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1. A term frequently used by politicians when accused of something scandalous. It means: "I did it, but as long as there's no smoking gun I will deny it completely." Most such scandals involve illicit sex, bribery, influence peddling or misuse of public funds.

2. A worn-out public relations phrase that nobody believes anymore. Nixon's famous remark -- "I am not a crook" -- sounds positively Shakespearian in comparison.
"The accusation is categorically false!," said South Carolina Republican Nikki Haley. She is accused of having an "inappropriate physical relationship" with the governor's former press secretary.
by Peter Kobs May 24, 2010
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2
In order to understand the meaning of Categorically False, one must understand the Categorical approach to defining crimes. Where there are two crimes that may be similar in nature, but defined differently in different areas (Such as "Burglary" and "Shoplifting") then one may or may not be the same as the other.

For example, State X defines walking into a store in the middle of the day and stealing X amount of product from the shelf as "Burglary". State Y defines the same action as "Shoplifting". It is in a defense attorney's best interest to argue that this conviction, especially as it applies to Federal Law (enhancing sentences based on prior convictions), does not fall in the same category as a specified crime.

So, in practice, it means that a reporter asking someone's opinion of whether or not the charges of "drug smuggling" to a relative are true. The interviewee would respond, "Those charges are categorically false". Meaning, this person did something... but not defined in the way you just asked about.
(From Luke Cage)

Reporter: "Have you been questioned by the NYPD about your cousin?"

Councilwoman Mariah Dillard: "Family first Robin. I love my cousin Cornell Stokes. The charges against him are categorically false..."
by toronado282 October 08, 2016
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For such a thing to exist, there must also exist its inseparable opposite. It's, very clearly, a non admission admission, that's synonymous with "compartmentalization", which is where we must look for an in depth understanding of its true meaning.
No clear examples of categorically false may be given without criminal implication, since it is only they who use it.
by imprismed October 24, 2013
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