Proof by Examples: Difference between revisions

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{{trope}}
{{trope}}
=== '''[http://en.wikipedia.org/wiki/Proof_by_example Proof By Example(s)]''': ===
=== '''[[wikipedia:Proof by example|Proof By Example(s)]]''': ===
==== Also called ====
==== Also called ====
:: Inappropriate Generalization
:: Inappropriate Generalization
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{{quote| "If I told you fifty years ago that you'd have a phone smaller than a deck of cards, that computers would be small enough to put into a pocket, and that your car would be able to call for help if it was involved in a crash, you'd have laughed at me. So if you say that faster-than-light travel is impossible, you're just being small-minded, since technology continues to improve all the time."}}
{{quote| "If I told you fifty years ago that you'd have a phone smaller than a deck of cards, that computers would be small enough to put into a pocket, and that your car would be able to call for help if it was involved in a crash, you'd have laughed at me. So if you say that faster-than-light travel is impossible, you're just being small-minded, since technology continues to improve all the time."}}


{{examples|Examples:}}
{{examples}}
* Usually, in mathematics, [http://en.wikipedia.org/wiki/Skewe%27s_number no matter how many examples] [http://en.wikipedia.org/wiki/Riemann_hypothesis you might have], proof by example is not a good idea.
* 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.
* 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.
* 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.
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==== Looks like this fallacy but is not ====
==== Looks like this fallacy but is not ====
* If the list of examples is exhaustive, in which case it is known as "[http://en.wikipedia.org/wiki/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:
* 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°.<br />
{{quote| The sum of the angles of any acute triangle on a Euclidean plane add up to 180°.<br />
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[[Category:Logic Tropes]]
[[Category:Logic Tropes]]
[[Category:Logical Fallacies]]
[[Category:Logical Fallacies]]
[[Category:Proof By Examples]]
[[Category:Proof by Examples]]
Retrieved from "https://allthetropes.org/wiki/Proof_by_Examples"