |

15 | Henri Poincare, Science and Hypothesis, The Walter Scott Publishing Co., Ltd., 1905. |

16 | George Polya, Mathematics and Plausible Reasoning: Vol. I Induction and Analogy in Mathematics, Princeton University Press, 1954. |

17 | Carveth Read, Logic: Deductive and Inductive, Fourth edition, Dodo Press (A. Morning Ltd.), 1914. https://www.gutenberg.org/ebooks/18440 |

18 | Ree Sangwook, Koh Youngmee, The Aims of Education in the Era of AI, Journal for History of Mathematics 30(6) (2017), 341-351. DOI |

19 | Alan H. Scheonfeld, How We Think: A Theory of Goal-Oriented Decision Making and its Educational Applications, Routledge, 2011. |

20 | Stuart Russell, Peter Norvig, Artificial Intelligence: A Modern Approach, 3rd edition, Pearson, 2009. (4th edition, Pearson, 2021. http://aima.cs.berkeley.edu/) |

21 | Brian Skyrms, Choice and Chance, Melbourne, Australia, and Belmont, CA: Wadsworth/ Thompson Learning, 2000. |

22 | Wikipedia, Inductive Reasoning. https://en.wikipedia.org/wiki/Inductive_reasoning (16 December 2021) |

23 | Wikipedia, Logic. https://en.wikipedia.org/wiki/Logic (23 December 2021) |

24 | Noga Alon, Joel H. Spencer, The Probabilistic Method, 4th edition, Wiley, 2016. |

25 | A. J. Ayer, Hume: A Very Short Introduction, Oxford University Press, 2000. |

26 | Rudolf Carnap, On Inductive Logic, Philosophy of Science, 12(2) (1945), 72-97. DOI |

27 | Rudolf Carnap, Logical Foundations of Probability, 2nd ed., The University of Chicago Press, 1962 (first edition in 1950). |

28 | Gerd Gigerenzer, Zeno Swijtink, Theodore Porter, Lorraine Daston, John Beatty, Lorenz Kruger, The Empire of Chance: How probability changed science and everyday life, Cambridge University Press, 1989. |

29 | Hardy Grant, Israel Kleiner, Turning Points in the History of Mathematics, Birkhauser, 2015. |

30 | Ian Hacking, An Introduction to Probability and Inductive Logic, Cambridge University Press, 9th edition, 2009 (First published 2001). |

31 | Philip Kitcher, William Aspray, An Opinionated Introduction, History and Philosophy of Modern Mathematics, W. Aspray and P. Kitcher eds., Minnesota Studies in the Philosophy of Science Vol. XI, University of Minnesota Press, 1988, p. 3-57. |

32 | Evan Heit, What is Induction and Why Study It? Inductive Reasoning: Experimental, Developmental, and Computational Approaches, Aidan Feeney, Evan Heit eds., Cambridge University Press, 2007. |

33 | Koh Youngmee, Ree Sangwook, Paul Erdos and Probabilistic Methods, The Korean Journal for History of Mathematics 18(4) (2005), 101-112. |

34 | Thomas S. Kuhn, The Structure of Scientific Revolutions, 50th Anniversary Edition (4th edition), The University of Chicago Press, 2012. |