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
- Jevons, Stanley W.. Logic. pp 11. www.archive.org. Science Primers. American Book Company. Last Accessed 8/6/2018. http://www.archive.org/stream/logicjevons00jevoiala#page/11/mode/1up/search/inductive+reasoning. Buy the book
- Hyslop, James H.. Logic and Argument. pp 185-191. www.archive.org. Charles Scribner's Sons. 1899. Last Accessed 8/6/2018. http://www.archive.org/stream/logicargument00hysliala#page/185/mode/1up/search/inductive+reasoning. Buy the book
- Woolley, J.. An Introduction to Logic. pp 120-123. www.archive.org. John Henry Parker. 1840. Last Accessed 8/6/2018. 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. 8/7/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/inductivereasoning.html.
Revision History
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.)