non se·qui·tur

[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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Based on the Random House Dictionary, © Random House, Inc. 2013.
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Collins
World English Dictionary
non sequitur (ˈnɒn ˈsɛkwɪtə) [Click for IPA pronunciation guide]
 
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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00:10
Non sequitur is always a great word to know.
So is callithumpian. Does it mean:
a children's mummer's parade, as on the Fourth of July, with prizes for the best costumes.
an extraordinary or unusual thing, person, or event; an exceptional example or instance.
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
That just sounds like a complete non sequitur.
The conclusion that an act is not unethical or unprofessional because it is not
  illegal is a non sequitur and patently false.
The non sequitur is to assume that the new service will be a revenue-generating
  business in its own right.
Those are fighting words, not non sequitur taunts.
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