Inductive Reasoning

Pronunciation: /ɪnˈdʌk tɪv ˈri zən ɪŋ/ ?

In inductive reasoning, a claim can be shown to be true for at least some instances, and is therefore assumed to be true for all cases. An example of inductive reasoning is:

This fire is hot, so all fires must be hot.

The problem with inductive reasoning in this case is that it does not prove absolutely that all fires are hot. A counter example is the false statement:

This apple is red, so all apples must be red.

Simple inductive reasoning is insufficient by itself for mathematical proof. However, proof by mathematical induction is a special case of inductive reasoning that can be used for proof.

References

  1. inductive reasoning. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-02-11). http://www.merriam-webster.com/dictionary/inductive reasoning.
  2. Jevons, Stanley W.. Logic, pp 11. Science Primers. American Book Company. (Accessed: 2010-02-11). http://www.archive.org/stream/logicjevons00jevoiala#page/11/mode/1up/search/inductive+reasoning.
  3. Hyslop, James H.. Logic and Argument, pp 185-191. Charles Scribner's Sons, 1899. (Accessed: 2010-02-11). http://www.archive.org/stream/logicargument00hysliala#page/185/mode/1up/search/inductive+reasoning.
  4. Woolley, J.. An Introduction to Logic, pp 120-123. John Henry Parker, 1840. (Accessed: 2010-02-11). http://www.archive.org/stream/introductionlogi00wooluoft#page/120/mode/1up/search/inductive+reasoning.

More Information

  • McAdams, David. Induction. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Induction.

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Inductive Reasoning. 2010-02-11. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/inductivereasoning.html.

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2010-02-11: Added "References" (McAdams, David.)
2008-08-11: Minor grammar changes (McAdams, David.)
2008-06-15: Added counter example. Changed 'proof by induction' to proof by 'mathematical induction' (McAdams, David.)
2007-09-03: Initial version (McAdams, David.)

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