non sequitur

[non sek-wi-ter, -toor; Latin nohn se-kwi-toor]
noun
1.
Logic. an inference or a conclusion that does not follow from the premises.
2.
a statement containing an illogical conclusion.

Origin:
< Latin: it does not follow

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World English Dictionary
non sequitur (ˈnɒn ˈsɛkwɪtə)
 
n
1.  a statement having little or no relevance to what preceded it
2.  logic a conclusion that does not follow from the premises
 
[Latin, literally: it does not follow]

Collins English Dictionary - Complete & Unabridged 10th Edition
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Etymonline
Word Origin & History

non sequitur
1533, from L., lit. "it does not follow."
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Cultural Dictionary
non sequitur [(non sek-wuh-tuhr)]

A thought that does not logically follow what has just been said: “We had been discussing plumbing, so her remark about astrology was a real non sequitur.” Non sequitur is Latin for “It does not follow.”

The American Heritage® New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Example sentences
The non sequitur is to assume that the new service will be a revenue-generating
  business in its own right.
Once again you're making a non sequitur interjection.
The chapter on Hemingway seems an odd non sequitur.
The conclusion that an act is not unethical or unprofessional because it is not
  illegal is a non sequitur and patently false.
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