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
- inductive reasoning. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-02-11). http://www.merriam-webster.com/dictionary/inductive reasoning.
- 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.
- 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.
- 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.
Printed Resources
Cite this article as:
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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Revision History
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.)