# Inductive Reasoning

Pronunciation: /ɪnˈdʌk.tɪv ˈri.zən.ɪŋ/ Explain

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. McAdams, David E.. All Math Words Dictionary, inductive reasoning. 2nd Classroom edition 20150108-4799968. pg 98. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Jevons, Stanley W.. Logic. pp 11. www.archive.org. Science Primers. American Book Company. Last Accessed 8/7/2018. http://www.archive.org/stream/logicjevons00jevoiala#page/11/mode/1up/search/inductive+reasoning. Buy the book
3. Hyslop, James H.. Logic and Argument. pp 185-191. www.archive.org. Charles Scribner's Sons. 1899. Last Accessed 8/7/2018. http://www.archive.org/stream/logicargument00hysliala#page/185/mode/1up/search/inductive+reasoning. Buy the book
4. Woolley, J.. An Introduction to Logic. pp 120-123. www.archive.org. John Henry Parker. 1840. Last Accessed 8/7/2018. http://www.archive.org/stream/introductionlogi00wooluoft#page/120/mode/1up/search/inductive+reasoning. Buy the book

### More Information

• McAdams, David E.. Induction. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/i/induction.html.

### Cite this article as:

McAdams, David E. Inductive Reasoning. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/inductivereasoning.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/11/2010: Added "References". (McAdams, David E.)
8/11/2008: Minor grammar changes. (McAdams, David E.)
6/15/2008: Added counter example. Changed 'proof by induction' to proof by 'mathematical induction' (McAdams, David E.)
9/3/2007: Initial version. (McAdams, David E.)

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