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{{Useful Notes|wppage=Proof by example}}
==== Also called ====▼
:: Inappropriate Generalization▼
:: Hasty Generalisation▼
:: No-Limits Fallacy▼
▲:: Taking one or more non-exhaustive examples from a group that have a property, and making a generalization that everything in that group has that property.
▲13 is odd, and it is a prime number.<br />
▲97 is odd, and it is a prime number.<br />
Therefore, all odd numbers are prime numbers. }}
{{quote|
{{examples}}▼
* Usually, in mathematics, [[wikipedia:Skewechr(27)s number|no matter how many examples]] [[wikipedia:Riemann hypothesis|you might have]], proof by example is not a good idea.▼
* Things like (literal) witch hunts and radical Islamic terrorism being used to imply that everything about a certain religion is wrong/dangerous.▼
* The idea that computers that can design replacements better than themselves could do so at a rate that accelerates infinitely, often citing a graph by Ray Kurzweil which appears to show an upward trend. This ignores that there are physical ceilings to such development; such a system might hit these ''faster'', but would not gain the magical ability to simply ignore them.▼
** Note Kurzweil himself does not argue that any particular method of computation can be improved infinitely and supports his arguments about where technology is headed with current research and mathematical theories about the absolute limits of computational density.▼
* If the list of examples is exhaustive, in which case it is known as "[[wikipedia:Proof by exhaustion|proof by exhaustion]]" or "proof by cases". Meaning that you prove, using groups as examples, both that the statement is true for all examples, and it is impossible for any relevant example to not be in one or more of the groups. For example:
{{quote|The sum of the angles of any acute triangle on a Euclidean plane add up to 180°.
The sum of the angles of any
* When you are ''disproving'' by example.
▲{{quote| 9 is not a prime number, and it is odd.<br />
Therefore, not all odd numbers are prime numbers. }}
* Proving an existential statement (i.e. "There exists...") by example. One example is plenty.
** The prime (pardon the pun) example might well be this: "2 is an even number and is prime. Therefore, there exists at least one prime number that is even."
* An attempt at real induction. Inductive logic admits that its conclusions are not ''necessarily'' true, but rather that they are ''probably'' true, and it tends to attempt to be as exhaustive as possible and to eliminate as many alternative explanations as possible, to reduce the possibility that the conclusion is wrong to as close to zero as possible. However, an honest scientist (i.e. practitioner of inductive logic) would freely admit that there is the possibility, however slim, that the entirety of his/her science is entirely wrong.▼
* If you are trying to prove that something is ''possible'', as opposed to trying to prove that something is ''true''. Demonstrating that X is ''always'' Y is a substantial burden of proof. Demonstrating that X is ''sometimes'' Y requires a minimum of one positive example.
* The speaker has a [[Word of God|definitive authority]] to name the characteristics of something. If [[Anne McCaffrey]] says that a dragon is a genetically-engineered beast ridden by an order of warriors on a planet called "Pern" one can assume that to be an accurate description of dragons, in the writings of Anne McCaffrey.
**On the other hand that would only refer to Pern dragons and has no bearing on dragons in Ring Cycle or Middle Earth, nor is it intended to.
▲{{examples}}
▲* An attempt at real induction. Inductive logic admits that its conclusions are not ''necessarily'' true, but rather that they are ''probably'' true, and it tends to attempt to be as exhaustive as possible and to eliminate as many alternative explanations as possible, to reduce the possibility that the conclusion is wrong to as close to zero as possible. However, an honest scientist (i.e. practitioner of inductive logic) would freely admit that there is the possibility, however slim, that the entirety of his/her science is entirely wrong.
▲* Usually, in mathematics, [[wikipedia:
▲* Things like (literal) witch hunts and radical Islamic terrorism being used to imply that everything about a certain religion is wrong/dangerous.
▲* The idea that computers that can design replacements better than themselves could do so at a rate that accelerates infinitely, often citing a graph by Ray Kurzweil which appears to show an upward trend. This ignores that there are physical ceilings to such development; such a system might hit these ''faster'', but would not gain the magical ability to simply ignore them.
▲** Note Kurzweil himself does not argue that any particular method of computation can be improved infinitely and supports his arguments about where technology is headed with current research and mathematical theories about the absolute limits of computational density.
{{Needs More Examples}}
{{reflist}}
[[Category:Logical Fallacies]]
[[Category:Proof by Examples]]
[[Category:Pages with working Wikipedia tabs]]
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